Multi-modality%20image%20registration%20using%20mutual%20information%20based%20on%20gradient%20vector%20flow

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
MI 0.9523
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
Pluim et al. (TMI 2000)
Individual contribution of voxel to gradient
function G T1 and T2 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

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)
• 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. lt 2, Rotation degree lt 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