Photogrammetry and projective geometry : an historical survey

Abstract

General Jean-Victor Poncelet published his treatise on projective geometry in 1822. This was the start of an enormous development in geometry in the 19th century. During this period geometry in the plane and in 3-dimensional space was studied in particular detail. The development culminated in the publishing of the Encyclopedia of Mathematics, which appeared in irregular installments from 1900 to 1934. Photogrammetry - the use of photographic images for surveying, mapping and reconnaissance - began in the second half of the 19th century. By the 1890's substantial theoretical contributions were made by Sebastian Finsterwalder. Finsterwalder reported on his foundational work in a keynote address to the German Mathematical Society in 1897; he also contributed an article on photogrammetry to the Encyclopedia of Mathematics. Among other things Finsterwalder observed that Rudolf Sturm's analysis of the "homography problem" (1869) can be used to solve the problem of 3D-reconstruction using point matches in two images. Subsequently, important theoretical advances were made by mathematicians at the Technical University of Vienna. An excellent reference for geometry and its relationship to photogrammetry is a book of Emil Muller on constructive geometry, which appeared in 1923. Muller's assistent and successor Erwin Kruppa established the "structure-from-motion" theorem in 1913. This theorem was rediscovered by Shimon Ullman in 1977.