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

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. 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… Shape Registration The 0.5 T open magnet system of the Brigham and Women’s Hospital http://splweb.bwh.harvard.edu:8000/

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. Generic Registration Problem • Given: two images, a referenceR and a templateT such that • Wanted:

6. Dissimilarity Measures: SSD: Appropriate for mono-modal registration& for aligning shapes without variations of scales. MI: Appropriate for multi-modal registration& for aligning shapes with variations of scales (Huang et al PAMI’06).

7. Registration as optimization problem • Ill Posed Problem in the sense of Hadamard • Regularization Ex.: Tikhonov Model

8. Euler-Lagrange equations Solve using a Gradient Descent strategy

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. Registration of Shapes ? Global Alignment • Shape Representation • Transformation Model • How to recover registration parameters?

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

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

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

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

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

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. Transformation model: Affine 2D case: 3D case:

18. Existing SDF-based alignment model • Paragios et al.(J. Comp. Vis. & Im. Unders.’03) where: • Assumption: • This model fails to handle the scale variation cases.

19. Alignment Using the VDF • Dissimilarity Measure • Euler Lagrange Equations where: