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ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation

ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation José J. Rodrigues, Pedro M. Q. Aguiar, João M. F. Xavier. Problem: shape representation (arbitrary sets of 2D points). Geometric transformations. Ilustrations. Experiments. quotient space.

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ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation

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  1. ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation José J. Rodrigues, Pedro M. Q. Aguiar, João M. F. Xavier Problem: shape representation (arbitrary sets of 2D points) Geometric transformations Ilustrations Experiments quotient space Point permutation is a quagmire: Translation and scale: Goal: anuniquerepresentation for each shape Shape-based classification (invariant) SHAPE TO CLASSIFY SHAPE 1 Similarity Sampling density: S H A P E 2 M Á X SHAPE 2 Similarity SHAPE 3 ( invariant) Similarity Approach: permutation invariant representation Storage, alignment, and comparison of ANSIGs: ANSIG: Rotation: (equivariant) same signature same shape

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