Dualizing Scene Reconstruction Algorithms

It has been known since the work of Carlsson [2] and Weinshall [17] that there is a dualization principle that allows one to interchange the role of points being viewed by several cameras and the camera centres themselves. In principle this implies the possibility of dualizing projective reconstruction algorithms to obtain new algorithms. In this paper, this theme is developed at a theoretical and algorithmic level. The nature of the duality mapping is explored and its application to reconstruction ambiguity is discussed. An explicit method for dualizing any projective reconstruction algorithm is given. At the practical implementation level, however, it is shown that there are difficulties which have so far defeated successful application of this dualization method to produce working algorithms.

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