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Journal for Geometry and Graphics 10 (2006), No. 2, 137--153
Copyright Heldermann Verlag 2006

Descriptive Geometry Meets Computer Vision -- The Geometry of Two Images

Hellmuth Stachel
Institute of Discrete Mathematics and Geometry, Technical University, Wiedner Hauptstr. 8-10/104, 1230 Vienna, Austria

The geometry of multiple images has been a standard topic in Descriptive Geometry and Photogrammetry (Remote Sensing) for more than 100 years. During the last twenty years great progress has been made within the field of Computer Vision, a topic with the main goal to endow a computer with a sense of vision. The previously graphical or mechanical methods of reconstruction have been replaced by mathematical methods as offered by computer algebra systems. This paper will explain to geometers how to reconstruct two digital images of the same scene and how to recover metrical data of the depicted object - using standard software only. Not the presented results are new, but the way how they are deduced by geometric reasoning. The arguments are based on Linear Algebra and classical Descriptive Geometry results.

Keywords: Descriptive Geometry, multiple images, two-views-system, essential matrix, Computer Vision.

MSC: 51N05

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