ANSIG – An Analytic Signature for Permutation-InvariantTwo 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

MÁX

SHAPE 1

Similarity

SHAPE 3

Similarity

SHAPE 2

Similarity

SHAPE

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)

( invariant)

Experiments