SOME EXPERIMENTS IN ANALYTICAL ABSOLUTE ORIENTATION INCLUDING GENERATION OF RELATIVELY ORIENTED MATHEMATICAL MODELS

Abstract

Analytical absolute orientation problem is one of the most important problem in analytical photogrammetry.. Absolute orientation can be applied in two ways% (1) For transforming models (strips/blocks) into ground system and (2) For connecting models'. Analytical absolute orientation was considered as a non linear problem prior to 1958.59'. Thompson in 1959 first time reduced this problem to a linear one. After Thompson in 1960 Schut gave a simple and elegant linear solution of absolute orientation problem using matrix and quaternion algebra. Further in 1968 Schut improved his method which is more simple and useful for computer analysis. In the same year Oswal 'and Bala - subramanian developed another approach for solving all nine elements of rotation matrix. This transformation is considered to be an affine one. Schut forms rotation matrix by computing only four parameters while Oswal forms it by computing all nine elements of rotation matrix. Blais also computed orthogonal matrix based on affine transformation-. In this study investigations in analytical absolute orientation for model connection and transformation of models from one model system to another model system have been done. For this purpose it was found necessary to have relatively oriented models. In present study,therefore, relatively oriented models from hypothetical photograms for four different blocks viz. 1201, 1211, 1221 and 1231 have been generated. These relatively oriented models have been used in further studies for absolute orientation'. Following experiments have been done in analytical absolute orientation using Schutt s method and Oswalt s method with a view to compare the two methods in respect of model connection'. 1. Transforming models from one model system to other model system from known coordinates before and after rotation for following two cases - (is) without introduction of error and with introduction of error in coordinates before rotation. 2. Performing model connection through adjacent relatively oriented model. The exact values of rotation Matrices and coordinates after rotation for case .1 have been procured by forming rotation matrices from known values of w,O,k . the rotations about X,Y,Z axis respectively. In case 2 the exact values have been taken from relative orientation results. Suitable computer programs have been developed in Fortran IV for relative orientation as well as for absolute orientation by Schutt s and ()swells method. The results obtained in all cases have been compared with exact values and it has been found that the results of both Schtte s and °swells methods do not differ significantly. Both methods are general:1y giving equally gocd results well within acceptable limits, except °swells method in cases where ,undulations are of the order of 5 percent to 10 percent of flying height