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Tuesday, August 31, 2010
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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)...
Continue Reading...»
free tutoring
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
What is Multiplication?
Can be a tricky question, this.
Primary schoolchildren are taught that it is repeated addition, which makes a lot of sense.
4 x 4 =
4 + 4 + 4 + 4 =
16
Four lots of four/groups of/sets of.
But multiplication is also a scaling quantity. It ratchets things up massively quickly. If you type 2x2 into your calculator, then keep multiplying every answer by 2, the calculator will quickly run out of digits. To compare this with addition misses the point that multiplication is the centre of all geometric operations.
It does through the squaring and cubing and so on effect. If you take four centimetres, and for each of these four, you add another four, you get 4 x 4. It is known as squaring because the Greeks used to see it geometrically as the way to find the area of a square. For each centimetre across, there are four up (and vice versa).
x2 is a powerful, recurring idea, which has ! its role in pretty much the entire universe. (E = mc2)
It's also worth noting the effect of multiplication by a fractional quantity.
4 x 1/4 will obviously increase the fraction, but it will have a decreasing effect on the whole number. Unlike multiplication by two whole numbers, where the answer is greater than either, in this operation, the answer will always be smaller than one of the inputted values.
factoring binomials calculator
Primary schoolchildren are taught that it is repeated addition, which makes a lot of sense.
4 x 4 =
4 + 4 + 4 + 4 =
16
Four lots of four/groups of/sets of.
But multiplication is also a scaling quantity. It ratchets things up massively quickly. If you type 2x2 into your calculator, then keep multiplying every answer by 2, the calculator will quickly run out of digits. To compare this with addition misses the point that multiplication is the centre of all geometric operations.
It does through the squaring and cubing and so on effect. If you take four centimetres, and for each of these four, you add another four, you get 4 x 4. It is known as squaring because the Greeks used to see it geometrically as the way to find the area of a square. For each centimetre across, there are four up (and vice versa).
x2 is a powerful, recurring idea, which has ! its role in pretty much the entire universe. (E = mc2)
It's also worth noting the effect of multiplication by a fractional quantity.
4 x 1/4 will obviously increase the fraction, but it will have a decreasing effect on the whole number. Unlike multiplication by two whole numbers, where the answer is greater than either, in this operation, the answer will always be smaller than one of the inputted values.
factoring binomials calculator
Semester 2 Finals
Semester 2 Finals Review Key Pg1, Pg2, Pg3, Pg4, Pg5, Pg6, Pg7, Pg8, Pg9, Pg10, Pg11, Pg12
Semester 2 Finals Review Notes
Semester 2 Finals Review
exponential decay calculator
Semester 2 Finals Review Notes
Semester 2 Finals Review
exponential decay calculator
The real meaning of E=MC2
In one of Albert Einstein’s revolutionary scientific papers published in 1905, E=mc2 was introduced. Since then, E=mc2 probably has been the most famous equation in the world. E=mc2 has become overwhelmingly popular in the society. Even people with no background in physics have at least heard of the equation and are aware of its prodigious influence on the world we live in. However, most people do not exactly know what the equation means.
This article will explain to you about the world’s most famous equation, E=mc2, in a simple and brief way.
The equation is a direct result of the work of Einstein on special relativity. Simply put, this equation tells us that mass and energy are two forms of the same thing; before the work o! f Einstein this concept had not been considered by the global intellectual community for explaining some of the basic laws of the Universe. In the right condition, mass can turn into energy and energy can turn into mass. Here, ‘right condition’ refers to near-to-light-speed. Maybe, that is why we humans feel difficult to perceive it - because we are too slow in comparison to light. Light moves at a speed of roughly 670 million miles per hour.
To find out how much energy an object has, multiply the mass of the object by the square of the speed of light. But why multiply? That’s because, when mass is converted into energy, the resulting energy is by definition moving at the speed of light. Pure energy is electromagnetic radiation and electromagnetic radiation always moves at the speed of light (light is also a kind of electromagnetic wave).
The equation requires you ! to use the square of speed of light because of the nature of ! energy. When a body begins to move twice as fast as it’s moving now, it does not use twice as much as energy. It uses four times more. This is related to the formula of kinetic energy: kinetic energy= (1/2) x mass x velocity2; did you notice that the velocity is squared? Oh, and by the way, speed and velocity is roughly the same thing.
Because the square of the speed of light is a very large figure: around 448,900,000,000,000,000 in units of mph; even a small chunk of matter can produce a large amount of energy.
Perhaps the reason why the equation is so widely celebrated is because of its capability to explain basic natural processes: from microscopic radioactivity to the big bang itself. It has explained the phenomenon of emission of huge amounts of energy from radioactive elements (such as Uranium). It has also explained how the sun produces energy, just to name a few.
I hope that this brief article has helped you build up a basic comprehension of the world’s most famous equation.
equation expander
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