Rank Conditions in Multiple View Geometry
Speaker: Yi Ma , ECE Department, UIUC
Date: November 1 2001
This talk is to report our recent progress on the subject of Multiple View Geometry in computer vision. For the first time, we are proposing a (both theoretically and algorithmically) unifying framework for multiple view geometry. The results are believed to be useful to researchers in computer vision, graphics, image processing, and robotic control.
We will show that *all* the known (and some unknown) algebraic or geometric constraintsamong multiple images of 3D features (point, line or plane) can be captured concisely and precisely through certain rank conditions on the so-called multiple view matrix M. The conditions are shown to be equivalent (but superior) to all the multilinear (or multifocal) constraints among multiple images (well-known in computer vision), but they tremendously simplify the derivation and proof for both algebraic and geometric relationships among those constraints. These conditions essentially allow a *global* analysis for multiple images simultaneously without relying on a particular choice of reduction to pair-wise, triple-wise or quadruple-wise images.Generally put, the rank conditions are *universal* for all types of features, incidence conditions, projections (perspective or orthographic), spaces (Euclidean, affine or projective) of arbitrary dimensions. Since such rank conditions are purely linear algebraic, they give rise to a set of natural linear algorithms for purposes such as feature matching, mapping images to a new (synthetic) view, and reconstruction from multiple images.
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