Structure from Motion: a New Look from the Point of View of Invariant Theory.

Pierre-Louis Bazin and Mireille Boutin

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Submission date: 10. Jul. 2003
published in: SIAM journal on applied mathematics, 64 (2004) 4, p. 1156-1174 
DOI number (of the published article): 10.1137/S003613990340246X
Bibtex
MSC-Numbers: 53, 22, 68
Keywords and phrases: structure from motion, moving frame method, invariants

Abstract:
We present a novel, simple formulation of the problem of 3D object reconstruction from images. In this formulation, the object is seen as lying at the intersection of the projection of orbits of custom-built Lie group actions. The group parameters correspond to unknown, irrelevant quantities such as the camera orientation, the depth parameters of the object with respect to the camera plane and the focal length. We then use an algorithmic method based on moving frames "a la Fels-Olver" to obtain a fundamental set of invariants of these group actions. The invariants are used to define a set of equations detemining the 3D object, thus providing a mathematical formulation of the problem where the irrelevant parameters do not appear.