1 / 30

# ANSIG  An Analytic Signature for Permutation Invariant 2D Shape Representation - PowerPoint PPT Presentation

ANSIG  An Analytic Signature for Permutation Invariant 2D Shape Representation. José Jerónimo Moreira Rodrigues. Outline. Motivation: shape representation Permutation invariance : ANSIG Dealing with geometric transformations Experiments Conclusion Real-life demonstration.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' ANSIG  An Analytic Signature for Permutation Invariant 2D Shape Representation' - juan

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

ANSIG  An Analytic Signature for

Permutation Invariant 2D Shape Representation

José JerónimoMoreiraRodrigues

Motivation: shape representation

Permutation invariance: ANSIG

Dealing with geometric transformations

Experiments

Conclusion

Real-life demonstration

The Permutation Problem

Shape diversity

When the labels are known: Kendall’s shape

‘Shape’ is the geometrical information that remains when location/scale/rotation effects are removed.

Limitation:points must have labels, i.e.,vectors must be ordered, i.e.,correspondences must be known

Without labels: the permutation problem

permutation matrix

Our approach:seek permutation invariant representations

The analytic signature (ANSIG) of a shape

Maximal invariance of ANSIG

same signature equal shapes

same signature equal shapes

Maximal invariance of ANSIG

Consider , such that

Since , their first nth order derivatives are equal:

Maximal invariance of ANSIG

The derivatives are the moments of the zeros of the polynomials

This set of equalities implies that - Newton’s identities

StoringANSIGs

The ANSIG maps to an analytic function

How to store an ANSIG?

StoringANSIGs

1) Cauchy representation formula:

2) Approximated by uniform sampling:

512

transformations

Remove mean and normalize scale:

Shape rotation: circular-shift of ANSIG

Optimization problem:

Solution: maximum of correlation. Using FFTs,

“time” domain frequency domain

SHAPE TO

CLASSIFY

SHAPE 1

DATABASE

Similarity

S

H

A

P

E

2

M

Á

X

SHAPE 2

Similarity

SHAPE 3

Similarity

MPEG7 database (216 shapes)

Robustness to model violation

• ANSIG: novel 2D-shape representation

• - Maximally invariant to permutation (and scale, translation)

• - Deals with rotations and very different number of points

• - Robust to noise and model violations

• Relevant for several applications

• Development of software packages for demonstration

• Publications:

• - IEEE CVPR 2008

• - IEEE ICIP 2008

• - Submitted to IEEE Transactions on PAMI

Different sampling schemes

More than one ANSIG per shape class

Incomplete shapes, i.e., shape parts

Analytic functions for 3D shape representation

demonstration

Pre-processing: morphological filter operations, segmentation, etc.

Shape-based image classfication

Image acquisition system

Shape-based classification

Shape

database