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

Image Registration Framework

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

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

Histogram Estimation of probability distribution by Histogramming

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

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

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

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

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

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

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

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:

Illustration of DI map

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)

Salient measure PD,T1 image and their salient measure

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…

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

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

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

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

GVFI

Illustration of GVFI

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

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

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

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

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

Accuracy (II)

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

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