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A Method for Registration of 3-D Shapes
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Similarity-invariant signatures for partially occluded planar shapes
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Iterative point matching for registration of free-form curves and surfaces
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Shape Similarity Measure Based on Correspondence of Visual Parts
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Classification with Nonmetric Distances: Image Retrieval and Class Representation
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Texture Mapping Using Surface Flattening via Multidimensional Scaling
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Computational Surface Flattening: A Voxel-Based Approach
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On interactive visualization of high-dimensional data using the hyperbolic plane
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A new point matching algorithm for non-rigid registration
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This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their advantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sensitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topology-invariant similarity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a set-valued distance. Numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail.