Loading in 5 sec....

ANSIG An Analytic Signature for Permutation Invariant 2D Shape RepresentationPowerPoint Presentation

ANSIG An Analytic Signature for Permutation Invariant 2D Shape Representation

- By
**juan** - Follow User

- 75 Views
- Uploaded on

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

**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

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

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

transformations

(Maximal) Invariance to translation and scale

Remove mean and normalize scale:

Shape rotation: circular-shift of ANSIG

Efficient computation of rotation

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

Download Presentation

Connecting to Server..