Linearized Collinearity Equations for Scanned Data

by James R. Baker, (A.M.ASCE), Assoc. Prof. of Engrg.; Fort Lewis Coll., Durango, Colo.,

Serial Information: Journal of the Surveying and Mapping Division, 1977, Vol. 103, Issue 1, Pg. 25-35

Document Type: Journal Paper


The collinearity equations, based upon modification of those common in conventional photogrammetry, must accommodate the continuous dynamic nature of the exterior orientation elements. Therefore, some types of functional behavior (polynomials, harmonics, etc.) must be assumed for those orientation elements. In order to investigate image and object point coordinate deformations, and to perform space resection utilizing the method of least squares, it is desirable to generate linear approximations for these collinearity equations. The technique presented for this linearization utilizes a Taylor's series expansion about some approximations for the variables involved. The functions assumed to approximate the dynamic nature of the orientation elements are included in the linearization through the use of matrix premultipliers. The resulting linearized form of analytic expressions may be used to analyze the geometric aspects of scanned imagery.

Subject Headings: Linear functions | Imaging techniques | Least squares method | Approximation methods | Photogrammetry | Polynomials | Deformation (mechanics) | Matrix (mathematics)

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