# photogrammetry

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## photogrammetry:

see aerial and satellite photography**aerial and satellite photography,**

technology and science of taking still or moving-picture photographs from a camera mounted on a balloon, airplane, satellite, rocket, or spacecraft. In the 19th cent., photographers such as Thaddeus Lowe and George R.

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## Photogrammetry

## Photogrammetry

the scientific and technical discipline concerned with the determination of the dimensions, shape, and position of objects from examination of their images in photographs. The photographs are obtained either directly by conventional, moving-film aerial, or panoramic cameras or by using radar, television, infrared-heat-sensing, or laser systems. Photographs produced by conventional cameras are the most widely used, especially in aerial photographic surveys. In the theory of photogrammetry these photographs are considered the central projection of the object. Deviations from the central projection caused by lens distortion, deformation of the film and print paper, and other sources of error are taken in account in the calibration data for the aerial camera and the photographs. Photogrammetry uses both individual photographs and stereoscopic pairs; the use of stereopairs makes it possible to obtain a stereoscopic model of objects. The branch of photogrammetry that studies objects by means of stereopairs is called stereophotogrammetry.

The positioning at the moment the photograph is taken (see Figure 1) is determined by three elements of relative orientation—the camera focusing distance *f* and the coordinates of the principal point *o* (*x _{o}* and

*i*)—and by six elements of absolute orientation—the coordinates of the center of projection

_{o}*S*(

*X*,

_{s}*Y*, and

_{s}*Z*, the longitudinal (α) and transverse (ω) angles of inclination of the photograph, and the angle of rotation (K).

_{s}The following relationship exists between the coordinates of the point of an object and the object’s image on the photograph:

where *X*, *Y*, *Z* and *X _{s}*,

*Y*, and

_{s}*Z*are the coordinates of the points

_{s}*M*and

*S*in the system

*OXYZ*;

*X*’,

*Y*’, and

*Z*’ are the coordinates of point

*m*in the system

*SXYZ*, parallel to

*OXYZ*, as computed by the plane coordinates

*x*and

*y*:

In this case

(3)

*a*_{1} = cos α cos κ – sin α sin ω sin κ

*a*_{2} = – cos α sin κ – sin α sin ω cos κ

*a*_{3} = – sin α cos ω

*b*_{1} = cos ω sin κ

*b*_{2} = cos ω cos κ

*b*_{3} = – sin ω

*c*_{1} = sin α cos κ + cos α sin ω sin κ

*c*_{2} = – sin α sin κ + cos α sin ω cos κ

*c*_{3} = cos α cos ω

are the direction cosines.

The formulas of the relationship between the coordinates of point *M* of the object (see Figure 2) and the coordinates of the object’s images *m*_{1} and *m _{2}* in the stereopair

*P*

_{1}–

*P*

_{2}have the following form:

where

*B _{X}*,

*B*, and

_{Y}*B*are projections of base

_{Z}*B*on the axes of the coordinate. If the elements of absolute orientation of the stereopair are known, then the coordinates of the point of the object can be determined from formula (4). This is known as the direct intersection method. The position of a point of an object may be found by means of a single photograph in the special case where the object is flat, for example with geographical plains (Z = const). The coordinates

*x*and

*y*of the points of the photograph are measured on a monocular comparator or stereocomparator. The elements of relative orientation are known from the results of camera calibration; the elements of absolute orientation can be determined when photographing the objects or during the process of aerial triangulation.

If the elements of absolute orientation of the photographs are unknown, the coordinates of the point of an object are found by using control points; this is called the reverse intersection method. The control point is a contour point of an object recognized on the photograph, the coordinates of which are obtained by geodetic measurement or from aerial triangulation. When reverse intersection is used, it is first necessary to determine the elements of mutual orientation of the photographs *P*_{1}–*P*_{2} (see Figure 3)—α_{1}′, κ_{1}′, α_{2}′, ω_{2}, κ_{2}′ in the system *S*_{1}*X′Y′Z′*, whose axis *X* coincides with the base and whose axis *Z* lies in the main base plane *S*_{1}*o*_{1}*S*_{2} of photograph *P*_{1} The coordinates of the points of the model are then computed in the same system. Finally, by using the control points, the transition is made from the coordinates of the points of the model to the coordinates of the points of the objects.

The elements of mutual orientation make it possible to establish photographs in the same position relative to one another that they occupied when the object was photographed. In this case, each pair of corresponding rays, for example, *S*_{1}*m*_{1} and *S*_{2}*m*_{2}, intersects and forms a point (*m*) of the model. The set of rays belonging to the photograph is called a bundle and the center of projection *S*_{1} or *S*_{2} is called the vertex of the bundle. The scale of the model remains unknown because the distance *S*_{1}*S*_{2} between the peaks of the bundles is chosen arbitrarily. The corresponding points *m*_{1} and *m*_{2} of the stereopair are set in a single plane passing through the base *S*_{1}*S*_{2}. Therefore,

Assuming that the approximate values of the elements of mutual orientation are known, equation (6) can be put in the linear form

(7) *a*δα_{1}’ + *b*δα_{2}’ + *c*δω_{2}’ + *d*δκ_{1}’ + *e*δκ_{2}’ + *l* = *V*

where δα_{1}’, . . ., δκ_{2}’ are corrections to the approximate values of the unknowns; *a*,. . . ., *e* are partial derivatives of function (6) with respect to the variables α_{1}’, . . ., κ’; and *I* is the value of function (6) computed for the approximate values of the unknowns. In order to determine the elements of mutual orientation, the coordinates of at least five points of the stereopair are measured; then equation (7) is compiled and solved by the method of successive approximations. The coordinates of the points of the model are computed according to formula (4); an arbitrary length is selected for base *B* with the following assumptions: *X*_{S1} = *Y*_{S1} = *Z*_{S1} = 0; *B*_{X} = *B*; and *B _{Y}* =

*B*= 0. In this case the spatial coordinates of points

_{z}*m*

_{1}and

*m*

_{2}are found from formula (2), and the direction cosines by formula (3). For photograph

*P*

_{1}the coordinates are found from the elements α

_{1}’, ω

_{1}’ = 0, κ

_{1}’; for photograph

*P*

_{2}they are found from the elements α

_{2}’; ω

_{2}’, κ

_{2}’.

The coordinates of the point of the object are determined with respect to the coordinates *X*’, *Y*’, *Z*’ of the point of the model, as follows:

where *t* is the denominator of the scale of the model. The direction cosines are obtained from formula (3) by substituting the model’s longitudinal angle of inclination ξ, transverse angle of inclination η, and angle of rotation θ for the angles α, ω, and κ, respectively.

In order to determine the seven elements of absolute orientation of the model (*X*_{S1}, *Z*_{S1}, *Z*_{S1}, ξ, η, θ and *t*), equation (8) is written for three or more control points and then solved. The coordinates of the control points are found by geodetic methods or by means of aerial triangulation. The set of points of an object whose coordinates are known forms a numerical model of the object, which may be used for drawing a map and solving various engineering problems, for example, finding the optimum route for a road. In addition to analytic methods of processing photographs, analogue methods based on the use of various photogrammetric instruments, such as rectifiers, stereographs, and stereoprojectors, also find application.

Panoramic photographs and photographs from moving-film aerial cameras, as well as radar, television, infrared-heat-sensing, and other photographic systems, greatly expand the possibilities of photogrammetry, particularly in space studies. However, they do not present a single center of projection, and their elements of absolute orientation change continuously in the process of constructing an image, which makes it difficult to use such photographs for measurement purposes.

Photogrammetric techniques possess several fundamental advantages: high productivity, since the images of objects, rather than the objects themselves, are measured; high accuracy, due to the use of precision equipment to obtain and measure the photographs and the use of strict procedures for processing the results of measurements; the possibility of studying both fixed and moving objects; and completely objective measurement results. In addition, measurements can be made at some distance removed from the object, which is particularly important where objects are inaccessible (such as an airplane or projectile in flight) or when there would be danger to an observer in the area of the object (as with an active volcano or nuclear explosion).

Photogrammetry is widely used to make maps of the earth, other planets, and the moon; to measure the geologic elements of rock beds and to document mining excavations; to study the movement of glaciers and the dynamics of the thawing of the snow cover; to determine forest valuation characteristics; and to investigate soil erosion and observe changes in vegetation cover. It is also used in the study of sea waves and currents and in underwater surveys and prospecting; in the design, construction, and operation of engineering structures; in the monitoring of the condition of architectural ensembles, buildings, and monuments; and in the determination of coordinates of fire positions and targets in military operations.

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A. N. LOBANOV