Invariance to Affine-Permutation Distortions

An object imaged from various viewpoints appears very different. Hence, effective shape representation of objects becomes central in many applications of computer vision. We consider affine and permutation distortions. We derive the affine-permutation shape space that extends, to include permutation distortions, the affine only shape space (the Grassmannian). We compute the affine-permutation shape space metric, the sample mean of multiple shapes, the geodesic defined by two shapes, and a canonical representative for a shape equivalence class. We illustrate our approach in several applications including clustering and morphing of shapes of different objects along a geodesic path. The experimental results on key benchmark datasets demonstrate the effectiveness of our framework.

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