DEVELOPMENTS IN ANALYTICAL EXTERIOR ORIENTATION INCLUDING GENERATION OF ANALYTICAL PHOTOGRAMMETRIC BLOCKS

Abstract

In this thesis, the exterior orientation geometry of a photogram has been critically analysed. New formulations and solutions of the problem have been developed with a view to adapt exterior orientation geometry as the working basis of photogrammetric measurement and control extension. Figure 1.1 (p. 2) presents a novel way of looking at the problem of control extension through a strip. The diff erent methods of triangulation are seen as chains of ortho gonal transformation. It would be readily appreciated that photograms of a strip could be connected geometrically either through relative-absolute orientation sequence, or more direct ly, via exterior orientation geometry. The latter route is not only shorter but may be expected to give a more favourable error propagation pattern, since no intermediate entity (stereomodel) is created. While control extension systems based on the former approach are well-investigated, almost no data is available on the working of exterior-orientation-based systems. This thesis makes a serious start in this direction and is partly devoted to developing planimetric and spatial control extension methods based on the new approach. New for mulae have been developed for the computation of coordinates of pass points from image and exterior orientation data, and are note-worthy for their simplicity and elegance. The results of planimetric and spatial triangulation by the developed procedures have been presented and analysed for error propagation through a strip. These are encouraging for the hypothetical photograms. Additional experiments with actual photograms are suggested for obtaining confirmation of preliminary results, and further information. The basic problem of exterior orientation has thus held out more than mere academic interest. A theoretical study has revealed that the basic equation for the exterior, relative and absolute orientation problems is the same, the differences arising only from the choice of orthogonal systems, and from conditions imposed by the planar nature of photogram imagery. Transformation relationships among the matrices of the three orientation problems have been derived in elegant and interest ing form. It is generally believed that two collinearity constrained condition equations can be obtained per image point. The author, however, has successfully used, in many problems, three equations per image point obtainable from the well-known orthogonal trans formation equations (x- v' -f )T = arc *-** y'y* z~z>y A theoretical interpretation of these equations has led to the conclusion that the scale. A, of transformation, is independent of the rotations involved in the transformation. It has been further established that only part of the exterior orient ation problem (concerned with the resection of the exposure station) is non-linear; the other part dealing with the evaluation of the rotation matrix is linear. A critical review of the available methods of analytical exterior orientation has shown that, with the exception of Schmid's, few methods are suitable for modern photogrammetric work. Church's method is excellent for the resection of the exposure station, but unsuitable for the determination of angular orientation. A modification suggested in this thesis has considerably improved its performance as a basic method in control extension. Applying Schmid's technique to the set of three equations per image point, an entirely new set of general photogrammetric differential equations has been constructed. Like Schmid's equations, these are capable of dealing with any of the three orientation problems in photogrammetry, and of evaluating corrections to image and terrain coordinates. But, the new equations are more powerful than Schmid's, since they can eval uate corrections to all the three image coordinates, while Schmid's can deal with only two of the three image coordinates. Further, the new set requires fewer control points. Two of the solutions have been specially modified to suit desk calculators. To meet the needs of error-free data for practically proving the various theoretical deductions, and for obtaining results of strip triangulation based on exterior orientation geometry, a project for creating blocks of hypothetical photo grams was undertaken. Although only a few strip of photograms were sufficient for the needs of the present work, the immense utility of such pure data for various researches in the fields of analytical photogrammetry, and for error behaviour study, was appreciated, justifying the creation of a full range lib rary of 45 photogrammetric blocks of 105 photograms each (21 photograms per stripx5strips). Five different terrain types, three different formats and three different camera angles provid ed the 45 permutations. Each block thus has a unique specification, During the progress of the present work, a number of interesting points of theoretical value arose and some time was devoted to their study. These are incorporated in a separate chapter in the form of Notes, and form an important contribution to the thesis. The work presented is predominantly theoretical, practi cal solutions having been obtained in proof in most cases. Impor tant conclusions and suggestions for further work are given at the end.