Abstract:
We propose a theoretical solution to 2D and 3D affine invariant feature matching, a longstanding computer vision problem. Our two-stage Grassmannian Graph (GrassGraph) framework robustly recovers correspondences between two unorganized, affinely related feature (point) sets.
The first stage maps feature sets to an affine invariant Grassmannian representation in the same subspace in the ideal case. Grassmannian coordinate representations differ by an arbitrary orthonormal matrix.
In the second stage, approximating the Laplace-Beltrami operator (LBO) on these coordinates nullifies this extra orthonormal factor, giving true affine invariant coordinates that we use to recover correspondences via simple mutual nearest neighbor relations.
Our validation benchmarks use many 2D and 3D dataset experiments. Grass-Graph recovers large affine transformations in experiments.
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