Anharmonic Properties of an Air Photograph: Cutting Lines (Especially for GATE-Geospatial 2022)

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The aerial photograph, as has been indicated, is a graphic record of visible light rays through the medium of a light-sensitive emulsion coated on a stable base. As it is two-dimensional, only pencils of rays can be presented, which relate the photograph with the ground by means of projective geometry. As can be seen in below Figure, the points A, B, C, D and E on the ground are imaged as a, b, c, d and e on the photograph. Thus, by virtue of the projection principles, OaA and ObB form two straight lines. Therefore, points 0, a, b, A and B all lie in the same plane. Then the line ab produced will meet AB produced at Si on the line of intersection between the photographic plane and the ground plane. This applies to other points in relation to OaA.

Anharmonic Properties of an Aerial Photograph

If the photograph plane is turned about the line S1S4 until it lies flat with the ground plane, the projective relationship between the two can be seen more clearly in below Figure. These projectively related figures possess a metric characteristic, called the anharmonic or cross ratio. Thus, the cross ratio does not depend on the position of the cutting line and the distance along the cutting line such as S1S4 but depends only on the angles from which the rays come. Therefore, any cutting line can be drawn to intersect the pencil of rays in four points, such as S1S4, which determine the value of A. This ratio is very useful for photogrammetric mapping using a single aerial photograph.

Photograph Plane Having Been Rotated About S1S4

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