Rachid FAHMI Ph.D. Defense April 30, 2008

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CVIP Laboratory CVIP Laboratory 1 Rachid FAHMI Ph.D. Defense April 30, 2008 CVIP Laboratory CVIP Laboratory Variational Methods For Shape And Image Registrations Advisor: Prof. Aly A. Farag

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CVIP Laboratory. Variational Methods For Shape And Image Registrations. Rachid FAHMI Ph.D. Defense April 30, 2008. Advisor: Prof. Aly A. Farag. Outline. Generic Image Registration Problem. Shape Registration: Representation of shapes Global Alignment - PowerPoint PPT Presentation

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Page 1: Rachid FAHMI Ph.D. Defense April 30, 2008

1CVIP LaboratoryCVIP Laboratory1

Rachid FAHMI

Ph.D. Defense

April 30, 2008

CVIP LaboratoryCVIP Laboratory

Variational Methods For Shape And Image

Registrations

Advisor: Prof. Aly A. Farag

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Outline

Generic Image Registration Problem.

Shape Registration: Representation of shapes

Global Alignment

Statistical shape modeling and shape-based

segmentation.

Elastic shape registration

Application: 3D face recognition in presence of

expression.

Image/Volume registration & F.E.-based

validation.

Application: Autism and dyslexia research.

Conclusions and future work.

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Why Registration? Goal: find geometric transformation between two or more images that aligns corresponding features.

Applications:

•Surgical Planning and decisions.

•Diagnosis + Assess clinical outcome.

•Longitudinal studies (Brain disorder, developmental growth).

•Segmentation.

•Object recognition and retrieval.

•Tracking and animation…

The 0.5 T open magnet system of the Brigham and Women’s Hospital

http://splweb.bwh.harvard.edu:8000/

Shape Registrati

on

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Outline

Generic Image Registration Problem.

Shape Registration: Representation of shapes

Global Alignment

Statistical shape modeling and shape-based

segmentation.

Elastic shape registration

Application: 3D face recognition in presence of

expression.

Image/Volume registration & F.E.-based

validation.

Application: Autism and dyslexia research.

Conclusions and future work.

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Generic Registration Problem

Given: two images, a reference R and a template T

Wanted:

: ,TR

such that

R

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SSD:

MI:

Dissimilarity Measures:

Appropriate for mono-modal registration & for aligning shapes without variations of scales.

Appropriate for multi-modal registration & for aligning shapes with variations of scales (Huang et al PAMI’06).

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Ill Posed Problem in the sense of Hadamard

Registration as optimization problem

Regularization

Ex.: Tikhonov Model

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Euler-Lagrange equations

Solve using a Gradient Descent strategy

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Outline

Generic Image Registration Problem.

Shape Registration: Representation of shapes

Global Alignment

Statistical shape modeling and shape-based

segmentation.

Elastic shape registration

Application: 3D face recognition in presence of

expression.

Image/Volume registration & F.E.-based

validation.

Application: Autism and dyslexia research.

Conclusions and future work.

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Registration of Shapes

Shape Representation

Transformation Model

How to recover registration parameters?

?Global Alignment

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• Scale variations are not handled.Scale variations are not handled.

• Dependency on the initialization.Dependency on the initialization.

• Local deformations can not be covered Local deformations can not be covered efficiently.efficiently.

TransformationTransformation

==Global + LocalGlobal + Local

Source Target

Several approaches Several approaches (Cohen’98, Fitzgibbon’01, (Cohen’98, Fitzgibbon’01,

Paragios’02, Huang’06)Paragios’02, Huang’06) are proposed but they have the are proposed but they have the following problems:following problems:

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Shape Representation Through VDF

Given a closed subset

X-component of VDF

Y-component of VDF

For all

with

(Gomes & Faugeras’01)

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Shape Representation Using Signed Distance (SD) S is an imaged shape s.t., the image domain )\( SS

S \

S

x +-

is continuous and differentiable around the zero level.

dist(x,S) is the min Euclidean distance

from x to S.

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Examples : Signed Distance Representation

Direct computations of the distance map for “moderate”

2D shapes

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Use the FMM to solve the following Eickonal

equation to approximate the distance map for

3D shapes

3D Cases

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Global Matching of Shapes

Given: Two shapes, S and T (one is a deformed version of the other) with representations

Goal: recover the transformation that aligns S and T

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Transformation model: Affine

2D case:

3D case:

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where:

Paragios et al. (J. Comp. Vis. & Im. Unders.’03)

Existing SDF-based alignment model

This model fails to handle the scale variation cases.

Assumption: sss yx

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Euler Lagrange Equations

where:

Alignment Using the VDF

Dissimilarity Measure