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