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

2 CVIP Laboratory 2 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.

3 CVIP Laboratory 3 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 Shape Registration

4 CVIP Laboratory 4 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.

5 CVIP Laboratory 5 Generic Registration Problem  Given: two images, a reference R and a template T  Wanted: such that

6 CVIP Laboratory 6 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).

7 CVIP Laboratory 7  Ill Posed Problem in the sense of Hadamard  Registration as optimization problem  Regularization Ex.: Tikhonov Model

8 CVIP Laboratory 8  Euler-Lagrange equations Solve using a Gradient Descent strategy

9 CVIP Laboratory 9 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.

10 CVIP Laboratory 10 Registration of Shapes  Shape Representation  Transformation Model  How to recover registration parameters? ? Global Alignment

11 CVIP Laboratory 11 Scale variations are not handled. Scale variations are not handled. Dependency on the initialization. Dependency on the initialization. Local deformations can not be covered efficiently. Local deformations can not be covered efficiently. Transformation= Global + Local Source Target Several approaches (Cohen’98, Fitzgibbon’01, Paragios’02, Huang’06) are proposed but they have the following problems:  Several approaches (Cohen’98, Fitzgibbon’01, Paragios’02, Huang’06) are proposed but they have the following problems:

12 CVIP Laboratory 12 Shape Representation Through VDF  Given a closed subset X-component of VDF Y-component of VDF For all with (Gomes & Faugeras’01)

13 CVIP Laboratory 13 Shape Representation Using Signed Distance (SD)  S is an imaged shape s.t., the image domain + -  is continuous and differentiable around the zero level. dist(x,S) is the min Euclidean distance from x to S.

14 CVIP Laboratory 14 Examples : Signed Distance Representation Direct computations of the distance map for “moderate” 2D shapes

15 CVIP Laboratory 15 Use the FMM to solve the following Eickonal equation to approximate the distance map for 3D shapes 3D Cases

16 CVIP Laboratory 16 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

17 CVIP Laboratory 17 Transformation model: Affine 2D case: 3D case:

18 CVIP Laboratory 18 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:

19 CVIP Laboratory 19  Euler Lagrange Equations where: Alignment Using the VDF  Dissimilarity Measure