Non-Rigid Registration between Color Channels based on Joint-Histogram Entropy in Subspace

1. Non-Rigid Registration between Color Channels based on Joint-Histogram Entropy in Subspace Masao Shimizu, Rafael H. C. de Souza, Shin Yoshimura, and Masatoshi Okutomi Tokyo Institute of Technology

2. Outline • Introduction • Joint histogram of time-sequential sampled images • Joint entropy of a projected histogram • Non rigid motion model • Non rigid registration • Experimental results • Conclusions and future work

3. Introduction • Color Image sampling methods: • Color decoupling • Spatial sampling • Endoscopic images and time-sampling

4. Introduction • Color Image sampling methods: • Color decoupling

5. Introduction • Color Image sampling methods: • Spatial sampling

6. Introduction • Endoscopic images

7. Introduction • Endoscopic images

8. Introduction • Color Image sampling methods: • Time-sequential • Objective: • Implement a registration algorithm to remove the color artifacts

9. Joint histogram of time-sequential sampled images • Natural image x channel shifted image

10. Joint entropy of a projected histogram • Dominant plane

11. Joint entropy of a projected histogram • Joint entropy of a two-dimensional color space Probability of the same coordinate to have a pixel value of a in image A and b in image B. ξϵ projected color space RGB value of a pixel Projection matrix

12. Joint entropy of a projected histogram • Choosing the subspace: • There are not much artifacts on the brightness component • Changes are concentrated in CbCr space *figure to be improved

13. Non rigid motion model • Non-rigid model • Problems with SSD • Minimization by Entropy

14. Non rigid motion model • Minimization by Entropy set of vectors Area affected by control point

15. Non rigid registration Similarity function Regularization term Warping parameters Also known as correlation-like methods General registration problem definition (Fischer & Modersitzki 2003):

16. Non rigid registration • Problems with SSD Poor correlation with the other channels Red channel Green channel Blue channel Registration with SSD

17. Non rigid registration • Mutual Information: • Generaly yield the correct registration • However, 2 registrations are required

18. Non rigid registration • Entropy: • Generaly yield the correct registration • Only one registration is required

19. Non rigid registration • Minimization by Entropy For natural images, a good projection is The CbCr space. Joint probability over the projected space Projection Matrix RGB value

20. Non rigid registration • Minimization by Entropy

21. Experimental results • Results with real images • 14x11 • Up to convergence • Simulated results • 7x5 grid • 20 iterations

22. Experimental results • Results with real images No registration

23. Experimental results • Results with real images SSD

24. Experimental results • Results with real images MI

25. Experimental results • Results with real images Proposed method

26. Experimental results • Simulated results

27. Experimental results • Simulated results

28. Conclusions and future work • Conclusion • A method for aligmment of time-sampled images • Non-rigid model • Channels with different spectra • Future work • Multiple images • Regularization • Better optimization