The Chern-Mather class of the multiview variety |
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Authors: | Corey Harris Daniel Lowengrub |
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Institution: | 1. Max-Planck-Institut fur Mathematik in den Naturwissenschaften, Leipzig, Germany;2. Department of Mathematics, University of California, Berkeley, California, USA |
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Abstract: | The multiview varietyassociated to a collection of N cameras records which sequences of image points in ?2N can be obtained by taking pictures of a given world point x∈?3 with the cameras. In order to reconstruct a scene from its picture under the different cameras, it is important to be able to find the critical points of the function which measures the distance between a general point u∈?2N and the multiview variety. In this paper we calculate a specific degree 3 polynomial that computes the number of critical points as a function of N. In order to do this, we construct a resolution of the multiview variety and use it to compute its Chern-Mather class. |
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Keywords: | Chern-Mather class Chern-Schwartz-MacPherson class Computer vision Euclidean distance degree Higher discriminants |
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