1. Image Registration with Hierarchical B-Splines Z. Xie and G. Farin

2. Support Arizona Alzheimer Disease Research Center

3. Motivation Image Fusion Image Comparison Image Segmentation Pattern Recognition

4. Classification Landmark based methods – Point based method – Curve based method – Surface based method Intensity based methods

5. Free Form Deformation (FFD)

6. FFD with Hierarchical B-Splines 1.Putting the object into the B-Spline hyperpatchs. 2.Moving the B-Spline control points to deform the object. 3.Refining the control points related to complex regions. 4.Adjusting the refined control points for detail deformation.

7. Point based registration This problem naturally breaks down into two scattered data approximation problems. The least squares solution of this problem can be found by solving the linear systems.

8. How does it work? Local refinement by knot insertion. Recomputing related control points.

9. Why hierarchical B-Splines? Efficiency Global to local influence

10. Example of point based registration Source TargetDeformed Source

11. Surface based registration Together with the Iterative Closest Point (ICP) approach, this problem can be converted into a scattered data approximation problem.

12. Iterative Closest Point

13. Distance Transform

14. Hierarchical Deformation with Hierarchical B-Splines Initialize: Rigid Transformation Linear matching: Iterative Affine Deformation Nonlinear matching: Hierarchical Cubic B-Splines – Increase level of detail iteratively

15. Advantage Validity. Right matching between individual points by matching big shape feature first, then refine the detail gradually. Efficiency. Only pay attention to complex regions. Precision. Enough of degrees of freedom for matching detail.

16. Example of 2-D registration

17. Example of 3D matching

18. Movie of 3D Deformation

19. Intensity-based registration Together with optic flow, this problem can be converted into scattered data approximation problem.

20. Optic flow Optic flow is a visual displacement flow field associated with the variation in an image sequence. It can be used as an estimator of the displacement of one pixel on the source image to its matching pixel on target image.

21. Hierarchical Deformation vs. multi-resolution data representation

22. Example of intensity based registration Source Target Deformed source

23. Movie of intensity based registration

24. Future Work Multi-resolution surface representation More robust displacement estimator for intensity based registration. Multi-modal intensity based registration