Photogrammetry and projective geometry: an historical survey

Thomas Buchanan

doi:10.1117/12.155817

24 September 1993 Photogrammetry and projective geometry: an historical survey

Thomas Buchanan

Proceedings Volume 1944, Integrating Photogrammetric Techniques with Scene Analysis and Machine Vision; (1993) https://doi.org/10.1117/12.155817
Event: Optical Engineering and Photonics in Aerospace Sensing, 1993, Orlando, FL, United States

Abstract

Général 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 relationshipto 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 Uliman in 1977

Citation Download Citation

Thomas Buchanan "Photogrammetry and projective geometry: an historical survey", Proc. SPIE 1944, Integrating Photogrammetric Techniques with Scene Analysis and Machine Vision, (24 September 1993); https://doi.org/10.1117/12.155817

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