1. Multi-modality image registration using mutual information based on gradient vector flow
Yujun Guo
May 1,2006

2. Image Registration Framework

3. Similarity Measure Absolute Difference, Sum of Squared Diff.
Cross-Correlation (CC), Normalized CC
Gradient difference, Gradient correlation
Woods’ criteria
Mutual information
Correlation ratio

4. Mutual information From information theory
Measure the shared information between images
Maximal when registration

5. Histogram
Estimation of probability distribution by Histogramming

6. Joint histogram Comparison of aligned and non-aligned MI= 2.1188

7. Normalized mutual information
MI is sensitive to the amount of overlap between two images
NMI is proposed by Studholme et al.

8. However…
MI is proved to be a promising measure for both mono-modality and multi-modality registration
However, NO spatial information is taken into consideration
A random reshuffling of the image voxels (identical for both images) will yield the same MI as for original images

9. To incorporate spatial info. into MI
Pluim et al. (2000) Combine MI and gradient term
Rueckert et al. (2000) Higher-order MI
Butz et al. (2001) MI on feature space
Gan et al. (2005) Distance-intensity
Luan et al. (2005) Quantitative-Qualitative measure (Q-MI)
Other efforts…
Guo and Lu (ICPR 2006) GVFI

10. Individual contribution of voxel to gradient function G
Pluim et al. (TMI 2000)
Individual contribution of voxel to gradient function G
T1 and T T1 and CT T1 and PET

11. Rueckert et al. (SPIE 2000) Second-order entropy of the image
Second-order joint entropy of two images
Second-order MI

12. Butz et al. (2001 MICCAI)
MI is based on feature space instead of intensity
Features
Normal of gradient
Edgeness:
Variance of intensity within variant distance from a voxel
G is the intensity, d_i is the voxel coordinate, d is a fixed constant

13. Gan et al. (CVBIA 2005)
Distance-intensity (DI) encodes spatial information at a global level with image intensity.
Optimal solution of DI is derived to minimize energy functional:

14. Illustration of DI map

15. Luan et al. (CVBIA 2005)
Quantitative-Qualitative measure by Belis (1968)
Luan et al. proposed Quantitative-Qualitative MI
Utility of image intensity pair (i,j)

16. Salient measure
PD,T1 image and their salient measure

17. Other efforts Russakoff et al. (ECCV 2004) Ji et al. (ISMRA 1999)
Regional MI
Ji et al. (ISMRA 1999)
Region-based MI
Holden et al. (MICCAI 2004)
Multi channel MI
More…

18. GVFI
Gradient information can not be used directly because its limited capture range
Gradient vector flow (GVF) was proposed to extend the capture range of object boundary in active contour model
We proposed to incorporate spatial information into MI via GVF-intensity

19. GVF
GVF field is computed for each voxel to minimize the energy functional
GVF is found by solving Euler equations
GVFI is defined as

20. Edge maps Four edge maps in the experiments
Parameters μ and iteration number is fixed

21. GVF image
Four images are corresponding to four definition of edge maps

22. GVFI

23. Illustration of GVFI

24. Datasets BrainWeb MR simulator
Simulated T1, T2, PD MR brain image at different noise levels
0%,3%,5%,7%,9%
T1/T2, T1/PD in pairs
One is randomly transformed with known parameters, and the other image is registered to the transformed image to find the parameters
300 experiments for each pair

25. Robustness (I) MI changes with respect to rotation around Z-axis
Traditional MI
GVFI-based MI

26. Robustness (II) MI changes with respect to translation on X-axis
Traditional MI
GVFI-based MI

27. Robustness (III) MI changes with respect to translation on Y-axis
Traditional MI
GVFI-based MI

28. Accuracy (I)
Success: Trans. < 2, Rotation degree < 2

29. Accuracy (II)

30. Future work Implementation in 3D
The parameter selection in GVF computation
Currently only magnitude information is included, direction information is lost

31. References Pluim et al. TMI 2000 Rueckert et al. SPIE 2000
Butz et al. MICCAI 2001
Gan et al. CVBIA 2005
Luan et al. CVBIA 2005
Xu et al. TMI 1998