ANSIG
This presentation is the property of its rightful owner.
Sponsored Links
1 / 30

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


  • 49 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

ANSIG  An Analytic Signature for Permutation Invariant 2D Shape Representation

An Image/Link below is provided (as is) to download presentation

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

ANSIG  An Analytic Signature for

Permutation Invariant 2D Shape Representation

José JerónimoMoreiraRodrigues


Ansig an analytic signature for permutation invariant 2d shape representation

Outline

Motivation: shape representation

Permutation invariance: ANSIG

Dealing with geometric transformations

Experiments

Conclusion

Real-life demonstration


Ansig an analytic signature for permutation invariant 2d shape representation

Motivation

The Permutation Problem


Ansig an analytic signature for permutation invariant 2d shape representation

Shape diversity


Ansig an analytic signature for permutation invariant 2d shape representation

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


Ansig an analytic signature for permutation invariant 2d shape representation

Without labels: the permutation problem

permutation matrix


Ansig an analytic signature for permutation invariant 2d shape representation

Our approach:seek permutation invariant representations


Ansig an analytic signature for permutation invariant 2d shape representation

ANSIG


Ansig an analytic signature for permutation invariant 2d shape representation

The analytic signature (ANSIG) of a shape


Ansig an analytic signature for permutation invariant 2d shape representation

Maximal invariance of ANSIG

same signature equal shapes

same signature equal shapes


Ansig an analytic signature for permutation invariant 2d shape representation

Maximal invariance of ANSIG

Consider , such that

Since , their first nth order derivatives are equal:


Ansig an analytic signature for permutation invariant 2d shape representation

Maximal invariance of ANSIG

The derivatives are the moments of the zeros of the polynomials

This set of equalities implies that - Newton’s identities


Ansig an analytic signature for permutation invariant 2d shape representation

StoringANSIGs

The ANSIG maps to an analytic function

How to store an ANSIG?


Ansig an analytic signature for permutation invariant 2d shape representation

StoringANSIGs

1) Cauchy representation formula:

2) Approximated by uniform sampling:

512


Ansig an analytic signature for permutation invariant 2d shape representation

Geometric

transformations


Ansig an analytic signature for permutation invariant 2d shape representation

(Maximal) Invariance to translation and scale

Remove mean and normalize scale:


Ansig an analytic signature for permutation invariant 2d shape representation

Sampling density


Ansig an analytic signature for permutation invariant 2d shape representation

Rotation

Shape rotation: circular-shift of ANSIG


Ansig an analytic signature for permutation invariant 2d shape representation

Efficient computation of rotation

Optimization problem:

Solution: maximum of correlation. Using FFTs,

“time” domain frequency domain


Ansig an analytic signature for permutation invariant 2d shape representation

Shape-based classification

SHAPE TO

CLASSIFY

SHAPE 1

DATABASE

Similarity

S

H

A

P

E

2

M

Á

X

SHAPE 2

Similarity

SHAPE 3

Similarity


Ansig an analytic signature for permutation invariant 2d shape representation

Experiments


Ansig an analytic signature for permutation invariant 2d shape representation

MPEG7 database (216 shapes)


Ansig an analytic signature for permutation invariant 2d shape representation

Automatic trademark retrieval


Ansig an analytic signature for permutation invariant 2d shape representation

Robustness to model violation


Ansig an analytic signature for permutation invariant 2d shape representation

Object recognition


Ansig an analytic signature for permutation invariant 2d shape representation

Conclusion


Ansig an analytic signature for permutation invariant 2d shape representation

Summary and conclusion

  • 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


Ansig an analytic signature for permutation invariant 2d shape representation

Future developments

Different sampling schemes

More than one ANSIG per shape class

Incomplete shapes, i.e., shape parts

Analytic functions for 3D shape representation


Ansig an analytic signature for permutation invariant 2d shape representation

Real-life

demonstration


Ansig an analytic signature for permutation invariant 2d shape representation

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

Shape-based image classfication

Image acquisition system

Shape-based classification

Shape

database


  • Login