Here's a site to help those of us who are statistically challenged.
statistics help for Journalists: "Statistics Every Writer Should Know
A simple guide to understanding basic statistics, for journalists and other writers who might not know math."
statistics help
Tuesday, August 31, 2010
Removing GATE
A recent article in NY Times discusses the trouble with using SAT as the sole criterion for admission. This is actually one of the followups from several articles published on this issue in the Chronicle of Higher Education. This is based on the report by the National Association for College Admission Counseling. which discusses that tests like the SAT and ACT were never meant to be viewed in isolation but considered as one of the factors that include grades, essays and so on. But with the college ranking systems considering SAT as one of the main criteria for ranking, the colleges seem to have preferred the exam as the one of the major criteria of admission until recently. Now many colleges in USA have made SAT optional, though the major institutes like MIT and Harvard still require SAT.
This backdrop is interesting! considering that IISc is planning to drop GATE as one of the requirements for admission to its research degrees (masters and doctoral programs) in engineering. Under this proposal, the main criteria is the percentage of marks obtained by the candidate in the B.E/B.Tech examination and anyone who secures more than 70% marks in their undergraduation will be eligible for admission.
My opinion on the above has always been that we should not obsess with admissions tests like GATE for doctoral programs and we should take an expansive view of merit that would include GATE, the undergraduate scores, communication skills and motivation. However, for masters program, we need an all-India entrance exam just to screen the huge numbers. With nearly six undergraduates in engineering (and 2.5 lakhs of them expressing an interest in higher studies by writing GATE) with wide variations in the undergraduate marks awarded in each university, it would be nearly impossible to screen! them only by interviews.
statistics formula cheat sheet
This backdrop is interesting! considering that IISc is planning to drop GATE as one of the requirements for admission to its research degrees (masters and doctoral programs) in engineering. Under this proposal, the main criteria is the percentage of marks obtained by the candidate in the B.E/B.Tech examination and anyone who secures more than 70% marks in their undergraduation will be eligible for admission.
My opinion on the above has always been that we should not obsess with admissions tests like GATE for doctoral programs and we should take an expansive view of merit that would include GATE, the undergraduate scores, communication skills and motivation. However, for masters program, we need an all-India entrance exam just to screen the huge numbers. With nearly six undergraduates in engineering (and 2.5 lakhs of them expressing an interest in higher studies by writing GATE) with wide variations in the undergraduate marks awarded in each university, it would be nearly impossible to screen! them only by interviews.
statistics formula cheat sheet
Quadratic Formula Rap
If there's one thing my students learn by the end of the year and actually still remember in later years, it's the quadratic formula. The class where I introduce the formula goes down like this: First I tell them about the quadratic formula in a traditional way. I explain that now with the QF we can solve any quadratic equation, and do it much easier than we could with completing the square. I show them how to use it and they solve a couple quadratics themselves. I then tell them that for homework they have to memorize the quadratic formula overnight and there will be a quiz on it at the beginning of next class.(This is not my usual style) I always receive a chorus of groans. "But!" I interject "It will be much easier than you think. I've gotten someone to come in and help you all with this, let me go get him." I go into the hallway, put my tie around my head, half untuck my shirt and start a live performance of this. (my rapping name is SweenDawg, of course)
The live performance helps make it really fun for them, and I would highly suggest doing it if you decide to use a rap in your classroom. Any time I do a song in class (there are others) I typically do one "live" and then have a recording so I can play it for the kids multiple times and in later classes to help it stick in their memories. Now I realize this is not the most groundbreaking or new idea, but I want to stress its effectiveness and fun. The kids who have been generally uninterested throughout the year usually love this lesson the most and really get into it. Not only that, but I work in a small school and when I have students in later years they almost always remember how to solve quadratics without any prompting... or maybe just an "op-op-op" to get them started.
I also tend to plug the idea of making their own strategies when they have to memorize something, and how making a song is just one example of a memorization technique.
Shoutout to Mr. Mellor for helping lay down the track.
Have your own fun song that you like to do with your students? Tell me about it!
solving quadratic formula
The live performance helps make it really fun for them, and I would highly suggest doing it if you decide to use a rap in your classroom. Any time I do a song in class (there are others) I typically do one "live" and then have a recording so I can play it for the kids multiple times and in later classes to help it stick in their memories. Now I realize this is not the most groundbreaking or new idea, but I want to stress its effectiveness and fun. The kids who have been generally uninterested throughout the year usually love this lesson the most and really get into it. Not only that, but I work in a small school and when I have students in later years they almost always remember how to solve quadratics without any prompting... or maybe just an "op-op-op" to get them started.
I also tend to plug the idea of making their own strategies when they have to memorize something, and how making a song is just one example of a memorization technique.
Shoutout to Mr. Mellor for helping lay down the track.
Have your own fun song that you like to do with your students? Tell me about it!
solving quadratic formula
Rate-Time-Distance Word Problems
Or otherwise known as those dreaded train problems. These are always tricky for algebra students. Ask someone you know which problems they remember from Algebra I and almost all of them will have something to say about the train problems.
Train problems can be separated into two categories: same direction travel and opposite direction travel. Each are handled differently, but using a chart makes it easier to set up the equations. You also have to remember that distance equals rate times time or d=rt.
Here is an example. A train leaves the train station at 2:00 p.m. Its average rate of speed is 90 mph. Another train leaves the same station a half hour later. Its average rate of speed is 120 mph. If the second train follows the same route on a parallel track to the first, how many hours will it take the second train to catch the first?
Since the trains are travelling in the same direction, their distances are equal when the 2nd one catches the 1st. Therefore, to solve this equation, we set the distance of Train 1 equal to Train 2.
90t = 120(t-0.5)
90t = 120t - 60
-30t = -60
t = 2
The first train travelled for 2 hours before the 2nd train caught up to it. The problem asks how long it takes the 2nd train to catch the first. So it takes the 2nd train a half h! our less than it did the first train which is 1.5 hours.
Check back tomorrow for information on opposite direction travel.
solve algebra word problems
Train problems can be separated into two categories: same direction travel and opposite direction travel. Each are handled differently, but using a chart makes it easier to set up the equations. You also have to remember that distance equals rate times time or d=rt.
Here is an example. A train leaves the train station at 2:00 p.m. Its average rate of speed is 90 mph. Another train leaves the same station a half hour later. Its average rate of speed is 120 mph. If the second train follows the same route on a parallel track to the first, how many hours will it take the second train to catch the first?
Train | Rate | Time | Distance |
1 | 90 | t | 90t |
2 | 120 | t-0.5 | 120(t-0.5) |
Since the trains are travelling in the same direction, their distances are equal when the 2nd one catches the 1st. Therefore, to solve this equation, we set the distance of Train 1 equal to Train 2.
90t = 120(t-0.5)
90t = 120t - 60
-30t = -60
t = 2
The first train travelled for 2 hours before the 2nd train caught up to it. The problem asks how long it takes the 2nd train to catch the first. So it takes the 2nd train a half h! our less than it did the first train which is 1.5 hours.
Check back tomorrow for information on opposite direction travel.
solve algebra word problems
Custom Shape Tool -PhotoshopTools
The Custom Shape Tool creates custom shapes
How to use Custom Shape tool?
1.Choose the Custom Shape tool
2.Position the pointer inside the work area and just click and drag.
3.Next to Custom shape on the menu bar one arrow is there.Click that arrow.Option palette will open.
From Center - Used to draw th! e image from center.
- UnCon strained - According to our taste we can draw Custom Shape.But there is no need all the sides will be proportional to each other.
- Defined Size - Using this we can get What is the predefined size of image.We can't change or specify the size.
- DefinedProportions - Using this option we change the size.But all the sides will be automatically proportional to each other.
- Fixed Size - Using this option we can specify/change the height and width of the shape.But run time the size of the shape is fixed ie what we specified in the width and height column.
Drawing modes:
To create vector shape layers click Shape layers button
To draw paths (shape outlines) click Paths button
To create rasterized shapes in current layer click Fill pixels
Options:
- Create new shape layer - to create every new shape in a separate layer
- Add to shape area - to create multiple shapes in the same vector shape layer.
- Subtract from shape area - to subtract shapes from the current shape layer.
- Intersect with shape area - to intersect new shapes with existing one in the same layer.
- Exclude overlapping shape areas - to subtract overlapping areas.
shape areas
EPR Experiment (Designed by David Bohm)
Description of the paradox
The EPR paradox draws on a phenomenon predicted by quantum mechanics, known as quantum entanglement, to show that measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. This effect is now known as "nonlocal behavior" (or colloquially as "quantum weirdness" or "spooky action at a distance"). In order to illustrate this, let us consider a simplified version of the EPR thought experiment put forth by David Bohm.
[edit] Measurements on an entangled state
We have a source that emits pairs of electrons, with one electron sent to destination A, where there is an observer named Alice, and another is sent to destination B, where there is an observer named Bob. According to quantum mechanics, we can arrange our source so that each emitted electron pair occupies a quantum state called a spin singlet. This can be viewed as a quantum super! position of two states, which we call state I and state II. In state I, electron A has spin pointing upward along the z-axis (+z) and electron B has spin pointing downward along the z-axis (-z). In state II, electron A has spin -z and electron B has spin +z. Therefore, it is impossible to associate either electron in the spin singlet with a state of definite spin. The electrons are thus said to be entangled.
The EPR thought experiment, performed with electrons. A source (center) sends electrons toward two observers, Alice (left) and Bob (right), who can perform spin measurements.
Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. Suppose she gets +z. According to quantum mechanics, the quantum state of the system collapses into state I. (Different interpretations of quantum mechanics have different ways of saying this, but the basic result is the same.) The quantum state determines the probable outcomes! of any measurement performed on the system. In this case, if ! Bob subs equently measures spin along the z-axis, he will obtain -z with 100% probability. Similarly, if Alice gets -z, Bob will get +z.
There is, of course, nothing special about our choice of the z-axis. For instance, suppose that Alice and Bob now decide to measure spin along the x-axis, according to quantum mechanics, the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction. We'll call these states Ia and IIa. In state Ia, Alice's electron has spin +x and Bob's electron has spin -x. In state IIa, Alice's electron has spin -x and Bob's electron has spin +x. Therefore, if Alice measures +x, the system collapses into Ia, and Bob will get -x. If Alice measures -x, the system collapses into IIa, and Bob will get +x.
In quantum mechanics, the x-spin and z-spin are "incompatible observables", which means that there is a Heisenberg uncertainty principle operating between them: a quantum state cannot possess a definite va! lue for both variables. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob's x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. Furthermore, it is fundamentally impossible to predict which outcome will appear until Bob actually performs the measurement.
So how does Bob's electron know, at the same time, which way to point if Alice decides (based on information unavailable to Bob) to measure x and also how to point if Alice measures z? Using the usual Copenhagen interpretation rules that say the wave function "collapses" at the time of measurement, there must be action at a distance or the electron must know more than it is supposed to. To make the mixed part quantum and part classical descriptions of this experiment local, we have to say that th! e notebooks (and experimenters) are entangled and have linear ! combinat ions of + and Рwritten in them, like Schr̦dinger's Cat.
Incidentally, although we have used spin as an example, many types of physical quantities — what quantum mechanics refers to as "observables" — can be used to produce quantum entanglement. The original EPR paper used momentum for the observable. Experimental realizations of the EPR scenario often use photon polarization, because polarized photons are easy to prepare and measure.
quantum entanglement simplified
The EPR paradox draws on a phenomenon predicted by quantum mechanics, known as quantum entanglement, to show that measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. This effect is now known as "nonlocal behavior" (or colloquially as "quantum weirdness" or "spooky action at a distance"). In order to illustrate this, let us consider a simplified version of the EPR thought experiment put forth by David Bohm.
[edit] Measurements on an entangled state
We have a source that emits pairs of electrons, with one electron sent to destination A, where there is an observer named Alice, and another is sent to destination B, where there is an observer named Bob. According to quantum mechanics, we can arrange our source so that each emitted electron pair occupies a quantum state called a spin singlet. This can be viewed as a quantum super! position of two states, which we call state I and state II. In state I, electron A has spin pointing upward along the z-axis (+z) and electron B has spin pointing downward along the z-axis (-z). In state II, electron A has spin -z and electron B has spin +z. Therefore, it is impossible to associate either electron in the spin singlet with a state of definite spin. The electrons are thus said to be entangled.
The EPR thought experiment, performed with electrons. A source (center) sends electrons toward two observers, Alice (left) and Bob (right), who can perform spin measurements.
Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. Suppose she gets +z. According to quantum mechanics, the quantum state of the system collapses into state I. (Different interpretations of quantum mechanics have different ways of saying this, but the basic result is the same.) The quantum state determines the probable outcomes! of any measurement performed on the system. In this case, if ! Bob subs equently measures spin along the z-axis, he will obtain -z with 100% probability. Similarly, if Alice gets -z, Bob will get +z.
There is, of course, nothing special about our choice of the z-axis. For instance, suppose that Alice and Bob now decide to measure spin along the x-axis, according to quantum mechanics, the spin singlet state may equally well be expressed as a superposition of spin states pointing in the x direction. We'll call these states Ia and IIa. In state Ia, Alice's electron has spin +x and Bob's electron has spin -x. In state IIa, Alice's electron has spin -x and Bob's electron has spin +x. Therefore, if Alice measures +x, the system collapses into Ia, and Bob will get -x. If Alice measures -x, the system collapses into IIa, and Bob will get +x.
In quantum mechanics, the x-spin and z-spin are "incompatible observables", which means that there is a Heisenberg uncertainty principle operating between them: a quantum state cannot possess a definite va! lue for both variables. Suppose Alice measures the z-spin and obtains +z, so that the quantum state collapses into state I. Now, instead of measuring the z-spin as well, Bob measures the x-spin. According to quantum mechanics, when the system is in state I, Bob's x-spin measurement will have a 50% probability of producing +x and a 50% probability of -x. Furthermore, it is fundamentally impossible to predict which outcome will appear until Bob actually performs the measurement.
So how does Bob's electron know, at the same time, which way to point if Alice decides (based on information unavailable to Bob) to measure x and also how to point if Alice measures z? Using the usual Copenhagen interpretation rules that say the wave function "collapses" at the time of measurement, there must be action at a distance or the electron must know more than it is supposed to. To make the mixed part quantum and part classical descriptions of this experiment local, we have to say that th! e notebooks (and experimenters) are entangled and have linear ! combinat ions of + and Рwritten in them, like Schr̦dinger's Cat.
Incidentally, although we have used spin as an example, many types of physical quantities — what quantum mechanics refers to as "observables" — can be used to produce quantum entanglement. The original EPR paper used momentum for the observable. Experimental realizations of the EPR scenario often use photon polarization, because polarized photons are easy to prepare and measure.
quantum entanglement simplified
Exam 70-536: TS: Microsoft .NET Framework - Application Development Foundation - PASSED
Why would I need to pass that exam at all?
There are many arguments to pass the exam. Most of them are simple bureaucracy. First of all, your resume will have additional strength if you will add few certification records on the bottom. Secondly, many companies are interested to have their employees to be certified, or maybe they want to make you promotion road more hard :) so to allow you to be promoted you need to pass some set of certificates and cope with lot of other requirements. At least this is situation which I have in my company.
Why would I need this exam for my blog?
Very easy: when YOU are on my blog first time, you read something and create your thought on topic you just read and then you decide to subscribe or not to subscribe. Question is following: what is guarantor that it worth to subscribe to my blog? And answer is "Nothing". But what will be your reaction if you will see MVP logo at the top-right of my blog? Are my chances better? Or course they are.
Why else would I need this exam?
Following point is very important but honestly I could not put it above (I will describe why). The point is to enhance you knowledge and learn something new. Of course during preparation to exam you read some books and search over MSDN on topics you are interested and which will be measured. But in real life you could be experienced .NET developer and still have difficulties to pass exam. In other words I have doubts if 10 years experienced developer could pass exam without at least some special preparation to it.
What else did I miss?
Of course - self-confidence. In order to be successful you need to feel yourself confident in things you do. In order to grow you should have something behind you, that could you help stand when you are with people who have certificates. And plus to that it is always very enjoyable to know that you know more then others. But a secret: do not show them that. It is very important. Do not praise yourself, let others do it instead.
How to prepare and how did I prepare?
You could find a lot of very interesting posts over internet on how to prepare.
I like this one:
http://lukecummins.me.uk/2009/08/70-536-my-tips-for-this-microsoft-exam/
I even found other blogs that are about certification.
My recommendation number 1: google on how to prepare... and you will find a lot of interesting stuff.
Also while you are trying some demo tests on MeasureUp or tests from TrainingKit and if you are not confident about answer do not try to remember it - go and figure answer in depth!
Also I wrote some tips on how to read TrainingKit. At least this works for me:
How was it?
Night before exam I felt confident about exam, but was still worrying.. so I was preparing till 3am. In the morning I came to work as usual and did few things... reviewed ones code, checked e-mails... expressed my thoughts on demo we should have today and wrote e-mail to team members that I will be out for about 2 hours. My company is Microsoft's parner so I do not need to move to other location - just get down 5 floors.
First couple of questions I was nervous, but then I felt that I'm confident with most of questions. I marked only 2 out of 40 for additional review. When I finished I got message saying that I PASSED EXAM with score 907. This means that I answered incorrectly for about 4 questions. I think that this is very good result.
Picture which I get is like following:
My next target is probably 70-505. Passing it is point of honour, because I already failed it twice because of overflow of confidence.
Also as I'm active in preparing developers meeting for developers from my project and I'm thinking to teach our developers in order to get certification - covering some areas from exam.
Express your thoughts on passing this exam.
person success net
There are many arguments to pass the exam. Most of them are simple bureaucracy. First of all, your resume will have additional strength if you will add few certification records on the bottom. Secondly, many companies are interested to have their employees to be certified, or maybe they want to make you promotion road more hard :) so to allow you to be promoted you need to pass some set of certificates and cope with lot of other requirements. At least this is situation which I have in my company.
Why would I need this exam for my blog?
Very easy: when YOU are on my blog first time, you read something and create your thought on topic you just read and then you decide to subscribe or not to subscribe. Question is following: what is guarantor that it worth to subscribe to my blog? And answer is "Nothing". But what will be your reaction if you will see MVP logo at the top-right of my blog? Are my chances better? Or course they are.
Why else would I need this exam?
Following point is very important but honestly I could not put it above (I will describe why). The point is to enhance you knowledge and learn something new. Of course during preparation to exam you read some books and search over MSDN on topics you are interested and which will be measured. But in real life you could be experienced .NET developer and still have difficulties to pass exam. In other words I have doubts if 10 years experienced developer could pass exam without at least some special preparation to it.
What else did I miss?
Of course - self-confidence. In order to be successful you need to feel yourself confident in things you do. In order to grow you should have something behind you, that could you help stand when you are with people who have certificates. And plus to that it is always very enjoyable to know that you know more then others. But a secret: do not show them that. It is very important. Do not praise yourself, let others do it instead.
How to prepare and how did I prepare?
You could find a lot of very interesting posts over internet on how to prepare.
I like this one:
http://lukecummins.me.uk/2009/08/70-536-my-tips-for-this-microsoft-exam/
I even found other blogs that are about certification.
My recommendation number 1: google on how to prepare... and you will find a lot of interesting stuff.
Also while you are trying some demo tests on MeasureUp or tests from TrainingKit and if you are not confident about answer do not try to remember it - go and figure answer in depth!
Also I wrote some tips on how to read TrainingKit. At least this works for me:
- Read accurately but quick if theme is familiar to you.Skip “Real Word” and pay attention on “Important” and “Exam Tip”, try to remember it!
- If there are boring explanation and then code, switch first to code and analyze if you understand everything there, and if that is true, don’t return back to text.
- Do not execute Labs unless you do not understand what you had read.
- If there are difficult chapters try to read them twice – I did this with Application Security.
How was it?
Night before exam I felt confident about exam, but was still worrying.. so I was preparing till 3am. In the morning I came to work as usual and did few things... reviewed ones code, checked e-mails... expressed my thoughts on demo we should have today and wrote e-mail to team members that I will be out for about 2 hours. My company is Microsoft's parner so I do not need to move to other location - just get down 5 floors.
First couple of questions I was nervous, but then I felt that I'm confident with most of questions. I marked only 2 out of 40 for additional review. When I finished I got message saying that I PASSED EXAM with score 907. This means that I answered incorrectly for about 4 questions. I think that this is very good result.
Picture which I get is like following:
My next target is probably 70-505. Passing it is point of honour, because I already failed it twice because of overflow of confidence.
Also as I'm active in preparing developers meeting for developers from my project and I'm thinking to teach our developers in order to get certification - covering some areas from exam.
Express your thoughts on passing this exam.
person success net
A Guide to Earn GOLD
If you are tired of trying to figure out who to trust, if you are tired of trying to figure out what voice to listen to for guidance, if you are tired of trying to be in the right place at the right time, whatever that means. Explore the world and see all the wonders. Give gold a try. It sounds like it may be right for you. Over the last 10 years gold has outperformed virtually every other investment out there. From stocks to bonds to real estate, there has not been any other investment that not only provides an above average return but also the feeling of security associated with just leaving your money in a savings account. Gold prices here are much worthy. You are assured of the quality and in time the prices will become higher and higher.
Gold is precious, though this time it is not that popular compare to real estate business. Bu! t it is a good business venture; you can earn much on this kind of business. Gold price will eventually go higher and higher as time pass by. A very good investment. Here are the The current five participants who fix the price of gold:
- Scotia-Mocatta - successor to Mocatta & Goldsmid and part of Bank of Nova Scotia
- Barclays Capital - Replaced N M Rothschild & Sons when they abdicated
- Deutsche Bank - Owner of Sharps Pixley, itself the merger of Sharps Wilkins with Pixley & Abell
- HSBC - Owner of Samuel Montagu & Co.
- Societe Generale - Replaced Johnson Matthey and CSFB as fifth seat
In our world right now, it’s always ! right to find something you can have in the future. For me GOL! D is the answer.
online free algebra tutor
Factoring the time
I stumbled upon this comic that you might enjoy... factoring the time (from xkcd.com).
math tutor online
Photogrammetric Terms
File Types
*.aoi. An Area of Interest file. Used to hold a point, line, or polygon that is selected as a training sample or as the image area to be used in an operation.
*.blk. An LPS block file. An LPS block file can contain only one image. A block file that contains two or more images with approximately 60% overlap can be viewed in stereo in other applications such as Stereo Analyst.
*.cam. An ASCII file with a fixed structure. Provides camera information such as focal length and principal point.
*.dat. An ASCII file. In LPS, exterior orientation parameters are often contained in a .dat file. Typically, this data comes from the airborne GPS or INS used during image capture. See also: Airborne GPS; Inertial Navigation System
*.img. An ERDAS IMAGINE image file. Data in the .img format are tiled data, which can be set to any size. A file containing raster image data. An .img file contains data such as sensor information, ! layer information, statistics, projection, pyramid layers, attribute data, etc.
*.shp. An ESRI shape file. Shape files are in vector format, and can store attribute data.
*.txt. An ASCII text file. Frequently used as an input GCP reference source for 2- and
3-dimensional control point and check point coordinates.
Symbols
k. (Kappa) In a rotation system, Kappa is positive rotation about the Z-axis.
w. (Omega) In a rotation system, Omega is positive rotation about the X-axis.
j. (Phi) In a rotation system, Phi is positive or negative rotation about the Y-axis. See also: Phi (-), Omega, Kappa; Phi (+), Omega, Kappa
Terms
A
Additional Parameter (AP). In block triangulation, additional parameters characterize systematic error within the block of images and observations, such as lens distortion. In LPS, four AP models can be used in the triangulation process, including: Bauer&#! 8217;s Simple Model, Jacobsen’s Simple Model, Ebner̵! 7;s Orth ogonal Model, and Brown’s Physical Model.
Adjusted stereopair. An adjusted stereopair is a pair of images displayed in a workspace that has a map projection associated and exterior orientation used to facilitate stereo viewing. A set of two remotely-sensed images that overlap, providing a 3D view of the terrain in the overlap area.
Aerial photographs. Photographs taken from positions above the Earth captured by aircraft. Photographs are used for planimetric mapping projects.
Aerial stereopair. Two photos with a common overlap area.
Aerial Triangulation (AT). The process of establishing a mathematical relationship between images, the camera or sensor model, and the ground. The information derived is necessary for orthorectification, DEM generation, and stereopair creation. This term is used when processing frame camera, digital camera, videography, and nonmetric camera imagery. See also: Triangulation
Affine transfo! rmation. A 2D plane-to-plane transformation that uses six parameters (coefficients) to account for rotation, translation, scale, and nonorthogonality in between the planes. Defines the relationship between two coordinate systems such as a pixel and image space coordinate system.
Air base. The distance between two image exposure stations. See also: Base-height ratio
Airborne GPS. GPS stands for Global Positioning System. Airborne GPS is a technique used to provide initial approximations of exterior orientation, which defines the position and orientation associated with an image as they existed during image capture. GPS provides the X, Y, and Z coordinates of the exposure station. See also: Global Positioning System
Airborne INS. INS stands for Inertial Navigation System. Airborne INS data is available for each image, and defines the position and orientation associated with an image as they existed during image capture. See also: Inertial Navi! gation System
Algorithm. "A procedure for solving a! mathema tical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an operation" (Merriam-Webster OnLine Dictionary 2001).
American Standard Code for Information Interchange (ASCII). A "basis of character sets…to convey some control codes, space, numbers, most basic punctuation, and unaccented letters a-z and A-Z" (Free On-Line Dictionary of Computing 1999).
Analog photogrammetry. In analog photogrammetry, optical or mechanical instruments, such as analog plotters, used to reconstruct 3D geometry from two overlapping photographs.
Analytical photogrammetry. The computer replaces some expensive optical and mechanical components by substituting analog measurement and calculation with mathematical computation.
a priori. Already or previously known.
Area of Interest (AOI). A point, line, or polygon that is selected as a training sample or as the image area to be ! used in an operation. AOIs can be stored in separate .aoi files.
Auto-correlation. A technique used to identify and measure the image positions appearing within the overlap area of two adjacent images in a block file.
Automated interior orientation. Technique based on template matching used to identify and measure fiducial mark positions.
Automated tie point collection. LPS’s ability to automatically measure tie points across multiple images. See also: Tie point
Average flying height. The distance between the camera position at the time of exposure and the average ground elevation. Average flying height can be determined by multiplying the focal length by the image scale. See also: Focal length; Image scale
B
Base-height ratio (b/h). The ratio between the average flying height of the camera and the distance between where the two overlapping images were captured.
Block. A term used to describe! and characterize all of the information associated with a pho! togramme tric mapping project, such as: projection, spheroid, and datum; imagery; camera or sensor model information; GCPs; and geometric relationship between imagery and the ground. A block file is a binary file.
Block footprint. A graphical representation of the extent of images in a block file. The images are not presented as raster images. Rather, they are displayed as vector outlines that depict the amount of overlap between images in the block file.
Block of photographs. Formed by the combined exposures of a flight. For example, a traditional frame camera block might consist of a number of parallel strips with a sidelap of 20- 30%, and an overlap of 60%.
Block triangulation. The process of establishing a mathematical relationship between images, the camera or sensor model, and the ground. The information derived is necessary for orthorectification, DEM generation, and stereopair creation.
Blunder. A blunder is a gross error resulting ! from incorrect data entry, incorrect measurement of ground points on imagery, and faulty identification of GCPs and tie points. In LPS, a blunder model identifies and removes errors from the photogrammetric network of observations.
Bundle. The unit of photogrammetric triangulation after each point measured in an image is connected with the perspective center by a straight light ray. There is one bundle of light rays for each image.
Bundle attitude. Defined by a spatial rotation matrix consisting of three angles: Omega (w), Phi (j), and Kappa (k). See also: Omega, Phi, Kappa
Bundle block adjustment. A mathematical technique (triangulation) that determines the position and orientation of each image as they existed at the time of image capture, determines the ground coordinates measured on overlap areas of multiple images, and minimizes the error associated with the imagery, image measurements, and GCPs. This is essentially a simultaneous trian! gulation performed on all observations.
Bundle loca! tion. De fined by the perspective center, expressed in units of the specified map projection.
C
Calibration certificate/report. In aerial photography, the manufacturer of the camera specifies the interior orientation in the form of a certificate or report. Information includes focal length, principal point offset, radial lens distortion data, and fiducial mark coordinates.
Cartesian coordinate system. "A coordinate system consisting of intersecting straight lines called axes, in which the lines intersect at a common origin. Usually it is a 2-dimensional surface in which a "x,y" coordinate defines each point location on the surface. The "x" coordinate refers to the horizontal distance and the "y" to vertical distance. Coordinates can be either positive or negative, depending on their relative position from the origin. In a 3- dimensional space, the system can also include a "z" coordinate, representing height or depth. The relative measurement of dista! nce, direction and area are constant throughout the surface of the system" (Natural Resources Canada 2001).
CellArray. In ERDAS IMAGINE, the CellArray is used to maintain and edit data in a tabular format.
Cell size. The area that one pixel represents, measured in map units. For example, one cell in the image may represent an area 30_ × 30_ on the ground. Sometimes called pixel size.
Charge-Coupled Device (CCD). A device in a digital camera that "contains an array of cells which record the intensity associated with a ground feature or object" (ERDAS 1999).
Check point. An additional ground point used to independently verify the degree of accuracy of a triangulation.
Check point analysis. The act of using check points to independently verify the degree of accuracy of a triangulation.
Coefficient limit. The limit for the cross-correlation coefficient. This value ranges from .10 to .99. A larger limit resul! ts in fewer points accepted and less error. A smaller limit re! sults in more correlated points, but also possibly more errors.
Collinearity. A nonlinear mathematical model that photogrammetric triangulation is based upon. Collinearity equations describe the relationship among image coordinates, ground coordinates, and orientation parameters.
Collinearity condition. The condition that specifies that the exposure station, ground point, and its corresponding image point location must all lie along a straight line.
Control point. A point with known coordinates in a coordinate system, expressed in the units (e.g., meters, feet, pixels, film units) of the specified coordinate system.
Control point extension. The process of converting tie points to control points. This technique requires the manual measurement of ground points on photos of overlapping areas. The ground coordinates associated with the GCPs are then determined using photogrammetric techniques.
Convergence value. A threshold to deter! mine the level and extent of processing during the iterative aerial triangulation procedure.
Coordinate system. "A system, based on mathematical rules, used to measure horizontal and vertical distance on a surface, in order to identify the location of points by means of unique sets of numerical or angular values" (Natural Resources Canada 2001).
Coplanarity condition. The coplanarity condition is used to calculate relative orientation. It uses an iterative least squares adjustment to estimate five parameters (By, Bz, Omega, Phi, and Kappa). The parameters explain the difference in position and rotation between two images making up the stereopair.
Correlation. Regions of separate images are matched for the purposes of tie point or mass point collection.
Correlation area. In LPS ATE, the default correlation area is the total overlap area reduced by the shrink percentage.
Correlation limit. Defines the correlation coeffici! ent threshold used to determine whether or not two points are ! to be co nsidered as possible matches.
Correlation size. Defines the size of the window to be used to compute the correlation between image points of common ground points appearing on multiple images.
Correlation threshold. A value used in image matching to determine whether to accept or discard match points. The threshold is an absolute value threshold ranging from 0.100 to 1.000.
Correlation windows. Windows that consist of a local neighborhood of pixels. One example is square neighborhoods (e.g., 3 × 3, 5 × 5, 7 × 7 pixels).
Corresponding GCPs. The GCPs that are located in the same geographic location as the selected GCPs, but are selected in different images.
Cross-correlation. A calculation that computes the correlation coefficient of the gray values between the template window and the search window. See also: Search windows; Template window
Cross-strips. Strips of image data that run perpendicular ! to strips collected along the flight line.
D
Data strip. A strip contained within aerial photographs. The strip commonly provides information such as the type of camera, the number of the camera, and the approximate focal length of the camera.
Datum. "A datum is a system of reference for specifying the horizontal and vertical spatial positions of points" (Wolf and Dewitt 2000). See also: Reference plane
Degrees of freedom. Also known as redundancy. In the bundle block adjustment process, the number of unknowns is subtracted from the number of knowns. The resulting number is the redundancy, or degree of freedom in a solution.
Digital correlation. "The process of automatically matching an image of a ground point to its corresponding (conjugate) image on another photo using digital correlation techniques. Also referred to as image matching and stereocorrelation" (ERDAS 1997).
Digital Elevation Model (DEM). Conti! nuous raster layers in which data file values represent elevat! ion. DEM s are available from the USGS at 1:24,000 and 1:250,000 scale, and can be produced with terrain analysis programs such as and LPS ATE.
Digital image matching. Also known as auto-correlation. The process of matching features common to two or more images for the purpose of generating a 3D representation of the Earth.
Digital orthoimage/orthophoto. An aerial photo or satellite scene that has been transformed by the orthogonal projection, yielding a map that is free of most significant geometric distortions.
Digital Photogrammetric Workstation (DPW). These include LPS and LPS ATE, PCI OrthoEngine, SOCET SET, Intergraph, Zeiss, and others. See also: Digital photogrammetry
Digital photogrammetry. Photogrammetry as applied to digital images that are stored and processed on a computer. Digital images can be scanned from photographs or can be directly captured by digital cameras.
Digital Stereo Model (DSM). Stereo models that use! imaging techniques of digital photogrammetry that can be viewed on desktop applications.
Digital Terrain Model (DTM). A discrete expression of topography in a data array, consisting of a group of planimetric coordinates (X,Y) and the elevations of the ground points and breaklines.
Digitizing. Any process that converts non-digital data into numeric data, usually to be stored on a computer. In ERDAS IMAGINE, digitizing refers to the creation of vector data from hardcopy materials or raster images. The data are traced using a digitizer keypad on a digitizing tablet, or a mouse on a display device.
Direction of flight. The direction in which the craft is moving (e.g., east to west). Images in a strip are captured along the aircraft or satellite’s direction of flight. Images overlap in the same manner as the direction of flight.
E
Elements of exterior orientation. Variables that define the position and orientation of ! a sensor as it obtained an image. It is the position of the pe! rspectiv e center with respect to the ground space coordinate system.
Ephemeris. Data contained in the header of the data file of an image, provides information about the recording of the data and the satellite orbit.
Epipolar line. "The line traced on each image representing the intersection of the epipolar plane with the image plane" (ERDAS 1997).
Epipolar plane. "The plane, in space, containing a ground point and both exposure stations" (ERDAS 1997).
Epipolar-resampled imagery. "Two images resampled (rectified or warped) such that clear stereo viewing is possible. Each line of the images is an epipolar line in which changes of height are effected by moving along the line (x-parallax); anomalies in stereo viewing represent displacement of images between lines (y-parallax)" (ERDAS 1997).
Epipolar stereopair. A stereopair in which Y-parallax has been removed.
Exclusion AOI. An AOI purposely excluded from processing. Th! e exclusion can be due to poor registration, or interest in some other feature. Exclusion AOIs are collected in the same manner as inclusion AOIs. LPS ATE makes use of exclusion AOIs for DTM extraction.
Exposure station. During image acquisition, each point in the flight path at which the camera exposes the film. The exposure station has elements that define its position and rotation: X, Y, Z, Omega, Phi, and Kappa. See also: Omega, Phi, Kappa
Exterior orientation. External sensor model information that describes the exact position and orientation of each image as they existed when the imagery was collected. The image’s position is defined as having 3D coordinates, and the orientation is defined as having three rotations that include Omega, Phi, and Kappa.
Exterior orientation parameters. The perspective center’s ground coordinates in a specified map projection and three rotation angles around the coordinate axes.
Eye-! base to height ratio. The eye-base is the distance between a p! erson 217;s eyes. The height is the distance between the eyes and the image datum. When two images of a stereopair are adjusted in the X and Y direction, the eye-base to height ratio is also changed. Change the X and Y positions to compensate for parallax in the images.
F
Fiducial. Four or eight reference markers fixed on the frame of an aerial metric camera and visible in each exposure. Fiducials are used to compute the transformation from pixel coordinates to image coordinates.
Fiducial center. The center of an aerial photo; the intersection point of lines constructed to connect opposite fiducials.
Fiducial orientation. Defines the relationship between the image/photo-coordinate system of a frame and the actual image orientation as it appears in a view.
Focal length. The distance between the optical center of the lens and where the optical axis intersects the image plane. Focal length of each camera is determined in a labora! tory environment.
Focal plane. The plane of the film or scanner used in obtaining an aerial photo.
Free-weighted iterative adjustment. In LPS, a free-weighted iterative adjustment does not assign statistical weights to the bundled adjustment used during aerial triangulation. See also: Aerial Triangulation
Full GCP. A GCP with X, Y, and Z coordinates. See also: Ground Control Point
Functional model. "The mathematical form of photogrammetric equations consisting of unknown and observed parameters which are to be incorporated in a least squares adjustment approach" (ERDAS 1997).
G
Geographic Information System (GIS). A unique system designed for a particular application that stores, enhances, combines, and analyzes layers of geographic data to produce interpretable information. A GIS may include computer images, hardcopy maps, statistical data, and any other data needed for a study, as well as computer software ! and human knowledge. GISs are used for solving complex geograp! hic plan ning and management problems. A GIS consists of spatial data stored in a relational database with associated ancillary information.
Global Positioning System (GPS). "A surveying method that uses a set of 24 satellites in geostationary position high above the Earth. Specially designed GPS receivers, when positioned at a point on Earth, can measure the distance from that point to three or more orbiting satellites. The coordinates of the point are determined through the geometric calculations of triangulation. GPS provides accurate geodetic data for any point on the Earth" (Natural Resources Canada 2001).
Ground Control Point (GCP). An easily identifiable point for which the ground coordinates of the map coordinate system are known.
H
Horizontal control. A set of points with defined planimetric positions in a map coordinate system.
I
Image. A picture or representation of an object or scene on paper, or a display ! screen. Remotely sensed images are digital representations of the Earth.
Image center. The center of the aerial photo or satellite scene.
Image coordinate space. A 2D space where measurements are recorded in pixels.
Image coordinate system. A 2D coordinate system defined in the photographic plane. The axes are constructed by the intersection of opposing fiducials.
Image scale (SI). Expresses the ratio between a distance in the image and the same distance on the ground.
Image space coordinate system. A coordinate system composed of the image coordinate system with the addition of a Z axis defined along the focal axis.
LPS block file. An LPS block file has the .blk extension. LPS block files contain at least one stereopair that is in a coordinate system. An LPS block file may also contain two or more sets of stereo images used for feature extraction and viewing.
Incidence angles. Angles specifying th! e position of sensors onboard a satellite. Also called inclina! tion ang les.
Inclination. The angle between a vertical on the ground at the center of the scene and a light ray from the exposure station, which defines the degree of off-nadir viewing when the scene was recorded.
Inclusion AOI. An AOI purposely included in processing, as in DTM extraction. See also: Exclusion AOI
Inertial Navigation System (INS). A technique that provides initial approximations to exterior orientation. This data is provided by a device or instrument. The instrument collects data about the attitude of the airplane in which it is located. The information it collects includes pitch (tilting forward and backward), roll (tilting sideways), and heading (the direction of flight) (National Oceanic and Atmospheric Administration 2001). See also: Omega, Phi, Kappa
Interior orientation. Describes the internal geometry of a camera such as the focal length, principal point, lens distortion, and fiducial mark coordinates for aerial pho! tographs.
International Society of Photogrammetry and Remote Sensing (ISPRS). An organization "devoted to the development of international cooperation for the advancement of photogrammetry and remote sensing and their application." For more information, visit the web site at http://www.isprs.org (ISPRS 2000).
Iterations with relaxation. During a free-weighted adjustment, each iteration of processing does not use the statistical weights associated with the GCPs in the block file.
K
Kappa. (k) In a rotation system, Kappa is positive rotation around the Z-axis.
Konrady coefficients. Coefficients that define radial lens distortion. Expressed as K0, K1, and K2. See also: Radial lens distortion
L
Latitude/Longitude (Lat/Lon). The coordinate components of a spherical map coordinate system.
Least squares adjustment. A technique by which the most probable values are computed for a measured or ind! irectly determined quantity based upon a set of observations. ! It is ba sed on the mathematical laws of probability and provides a systematic method for computing unique values of coordinates and other elements in photogrammetry based on a large number of redundance measurements of different kinds and weights.
Least squares correlation. Uses the least squares estimation to derive parameters that best fit a search window to a reference window.
Least squares regression. The method used to calculate the transformation matrix from the GCPs. This method is discussed in statistics textbooks.
Lens distortion. Caused by the instability of the camera lens at the time of data capture. Lens distortion makes the positional accuracy of the image points less reliable.
Lower Right X (LRX). The X map or file coordinate of the lower right pixel in the file.
Lower Right Y (LRY). The Y map or file coordinate of the lower right pixel in the file.
M
Map coordinates. A system of expressing l! ocations on the Earth’s surface using a particular map projection, such as UTM, State Plane, or Polyconic.
Map coordinate system. A map coordinate system that expresses location on the Earth’s surface using a particular map projection such as Universal Transverse Mercator (UTM), State Plane, or Polyconic.
Mass points. Points whose 3D coordinates are known (X, Y, and Z), which are used in creating a DEM or DTM. See also: Digital Elevation Model; Digital Terrain Model
Metric photogrammetry. The process of measuring information from photography and satellite imagery.
Multiple points. Multiple points can be collected from a DSM to create a TIN or DEM. Like a single point, multiple points have X, Y, and Z coordinate values. See also: Triangulated Irregular Network; Digital Elevation Model
N
Nadir. The area on the ground directly beneath a scanner’s detectors.
Nadir line. The average of! the left and right edge lines of a pushbroom image.
Nadir point. The intersection of the focal axis and the image plane.
Near vertical aerial photographs. Photographs taken from vertical or near vertical positions above the Earth captured by aircraft. Photographs are used for planimetric mapping projects.
Nonmetric camera. A camera that has not been calibrated in a laboratory to determine its internal geometry. See also: Focal length; Principal point; Lens distortion; Fiducial
Nonorthogonality. The deviation from perpendicularity between orthogonally defined axes.
O
Object space. "…the three-dimensional region that encompasses the physical features imaged in photographs" (Wolf and Dewitt 2000).
Off-nadir. Any point that is not directly beneath a scanner’s detectors, but off to an angle. The SPOT scanner allows off-nadir viewing.
Omega. (w) In a rotation system, Omega is rotation around the X-axis.
Omega, Phi, Kappa. A rotation system! that defines the orientation of a camera/sensor as it acquired an image. Omega, Phi, Kappa is used most commonly, where Omega is positive rotation around the X-axis, Phi is a positive rotation around the Y-axis, and Kappa is a positive rotation around the Z-axis. This rotation system follows the right-hand rule. See also: Phi(+), Omega, Kappa; Phi(-), Omega, Kappa; Right-hand rule
Optical axis. "…The line joining the centers of curvature of the spherical surfaces of the lens" (Wolf and Dewitt 2000).
Orientation. The position of the camera or satellite as it captured the image. Usually represented by six coordinates: X, Y, Z, Omega, Phi, and Kappa.
Orientation angle. The angle between a perpendicular to the center scan line and the North direction in a satellite scene.
Orientation matrix. A three-by-three matrix defining the relationship between two coordinate systems (i.e., image space coordinate system and ground space coo! rdinate system).
Orthogonal axes. Axes that interse! ct tradi tional frame camera images at right angles.
Orthorectification. Also called ortho resampling. The process of removing geometric errors inherent within photography and imagery caused by relief displacement, lens distortion, and the like.
Overlap. In a traditional frame camera, when two images overlap, they share a common area. For example, in a block or strip of photographs, adjacent images typically overlap by 60%.
P
Parallax. "The apparent angular displacement of an object as seen in an aerial photograph with respect to a point of reference or coordinate system. Parallax is caused by a difference in altitude or point of observation" (Natural Resources Canada 2001).
Perspective center. The optical center of a camera lens. 1. A point in the image coordinate system defined by the x and y coordinates of the principal point and the focal length of the sensor. 2. After triangulation, a point in the ground coordinate system th! at defines the sensor’s position relative to the ground.
Phi. (f) In a rotation system, Phi is rotation around the Y-axis.
Phi(-), Omega, Kappa. A rotation system in which Phi is a negative rotation about the
Y-axis, Omega is a positive rotation about the X-axis, and Kappa is a positive rotation about the Z-axis. Y is the primary axis.
Phi(+), Omega, Kappa. A rotation system in which Phi is a positive rotation about the
Y-axis, Omega is a positive rotation about the X-axis, and Kappa is a positive rotation about the Z-axis. Y is the primary axis. This system is most commonly used in Germany.
Photo direction. The direction of the optical axis looking down; Z. In close range photography, it is Y.
Photogrammetric quality scanners. Special devices capable of high image quality and excellent positional accuracy. Use of this type of scanner results in geometric accuracy similar to traditional analog and analyt! ical photogrammetric instruments.
Photogrammetry. T! he ̶ 0;art, science and technology of obtaining reliable information about physical objects and the environment through the process of recording, measuring, and interpreting photographic images and patterns of electromagnetic radiant imagery and other phenomena” (American Society of Photogrammetry 1980).
Plane table photogrammetry. Prior to the invention of the airplane, photographs taken on the ground were used to extract the geometric relationships between objects.
Principal point. The point in the image plane onto which the perspective center is projected.
Principal point of autocollimation. Part of the definition of principal point, the image position where the optical axis intersects the image plane. The principal point of autocollimation is near the principal point (Wolf 1983).
Principal point of symmetry. Part of the definition of principal point, the principal point of symmetry can best compensate for lens distortion. "The! point about which [distortions] are symmetrical" (Wolf 1983).
Principal point xo. A parameter used to define the location of the principal point in the x direction, which is relative to the origin of the image or photo-coordinate system. The location in the x direction where the optical axis of the camera intersects the image or photographic plane.
Principal point yo. A parameter used to define the location of the principal point in the y direction, which is relative to the origin of the image or photo-coordinate system. The location in the y direction where the optical axis of the camera intersects the image or photographic plane.
R
Radial lens distortion. Imaged points are distorted along radial lines from the principal point. Also referred to as symmetric lens distortion.
Rational functions. "Rational two-dimensional polynomials formed to handle the mapping of ground coordinates to an image space coordinate system a! fter triangulation is complete" (ERDAS 1997).
Redun! dancy. I n a block of data, the amount of data that is duplicated, thus providing strong geometric fidelity. See also: Degrees of freedom
Reference plane. In a topocentric coordinate system, the tangential plane at the center of the image on the Earth ellipsoid, on which the three perpendicular coordinate axes are defined.
Regular block of photos. A rectangular block in which the number of photos in each strip is the same; this includes a single strip or a single stereopair.
Residual. "The difference between any measured quantity and the most probable value for that quantity" (Wolf and Dewitt 2000).
Right-hand rule. "A convention in 3D coordinate systems (X, Y, Z) that determines the location of the positive Z-axis. If you place your right hand fingers on the positive X-axis and curl your fingers toward the positive Y-axis, the direction your thumb is pointing is the positive Z-axis direction" (ERDAS 1999).
Root Mean Square Error! (RMSE). Used to measure how well a specific calculated solution fits the original data. For each observation of a phenomena, a variation can be computed between the actual observation and a calculated value. (The method of obtaining a calculated value is application-specific.) Each variation is then squared. The sum of these squared values is divided by the number of observations and then the square root is taken. This is the RMSE value.
Rotation matrix. A 3 × 3 matrix used in the aerial triangulation functional model. Determines the relationship between the image space coordinate system and the ground space coordinate system.
S
Search size. The window size (in pixels) to search for corresponding points in two images during correlation.
Search windows. Candidate windows on the second image of an image pair that are evaluated relative to the reference window in the first image.
Self-calibrating Bundle Adjustment (S! CBA). Bundle adjustment which also estimates the interior orie! ntation parameters associated with a camera or sensor model.
Self-calibration. A technique used in block bundle adjustment to determine internal sensor model information.
Shrink percentage. In LPS ATE, the percentage by which the output DTM is shrunk versus the original scale. The shrink percentage is applied to each side of the output DTM.
Side fiducial. Fiducials that are located at the sides of an image, rather than at the corners of an image. See also: Fiducial
Side incidence angle. The angle between the vertical position of the satellite and the side viewing direction of the satellite when the sensor is scanning along the side. For example, SPOT imagery side incidence angles can range from +27 to -27 degrees. The scanning direction is perpendicular to the direction of flight.
Sidelap. In a block of photographs consisting of a number of parallel strips, the sidelap (measured vertically) is usually 20-30% in traditional frame! camera photos. Tie points are typically measured in the sidelap.
Softcopy photogrammetry. See Digital photogrammetry
Space forward intersection. A technique used to determine the ground coordinates X, Y, and Z of points that appear in the overlapping areas of two or more images based on known interior orientation and exterior orientation parameters.
Space intersection. A technique used to determine the ground coordinates X, Y, and Z of points that appear in the overlapping areas of two images, based on the collinearity condition.
Space resection. A technique used to determine the exterior orientation parameters associated with one image or many images, based on the collinearity condition.
Spatial resolution. A measure of the smallest object that can be resolved by the sensor, or the area on the ground represented by each pixel.
Standard deviation of unit weight. See RMSE
Stereopair. A set of two r! emotely-sensed images that overlap, providing a 3D view of the! terrain in the overlap area.
Strategy. In LPS ATE, a strategy is a set of correlation parameters defined for a specific area in a stereopair for the purpose of DTM extraction. An appropriate strategy can improve the likelihood of obtaining reliable image matching results.
Strip of photographs. In traditional frame camera photography, consists of images captured along a flight-line, normally with an overlap of 60% for stereo coverage. All photos in the strip are assumed to be taken at approximately the same flying height and with a constant distance between exposure stations. Camera tilt relative to the vertical is assumed to be minimal. See also: Cross-strips
T
Tangential lens distortion. Distortion that occurs at right angles to the radial lines from the principal point.
Template window. A small subset of an image that you want to try to locate in another image based on specific matching criteria. A template usually remains fi! xed in one image during the matching process.
Terrestrial photographs. Ground-based photographs and images taken with a camera stationed on or near the Earth’s surface. Photographs are usually used for archeology, geomorphology, and civil engineering.
Tie point. A point; its ground coordinates are not known, but can be recognized visually in the overlap or sidelap area between two images.
Topocentric coordinate system. A coordinate system that has its origin at the center of the image on the Earth ellipsoid. The three perpendicular coordinate axes are defined on a tangential plane at this center point. The x-axis is oriented eastward, the y-axis northward, and the z-axis is vertical to the reference plane (up).
Transformation matrix. A set of coefficients that is computed from GCPs, and used in polynomial equations to convert coordinates from one system to another. The size of the matrix depends upon the order of the transfo! rmation.
Triangulated Irregular Network (TIN). A sp! ecific r epresentation of DTMs in which elevation points can occur at irregular intervals forming triangles.
Triangulation. Process of establishing the geometry of the camera or sensor relative to objects on the Earth’s surface. See also: Aerial Triangulation
U
Upper Left X (ULX). The X map or file coordinate of the upper left pixel in the file.
Upper Left Y (ULY). The Y map or file coordinate of the upper left pixel in the file.
X
X-parallax. The difference in position of a common ground point appearing on two overlapping images, which is a function of elevation. X-parallax is measured horizontally.
Y
Y-parallax. The difference in position of a common ground point appearing on two overlapping images, which is caused by differences in camera position and rotation between two images. Y-parallax is measured vertically.
Z
Z. The vertical (height) component of a point, floa! ting cursor, or feature in a given coordinate system.
Z-axis. In the image space coordinate system, the Z-axis is the optical axis. The image space coordinate system directs the z-axis toward the imaged object. In object space, the Z axis is orthogonal to the X and Y axes and is directed out of the Earth’s surface.
geometry terms a-z
*.aoi. An Area of Interest file. Used to hold a point, line, or polygon that is selected as a training sample or as the image area to be used in an operation.
*.blk. An LPS block file. An LPS block file can contain only one image. A block file that contains two or more images with approximately 60% overlap can be viewed in stereo in other applications such as Stereo Analyst.
*.cam. An ASCII file with a fixed structure. Provides camera information such as focal length and principal point.
*.dat. An ASCII file. In LPS, exterior orientation parameters are often contained in a .dat file. Typically, this data comes from the airborne GPS or INS used during image capture. See also: Airborne GPS; Inertial Navigation System
*.img. An ERDAS IMAGINE image file. Data in the .img format are tiled data, which can be set to any size. A file containing raster image data. An .img file contains data such as sensor information, ! layer information, statistics, projection, pyramid layers, attribute data, etc.
*.shp. An ESRI shape file. Shape files are in vector format, and can store attribute data.
*.txt. An ASCII text file. Frequently used as an input GCP reference source for 2- and
3-dimensional control point and check point coordinates.
Symbols
k. (Kappa) In a rotation system, Kappa is positive rotation about the Z-axis.
w. (Omega) In a rotation system, Omega is positive rotation about the X-axis.
j. (Phi) In a rotation system, Phi is positive or negative rotation about the Y-axis. See also: Phi (-), Omega, Kappa; Phi (+), Omega, Kappa
Terms
A
Additional Parameter (AP). In block triangulation, additional parameters characterize systematic error within the block of images and observations, such as lens distortion. In LPS, four AP models can be used in the triangulation process, including: Bauer&#! 8217;s Simple Model, Jacobsen’s Simple Model, Ebner̵! 7;s Orth ogonal Model, and Brown’s Physical Model.
Adjusted stereopair. An adjusted stereopair is a pair of images displayed in a workspace that has a map projection associated and exterior orientation used to facilitate stereo viewing. A set of two remotely-sensed images that overlap, providing a 3D view of the terrain in the overlap area.
Aerial photographs. Photographs taken from positions above the Earth captured by aircraft. Photographs are used for planimetric mapping projects.
Aerial stereopair. Two photos with a common overlap area.
Aerial Triangulation (AT). The process of establishing a mathematical relationship between images, the camera or sensor model, and the ground. The information derived is necessary for orthorectification, DEM generation, and stereopair creation. This term is used when processing frame camera, digital camera, videography, and nonmetric camera imagery. See also: Triangulation
Affine transfo! rmation. A 2D plane-to-plane transformation that uses six parameters (coefficients) to account for rotation, translation, scale, and nonorthogonality in between the planes. Defines the relationship between two coordinate systems such as a pixel and image space coordinate system.
Air base. The distance between two image exposure stations. See also: Base-height ratio
Airborne GPS. GPS stands for Global Positioning System. Airborne GPS is a technique used to provide initial approximations of exterior orientation, which defines the position and orientation associated with an image as they existed during image capture. GPS provides the X, Y, and Z coordinates of the exposure station. See also: Global Positioning System
Airborne INS. INS stands for Inertial Navigation System. Airborne INS data is available for each image, and defines the position and orientation associated with an image as they existed during image capture. See also: Inertial Navi! gation System
Algorithm. "A procedure for solving a! mathema tical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an operation" (Merriam-Webster OnLine Dictionary 2001).
American Standard Code for Information Interchange (ASCII). A "basis of character sets…to convey some control codes, space, numbers, most basic punctuation, and unaccented letters a-z and A-Z" (Free On-Line Dictionary of Computing 1999).
Analog photogrammetry. In analog photogrammetry, optical or mechanical instruments, such as analog plotters, used to reconstruct 3D geometry from two overlapping photographs.
Analytical photogrammetry. The computer replaces some expensive optical and mechanical components by substituting analog measurement and calculation with mathematical computation.
a priori. Already or previously known.
Area of Interest (AOI). A point, line, or polygon that is selected as a training sample or as the image area to be ! used in an operation. AOIs can be stored in separate .aoi files.
Auto-correlation. A technique used to identify and measure the image positions appearing within the overlap area of two adjacent images in a block file.
Automated interior orientation. Technique based on template matching used to identify and measure fiducial mark positions.
Automated tie point collection. LPS’s ability to automatically measure tie points across multiple images. See also: Tie point
Average flying height. The distance between the camera position at the time of exposure and the average ground elevation. Average flying height can be determined by multiplying the focal length by the image scale. See also: Focal length; Image scale
B
Base-height ratio (b/h). The ratio between the average flying height of the camera and the distance between where the two overlapping images were captured.
Block. A term used to describe! and characterize all of the information associated with a pho! togramme tric mapping project, such as: projection, spheroid, and datum; imagery; camera or sensor model information; GCPs; and geometric relationship between imagery and the ground. A block file is a binary file.
Block footprint. A graphical representation of the extent of images in a block file. The images are not presented as raster images. Rather, they are displayed as vector outlines that depict the amount of overlap between images in the block file.
Block of photographs. Formed by the combined exposures of a flight. For example, a traditional frame camera block might consist of a number of parallel strips with a sidelap of 20- 30%, and an overlap of 60%.
Block triangulation. The process of establishing a mathematical relationship between images, the camera or sensor model, and the ground. The information derived is necessary for orthorectification, DEM generation, and stereopair creation.
Blunder. A blunder is a gross error resulting ! from incorrect data entry, incorrect measurement of ground points on imagery, and faulty identification of GCPs and tie points. In LPS, a blunder model identifies and removes errors from the photogrammetric network of observations.
Bundle. The unit of photogrammetric triangulation after each point measured in an image is connected with the perspective center by a straight light ray. There is one bundle of light rays for each image.
Bundle attitude. Defined by a spatial rotation matrix consisting of three angles: Omega (w), Phi (j), and Kappa (k). See also: Omega, Phi, Kappa
Bundle block adjustment. A mathematical technique (triangulation) that determines the position and orientation of each image as they existed at the time of image capture, determines the ground coordinates measured on overlap areas of multiple images, and minimizes the error associated with the imagery, image measurements, and GCPs. This is essentially a simultaneous trian! gulation performed on all observations.
Bundle loca! tion. De fined by the perspective center, expressed in units of the specified map projection.
C
Calibration certificate/report. In aerial photography, the manufacturer of the camera specifies the interior orientation in the form of a certificate or report. Information includes focal length, principal point offset, radial lens distortion data, and fiducial mark coordinates.
Cartesian coordinate system. "A coordinate system consisting of intersecting straight lines called axes, in which the lines intersect at a common origin. Usually it is a 2-dimensional surface in which a "x,y" coordinate defines each point location on the surface. The "x" coordinate refers to the horizontal distance and the "y" to vertical distance. Coordinates can be either positive or negative, depending on their relative position from the origin. In a 3- dimensional space, the system can also include a "z" coordinate, representing height or depth. The relative measurement of dista! nce, direction and area are constant throughout the surface of the system" (Natural Resources Canada 2001).
CellArray. In ERDAS IMAGINE, the CellArray is used to maintain and edit data in a tabular format.
Cell size. The area that one pixel represents, measured in map units. For example, one cell in the image may represent an area 30_ × 30_ on the ground. Sometimes called pixel size.
Charge-Coupled Device (CCD). A device in a digital camera that "contains an array of cells which record the intensity associated with a ground feature or object" (ERDAS 1999).
Check point. An additional ground point used to independently verify the degree of accuracy of a triangulation.
Check point analysis. The act of using check points to independently verify the degree of accuracy of a triangulation.
Coefficient limit. The limit for the cross-correlation coefficient. This value ranges from .10 to .99. A larger limit resul! ts in fewer points accepted and less error. A smaller limit re! sults in more correlated points, but also possibly more errors.
Collinearity. A nonlinear mathematical model that photogrammetric triangulation is based upon. Collinearity equations describe the relationship among image coordinates, ground coordinates, and orientation parameters.
Collinearity condition. The condition that specifies that the exposure station, ground point, and its corresponding image point location must all lie along a straight line.
Control point. A point with known coordinates in a coordinate system, expressed in the units (e.g., meters, feet, pixels, film units) of the specified coordinate system.
Control point extension. The process of converting tie points to control points. This technique requires the manual measurement of ground points on photos of overlapping areas. The ground coordinates associated with the GCPs are then determined using photogrammetric techniques.
Convergence value. A threshold to deter! mine the level and extent of processing during the iterative aerial triangulation procedure.
Coordinate system. "A system, based on mathematical rules, used to measure horizontal and vertical distance on a surface, in order to identify the location of points by means of unique sets of numerical or angular values" (Natural Resources Canada 2001).
Coplanarity condition. The coplanarity condition is used to calculate relative orientation. It uses an iterative least squares adjustment to estimate five parameters (By, Bz, Omega, Phi, and Kappa). The parameters explain the difference in position and rotation between two images making up the stereopair.
Correlation. Regions of separate images are matched for the purposes of tie point or mass point collection.
Correlation area. In LPS ATE, the default correlation area is the total overlap area reduced by the shrink percentage.
Correlation limit. Defines the correlation coeffici! ent threshold used to determine whether or not two points are ! to be co nsidered as possible matches.
Correlation size. Defines the size of the window to be used to compute the correlation between image points of common ground points appearing on multiple images.
Correlation threshold. A value used in image matching to determine whether to accept or discard match points. The threshold is an absolute value threshold ranging from 0.100 to 1.000.
Correlation windows. Windows that consist of a local neighborhood of pixels. One example is square neighborhoods (e.g., 3 × 3, 5 × 5, 7 × 7 pixels).
Corresponding GCPs. The GCPs that are located in the same geographic location as the selected GCPs, but are selected in different images.
Cross-correlation. A calculation that computes the correlation coefficient of the gray values between the template window and the search window. See also: Search windows; Template window
Cross-strips. Strips of image data that run perpendicular ! to strips collected along the flight line.
D
Data strip. A strip contained within aerial photographs. The strip commonly provides information such as the type of camera, the number of the camera, and the approximate focal length of the camera.
Datum. "A datum is a system of reference for specifying the horizontal and vertical spatial positions of points" (Wolf and Dewitt 2000). See also: Reference plane
Degrees of freedom. Also known as redundancy. In the bundle block adjustment process, the number of unknowns is subtracted from the number of knowns. The resulting number is the redundancy, or degree of freedom in a solution.
Digital correlation. "The process of automatically matching an image of a ground point to its corresponding (conjugate) image on another photo using digital correlation techniques. Also referred to as image matching and stereocorrelation" (ERDAS 1997).
Digital Elevation Model (DEM). Conti! nuous raster layers in which data file values represent elevat! ion. DEM s are available from the USGS at 1:24,000 and 1:250,000 scale, and can be produced with terrain analysis programs such as and LPS ATE.
Digital image matching. Also known as auto-correlation. The process of matching features common to two or more images for the purpose of generating a 3D representation of the Earth.
Digital orthoimage/orthophoto. An aerial photo or satellite scene that has been transformed by the orthogonal projection, yielding a map that is free of most significant geometric distortions.
Digital Photogrammetric Workstation (DPW). These include LPS and LPS ATE, PCI OrthoEngine, SOCET SET, Intergraph, Zeiss, and others. See also: Digital photogrammetry
Digital photogrammetry. Photogrammetry as applied to digital images that are stored and processed on a computer. Digital images can be scanned from photographs or can be directly captured by digital cameras.
Digital Stereo Model (DSM). Stereo models that use! imaging techniques of digital photogrammetry that can be viewed on desktop applications.
Digital Terrain Model (DTM). A discrete expression of topography in a data array, consisting of a group of planimetric coordinates (X,Y) and the elevations of the ground points and breaklines.
Digitizing. Any process that converts non-digital data into numeric data, usually to be stored on a computer. In ERDAS IMAGINE, digitizing refers to the creation of vector data from hardcopy materials or raster images. The data are traced using a digitizer keypad on a digitizing tablet, or a mouse on a display device.
Direction of flight. The direction in which the craft is moving (e.g., east to west). Images in a strip are captured along the aircraft or satellite’s direction of flight. Images overlap in the same manner as the direction of flight.
E
Elements of exterior orientation. Variables that define the position and orientation of ! a sensor as it obtained an image. It is the position of the pe! rspectiv e center with respect to the ground space coordinate system.
Ephemeris. Data contained in the header of the data file of an image, provides information about the recording of the data and the satellite orbit.
Epipolar line. "The line traced on each image representing the intersection of the epipolar plane with the image plane" (ERDAS 1997).
Epipolar plane. "The plane, in space, containing a ground point and both exposure stations" (ERDAS 1997).
Epipolar-resampled imagery. "Two images resampled (rectified or warped) such that clear stereo viewing is possible. Each line of the images is an epipolar line in which changes of height are effected by moving along the line (x-parallax); anomalies in stereo viewing represent displacement of images between lines (y-parallax)" (ERDAS 1997).
Epipolar stereopair. A stereopair in which Y-parallax has been removed.
Exclusion AOI. An AOI purposely excluded from processing. Th! e exclusion can be due to poor registration, or interest in some other feature. Exclusion AOIs are collected in the same manner as inclusion AOIs. LPS ATE makes use of exclusion AOIs for DTM extraction.
Exposure station. During image acquisition, each point in the flight path at which the camera exposes the film. The exposure station has elements that define its position and rotation: X, Y, Z, Omega, Phi, and Kappa. See also: Omega, Phi, Kappa
Exterior orientation. External sensor model information that describes the exact position and orientation of each image as they existed when the imagery was collected. The image’s position is defined as having 3D coordinates, and the orientation is defined as having three rotations that include Omega, Phi, and Kappa.
Exterior orientation parameters. The perspective center’s ground coordinates in a specified map projection and three rotation angles around the coordinate axes.
Eye-! base to height ratio. The eye-base is the distance between a p! erson 217;s eyes. The height is the distance between the eyes and the image datum. When two images of a stereopair are adjusted in the X and Y direction, the eye-base to height ratio is also changed. Change the X and Y positions to compensate for parallax in the images.
F
Fiducial. Four or eight reference markers fixed on the frame of an aerial metric camera and visible in each exposure. Fiducials are used to compute the transformation from pixel coordinates to image coordinates.
Fiducial center. The center of an aerial photo; the intersection point of lines constructed to connect opposite fiducials.
Fiducial orientation. Defines the relationship between the image/photo-coordinate system of a frame and the actual image orientation as it appears in a view.
Focal length. The distance between the optical center of the lens and where the optical axis intersects the image plane. Focal length of each camera is determined in a labora! tory environment.
Focal plane. The plane of the film or scanner used in obtaining an aerial photo.
Free-weighted iterative adjustment. In LPS, a free-weighted iterative adjustment does not assign statistical weights to the bundled adjustment used during aerial triangulation. See also: Aerial Triangulation
Full GCP. A GCP with X, Y, and Z coordinates. See also: Ground Control Point
Functional model. "The mathematical form of photogrammetric equations consisting of unknown and observed parameters which are to be incorporated in a least squares adjustment approach" (ERDAS 1997).
G
Geographic Information System (GIS). A unique system designed for a particular application that stores, enhances, combines, and analyzes layers of geographic data to produce interpretable information. A GIS may include computer images, hardcopy maps, statistical data, and any other data needed for a study, as well as computer software ! and human knowledge. GISs are used for solving complex geograp! hic plan ning and management problems. A GIS consists of spatial data stored in a relational database with associated ancillary information.
Global Positioning System (GPS). "A surveying method that uses a set of 24 satellites in geostationary position high above the Earth. Specially designed GPS receivers, when positioned at a point on Earth, can measure the distance from that point to three or more orbiting satellites. The coordinates of the point are determined through the geometric calculations of triangulation. GPS provides accurate geodetic data for any point on the Earth" (Natural Resources Canada 2001).
Ground Control Point (GCP). An easily identifiable point for which the ground coordinates of the map coordinate system are known.
H
Horizontal control. A set of points with defined planimetric positions in a map coordinate system.
I
Image. A picture or representation of an object or scene on paper, or a display ! screen. Remotely sensed images are digital representations of the Earth.
Image center. The center of the aerial photo or satellite scene.
Image coordinate space. A 2D space where measurements are recorded in pixels.
Image coordinate system. A 2D coordinate system defined in the photographic plane. The axes are constructed by the intersection of opposing fiducials.
Image scale (SI). Expresses the ratio between a distance in the image and the same distance on the ground.
Image space coordinate system. A coordinate system composed of the image coordinate system with the addition of a Z axis defined along the focal axis.
LPS block file. An LPS block file has the .blk extension. LPS block files contain at least one stereopair that is in a coordinate system. An LPS block file may also contain two or more sets of stereo images used for feature extraction and viewing.
Incidence angles. Angles specifying th! e position of sensors onboard a satellite. Also called inclina! tion ang les.
Inclination. The angle between a vertical on the ground at the center of the scene and a light ray from the exposure station, which defines the degree of off-nadir viewing when the scene was recorded.
Inclusion AOI. An AOI purposely included in processing, as in DTM extraction. See also: Exclusion AOI
Inertial Navigation System (INS). A technique that provides initial approximations to exterior orientation. This data is provided by a device or instrument. The instrument collects data about the attitude of the airplane in which it is located. The information it collects includes pitch (tilting forward and backward), roll (tilting sideways), and heading (the direction of flight) (National Oceanic and Atmospheric Administration 2001). See also: Omega, Phi, Kappa
Interior orientation. Describes the internal geometry of a camera such as the focal length, principal point, lens distortion, and fiducial mark coordinates for aerial pho! tographs.
International Society of Photogrammetry and Remote Sensing (ISPRS). An organization "devoted to the development of international cooperation for the advancement of photogrammetry and remote sensing and their application." For more information, visit the web site at http://www.isprs.org (ISPRS 2000).
Iterations with relaxation. During a free-weighted adjustment, each iteration of processing does not use the statistical weights associated with the GCPs in the block file.
K
Kappa. (k) In a rotation system, Kappa is positive rotation around the Z-axis.
Konrady coefficients. Coefficients that define radial lens distortion. Expressed as K0, K1, and K2. See also: Radial lens distortion
L
Latitude/Longitude (Lat/Lon). The coordinate components of a spherical map coordinate system.
Least squares adjustment. A technique by which the most probable values are computed for a measured or ind! irectly determined quantity based upon a set of observations. ! It is ba sed on the mathematical laws of probability and provides a systematic method for computing unique values of coordinates and other elements in photogrammetry based on a large number of redundance measurements of different kinds and weights.
Least squares correlation. Uses the least squares estimation to derive parameters that best fit a search window to a reference window.
Least squares regression. The method used to calculate the transformation matrix from the GCPs. This method is discussed in statistics textbooks.
Lens distortion. Caused by the instability of the camera lens at the time of data capture. Lens distortion makes the positional accuracy of the image points less reliable.
Lower Right X (LRX). The X map or file coordinate of the lower right pixel in the file.
Lower Right Y (LRY). The Y map or file coordinate of the lower right pixel in the file.
M
Map coordinates. A system of expressing l! ocations on the Earth’s surface using a particular map projection, such as UTM, State Plane, or Polyconic.
Map coordinate system. A map coordinate system that expresses location on the Earth’s surface using a particular map projection such as Universal Transverse Mercator (UTM), State Plane, or Polyconic.
Mass points. Points whose 3D coordinates are known (X, Y, and Z), which are used in creating a DEM or DTM. See also: Digital Elevation Model; Digital Terrain Model
Metric photogrammetry. The process of measuring information from photography and satellite imagery.
Multiple points. Multiple points can be collected from a DSM to create a TIN or DEM. Like a single point, multiple points have X, Y, and Z coordinate values. See also: Triangulated Irregular Network; Digital Elevation Model
N
Nadir. The area on the ground directly beneath a scanner’s detectors.
Nadir line. The average of! the left and right edge lines of a pushbroom image.
Nadir point. The intersection of the focal axis and the image plane.
Near vertical aerial photographs. Photographs taken from vertical or near vertical positions above the Earth captured by aircraft. Photographs are used for planimetric mapping projects.
Nonmetric camera. A camera that has not been calibrated in a laboratory to determine its internal geometry. See also: Focal length; Principal point; Lens distortion; Fiducial
Nonorthogonality. The deviation from perpendicularity between orthogonally defined axes.
O
Object space. "…the three-dimensional region that encompasses the physical features imaged in photographs" (Wolf and Dewitt 2000).
Off-nadir. Any point that is not directly beneath a scanner’s detectors, but off to an angle. The SPOT scanner allows off-nadir viewing.
Omega. (w) In a rotation system, Omega is rotation around the X-axis.
Omega, Phi, Kappa. A rotation system! that defines the orientation of a camera/sensor as it acquired an image. Omega, Phi, Kappa is used most commonly, where Omega is positive rotation around the X-axis, Phi is a positive rotation around the Y-axis, and Kappa is a positive rotation around the Z-axis. This rotation system follows the right-hand rule. See also: Phi(+), Omega, Kappa; Phi(-), Omega, Kappa; Right-hand rule
Optical axis. "…The line joining the centers of curvature of the spherical surfaces of the lens" (Wolf and Dewitt 2000).
Orientation. The position of the camera or satellite as it captured the image. Usually represented by six coordinates: X, Y, Z, Omega, Phi, and Kappa.
Orientation angle. The angle between a perpendicular to the center scan line and the North direction in a satellite scene.
Orientation matrix. A three-by-three matrix defining the relationship between two coordinate systems (i.e., image space coordinate system and ground space coo! rdinate system).
Orthogonal axes. Axes that interse! ct tradi tional frame camera images at right angles.
Orthorectification. Also called ortho resampling. The process of removing geometric errors inherent within photography and imagery caused by relief displacement, lens distortion, and the like.
Overlap. In a traditional frame camera, when two images overlap, they share a common area. For example, in a block or strip of photographs, adjacent images typically overlap by 60%.
P
Parallax. "The apparent angular displacement of an object as seen in an aerial photograph with respect to a point of reference or coordinate system. Parallax is caused by a difference in altitude or point of observation" (Natural Resources Canada 2001).
Perspective center. The optical center of a camera lens. 1. A point in the image coordinate system defined by the x and y coordinates of the principal point and the focal length of the sensor. 2. After triangulation, a point in the ground coordinate system th! at defines the sensor’s position relative to the ground.
Phi. (f) In a rotation system, Phi is rotation around the Y-axis.
Phi(-), Omega, Kappa. A rotation system in which Phi is a negative rotation about the
Y-axis, Omega is a positive rotation about the X-axis, and Kappa is a positive rotation about the Z-axis. Y is the primary axis.
Phi(+), Omega, Kappa. A rotation system in which Phi is a positive rotation about the
Y-axis, Omega is a positive rotation about the X-axis, and Kappa is a positive rotation about the Z-axis. Y is the primary axis. This system is most commonly used in Germany.
Photo direction. The direction of the optical axis looking down; Z. In close range photography, it is Y.
Photogrammetric quality scanners. Special devices capable of high image quality and excellent positional accuracy. Use of this type of scanner results in geometric accuracy similar to traditional analog and analyt! ical photogrammetric instruments.
Photogrammetry. T! he ̶ 0;art, science and technology of obtaining reliable information about physical objects and the environment through the process of recording, measuring, and interpreting photographic images and patterns of electromagnetic radiant imagery and other phenomena” (American Society of Photogrammetry 1980).
Plane table photogrammetry. Prior to the invention of the airplane, photographs taken on the ground were used to extract the geometric relationships between objects.
Principal point. The point in the image plane onto which the perspective center is projected.
Principal point of autocollimation. Part of the definition of principal point, the image position where the optical axis intersects the image plane. The principal point of autocollimation is near the principal point (Wolf 1983).
Principal point of symmetry. Part of the definition of principal point, the principal point of symmetry can best compensate for lens distortion. "The! point about which [distortions] are symmetrical" (Wolf 1983).
Principal point xo. A parameter used to define the location of the principal point in the x direction, which is relative to the origin of the image or photo-coordinate system. The location in the x direction where the optical axis of the camera intersects the image or photographic plane.
Principal point yo. A parameter used to define the location of the principal point in the y direction, which is relative to the origin of the image or photo-coordinate system. The location in the y direction where the optical axis of the camera intersects the image or photographic plane.
R
Radial lens distortion. Imaged points are distorted along radial lines from the principal point. Also referred to as symmetric lens distortion.
Rational functions. "Rational two-dimensional polynomials formed to handle the mapping of ground coordinates to an image space coordinate system a! fter triangulation is complete" (ERDAS 1997).
Redun! dancy. I n a block of data, the amount of data that is duplicated, thus providing strong geometric fidelity. See also: Degrees of freedom
Reference plane. In a topocentric coordinate system, the tangential plane at the center of the image on the Earth ellipsoid, on which the three perpendicular coordinate axes are defined.
Regular block of photos. A rectangular block in which the number of photos in each strip is the same; this includes a single strip or a single stereopair.
Residual. "The difference between any measured quantity and the most probable value for that quantity" (Wolf and Dewitt 2000).
Right-hand rule. "A convention in 3D coordinate systems (X, Y, Z) that determines the location of the positive Z-axis. If you place your right hand fingers on the positive X-axis and curl your fingers toward the positive Y-axis, the direction your thumb is pointing is the positive Z-axis direction" (ERDAS 1999).
Root Mean Square Error! (RMSE). Used to measure how well a specific calculated solution fits the original data. For each observation of a phenomena, a variation can be computed between the actual observation and a calculated value. (The method of obtaining a calculated value is application-specific.) Each variation is then squared. The sum of these squared values is divided by the number of observations and then the square root is taken. This is the RMSE value.
Rotation matrix. A 3 × 3 matrix used in the aerial triangulation functional model. Determines the relationship between the image space coordinate system and the ground space coordinate system.
S
Search size. The window size (in pixels) to search for corresponding points in two images during correlation.
Search windows. Candidate windows on the second image of an image pair that are evaluated relative to the reference window in the first image.
Self-calibrating Bundle Adjustment (S! CBA). Bundle adjustment which also estimates the interior orie! ntation parameters associated with a camera or sensor model.
Self-calibration. A technique used in block bundle adjustment to determine internal sensor model information.
Shrink percentage. In LPS ATE, the percentage by which the output DTM is shrunk versus the original scale. The shrink percentage is applied to each side of the output DTM.
Side fiducial. Fiducials that are located at the sides of an image, rather than at the corners of an image. See also: Fiducial
Side incidence angle. The angle between the vertical position of the satellite and the side viewing direction of the satellite when the sensor is scanning along the side. For example, SPOT imagery side incidence angles can range from +27 to -27 degrees. The scanning direction is perpendicular to the direction of flight.
Sidelap. In a block of photographs consisting of a number of parallel strips, the sidelap (measured vertically) is usually 20-30% in traditional frame! camera photos. Tie points are typically measured in the sidelap.
Softcopy photogrammetry. See Digital photogrammetry
Space forward intersection. A technique used to determine the ground coordinates X, Y, and Z of points that appear in the overlapping areas of two or more images based on known interior orientation and exterior orientation parameters.
Space intersection. A technique used to determine the ground coordinates X, Y, and Z of points that appear in the overlapping areas of two images, based on the collinearity condition.
Space resection. A technique used to determine the exterior orientation parameters associated with one image or many images, based on the collinearity condition.
Spatial resolution. A measure of the smallest object that can be resolved by the sensor, or the area on the ground represented by each pixel.
Standard deviation of unit weight. See RMSE
Stereopair. A set of two r! emotely-sensed images that overlap, providing a 3D view of the! terrain in the overlap area.
Strategy. In LPS ATE, a strategy is a set of correlation parameters defined for a specific area in a stereopair for the purpose of DTM extraction. An appropriate strategy can improve the likelihood of obtaining reliable image matching results.
Strip of photographs. In traditional frame camera photography, consists of images captured along a flight-line, normally with an overlap of 60% for stereo coverage. All photos in the strip are assumed to be taken at approximately the same flying height and with a constant distance between exposure stations. Camera tilt relative to the vertical is assumed to be minimal. See also: Cross-strips
T
Tangential lens distortion. Distortion that occurs at right angles to the radial lines from the principal point.
Template window. A small subset of an image that you want to try to locate in another image based on specific matching criteria. A template usually remains fi! xed in one image during the matching process.
Terrestrial photographs. Ground-based photographs and images taken with a camera stationed on or near the Earth’s surface. Photographs are usually used for archeology, geomorphology, and civil engineering.
Tie point. A point; its ground coordinates are not known, but can be recognized visually in the overlap or sidelap area between two images.
Topocentric coordinate system. A coordinate system that has its origin at the center of the image on the Earth ellipsoid. The three perpendicular coordinate axes are defined on a tangential plane at this center point. The x-axis is oriented eastward, the y-axis northward, and the z-axis is vertical to the reference plane (up).
Transformation matrix. A set of coefficients that is computed from GCPs, and used in polynomial equations to convert coordinates from one system to another. The size of the matrix depends upon the order of the transfo! rmation.
Triangulated Irregular Network (TIN). A sp! ecific r epresentation of DTMs in which elevation points can occur at irregular intervals forming triangles.
Triangulation. Process of establishing the geometry of the camera or sensor relative to objects on the Earth’s surface. See also: Aerial Triangulation
U
Upper Left X (ULX). The X map or file coordinate of the upper left pixel in the file.
Upper Left Y (ULY). The Y map or file coordinate of the upper left pixel in the file.
X
X-parallax. The difference in position of a common ground point appearing on two overlapping images, which is a function of elevation. X-parallax is measured horizontally.
Y
Y-parallax. The difference in position of a common ground point appearing on two overlapping images, which is caused by differences in camera position and rotation between two images. Y-parallax is measured vertically.
Z
Z. The vertical (height) component of a point, floa! ting cursor, or feature in a given coordinate system.
Z-axis. In the image space coordinate system, the Z-axis is the optical axis. The image space coordinate system directs the z-axis toward the imaged object. In object space, the Z axis is orthogonal to the X and Y axes and is directed out of the Earth’s surface.
geometry terms a-z
The Wizard
I think this just exemplifies how stupid the name 'wizard' is for 'a user interface element where the user is presented with a sequence of dialog boxes'.
geometry test 1 answers
LSAT Prep Book Recommendations
Here's the moment you've all been waiting for: my LSAT prep book recommendations.
Happy holidays to everyone. There WILL be more tips next week too, don't worry - not everyone is on vacation. :D Recommendations below. Stay warm!
PrepTests 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, and 56
by LSAC
Each are only sold individually, as LSAC has not yet published a book of ten exams containing them. Because the exam has changed in recent years, you'll need several of these to study effectively.
When to use: after you've completed the other PrepTests.
The Next 10 Actual, Official LSAT PrepTests
by LSAC (older edition)
Contains PrepTests 29-38 and is the newest book of ten. It's essential that you get your hands on these in order to study effectively.
When to use: during exam prep.
10 More Actual, Official LSAT PrepTests
by LSAC (older edition)
Contains PrepTests 19-28.
When to use: during exam prep.
10 Actual Official LSAT PrepTests < br />by LSAC (older edition)
Contains most PrepTests from 7-18. Only worth doing if you're studying far enough in advance that you'll have enough time to do the most recent exams as well.
Note: These exams are really old - from 12/92 - 9/95. Don't be concerned if some of the games are a bit difficult. You'll rarely see these types on recent exams.
When to use (if at all): in early stages of preparation to familiarize yourself with the exam.
The Official LSAT SuperPrep
by LSAC (older edition)
Contains a few exams you can't find anywhere else: 2/96, 2/99, and 2/00. The explanations within are the biggest selling point, but most people find them to be confusing and technical.
When to use (if at all): in early stages of preparation.
June 2007 LSAT exam (PDF)
by LSAC
Free sample exam. Treat it as if it were PrepTest 52.5 when making your study schedule.
LSAT Logic Games Bible (2003)
by Powerscore (2008)
This book contains the best Logic Games diagramming techniques I've seen, and I've reviewed all the LSAT prep books out there. The drills are useful, the organization is clear, and the book demonstrates its techniques on real LSAT PrepTests.
Skip the section on "Pattern Games" and "The Forgotten Few" unless you've already mastered other game types. Also, don't worry too much about the book's complicated subclassifications. You'll be fine if you can distinguish between the main game-types: linear/sequencing, grouping, and combination.
Unless you have a lot of time, I recommend the 2003 edition. Why? Because the 2008 edition is nearly twice the size. It appears the author beefed it up to justify the $65 retail price tag. Also, the 2008 edition exposes you to recent games you'll want to save for later practice tests.
When to use: Before you attempt logic games from the books of PrepTests.
Logic Made Easy: How to Know When Language Deceives You
by Deborah Bennett (older edition)
Although not explicitly written for test-prep purposes, this book contains several logical reasoning-type questions and reviews several common fallacies. The author is clearly familiar with the LSAT, and this makes the book more relevant for our purposes. I highly recommend reading this because it is clear, full of simple examples, and concise. You can skip the parts on the history of logic.
American Scientist's review.
When to read: Before you begin LSAT prep or when you need! a break from practice exams.
Informal Logic: A Pragmatic Approach
by Douglas N. Walton (older edition)
Clearly explains and demonstrate multiple examples of valid and invalid arguments. Walton is obsessed with logical fallacies and covers many of the common ones appearing on the LSAT.
When to read: Before you begin studying or when you need! a break.
Elementary Logic: Revised Edition
by William V. Quine
At 144 pages, it's short and sweet. It's also the first-ever logic textbook (originally published 1941, revised 1980). It discusses many basic issues (necessary/sufficient, etc.) relevant to LSAT logic. If you have the time/inclination, feel free to look it up, but it's by no means necessary.
When to read: Before you begin studying or when you need a break.
How to Solve It: A New Aspect of Mathematical Method
by George Polya (Older editions)
Simple advice on problem solving and logical thinking. It's useful because it gives you a framework to identify and analyze the relationship between evidence and conclusion. Wikipedia, this summary, and the following will probably be enough for you.
The book gives you some questions to ask yourself about any Logic Game or Logical Reasoning Stimulus:
1. What information is unknown/provided? Does the evidence/premise satisfy the conclusion?
2. How is this game/stimulus similar to others you've done? Questions do tend to come back in future exams (with different topics, of course).
3. ! Does a restatement (the contrapositive) of the argument help?
4. What inferences can you make?
5. How can you use these inferences?
Another nice summary.
When to read it: Before you begin studying or when you need a break.
The Little Luxe Book of Sudoku: 335 Easy to Hard Puzzles and The Little Black Book of Sudoku: 400 Puzzles
by Will Shortz
Number puzzles exercise your brain and get it ready for the logic games.
When to use: Before you begin studying or when you need a break.
T! hat's it - see you next year!
---------
! Next wee k: How to study for a retake (or what to do when you've already used too many PrepTests)...
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Happy holidays to everyone. There WILL be more tips next week too, don't worry - not everyone is on vacation. :D Recommendations below. Stay warm!
PrepTests 39, 40, 41
by LSAC
Each are only sold individually, as LSAC has not yet published a book of ten exams containing them. Because the exam has changed in recent years, you'll need several of these to study effectively.
When to use: after you've completed the other PrepTests.
The Next 10 Actual, Official LSAT PrepTests
by LSAC (older edition)
Contains PrepTests 29-38 and is the newest book of ten. It's essential that you get your hands on these in order to study effectively.
When to use: during exam prep.
10 More Actual, Official LSAT PrepTests
by LSAC (older edition)
Contains PrepTests 19-28.
When to use: during exam prep.
10 Actual Official LSAT PrepTests
Contains most PrepTests from 7-18. Only worth doing if you're studying far enough in advance that you'll have enough time to do the most recent exams as well.
Note: These exams are really old - from 12/92 - 9/95. Don't be concerned if some of the games are a bit difficult. You'll rarely see these types on recent exams.
When to use (if at all): in early stages of preparation to familiarize yourself with the exam.
The Official LSAT SuperPrep
by LSAC (older edition)
Contains a few exams you can't find anywhere else: 2/96, 2/99, and 2/00. The explanations within are the biggest selling point, but most people find them to be confusing and technical.
When to use (if at all): in early stages of preparation.
June 2007 LSAT exam (PDF)
by LSAC
Free sample exam. Treat it as if it were PrepTest 52.5 when making your study schedule.
LSAT Logic Games Bible (2003)
by Powerscore (2008)
This book contains the best Logic Games diagramming techniques I've seen, and I've reviewed all the LSAT prep books out there. The drills are useful, the organization is clear, and the book demonstrates its techniques on real LSAT PrepTests.
Skip the section on "Pattern Games" and "The Forgotten Few" unless you've already mastered other game types. Also, don't worry too much about the book's complicated subclassifications. You'll be fine if you can distinguish between the main game-types: linear/sequencing, grouping, and combination.
Unless you have a lot of time, I recommend the 2003 edition. Why? Because the 2008 edition is nearly twice the size. It appears the author beefed it up to justify the $65 retail price tag. Also, the 2008 edition exposes you to recent games you'll want to save for later practice tests.
When to use: Before you attempt logic games from the books of PrepTests.
Logic Made Easy: How to Know When Language Deceives You
by Deborah Bennett (older edition)
Although not explicitly written for test-prep purposes, this book contains several logical reasoning-type questions and reviews several common fallacies. The author is clearly familiar with the LSAT, and this makes the book more relevant for our purposes. I highly recommend reading this because it is clear, full of simple examples, and concise. You can skip the parts on the history of logic.
American Scientist's review.
When to read: Before you begin LSAT prep or when you need! a break from practice exams.
Informal Logic: A Pragmatic Approach
by Douglas N. Walton (older edition)
Clearly explains and demonstrate multiple examples of valid and invalid arguments. Walton is obsessed with logical fallacies and covers many of the common ones appearing on the LSAT.
When to read: Before you begin studying or when you need! a break.
Elementary Logic: Revised Edition
by William V. Quine
At 144 pages, it's short and sweet. It's also the first-ever logic textbook (originally published 1941, revised 1980). It discusses many basic issues (necessary/sufficient, etc.) relevant to LSAT logic. If you have the time/inclination, feel free to look it up, but it's by no means necessary.
When to read: Before you begin studying or when you need a break.
How to Solve It: A New Aspect of Mathematical Method
by George Polya (Older editions)
Simple advice on problem solving and logical thinking. It's useful because it gives you a framework to identify and analyze the relationship between evidence and conclusion. Wikipedia, this summary, and the following will probably be enough for you.
The book gives you some questions to ask yourself about any Logic Game or Logical Reasoning Stimulus:
1. What information is unknown/provided? Does the evidence/premise satisfy the conclusion?
2. How is this game/stimulus similar to others you've done? Questions do tend to come back in future exams (with different topics, of course).
3. ! Does a restatement (the contrapositive) of the argument help?
4. What inferences can you make?
5. How can you use these inferences?
Another nice summary.
When to read it: Before you begin studying or when you need a break.
The Little Luxe Book of Sudoku: 335 Easy to Hard Puzzles and The Little Black Book of Sudoku: 400 Puzzles
by Will Shortz
Number puzzles exercise your brain and get it ready for the logic games.
When to use: Before you begin studying or when you need a break.
T! hat's it - see you next year!
---------
! Next wee k: How to study for a retake (or what to do when you've already used too many PrepTests)...
free tutoring
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