doi:10.1016/j.imavis.2006.08.002 
Copyright © 2006 Elsevier B.V. All rights reserved.
Monomodal image registration using mutual information based methods
Zhiyong Gaoa, 
, 
, Bin Gub and Jiarui Linb
aCollege of Electronics and Information Engineering, South-Central University for Nationalities, Wuhan, Hubei 430074, China
bInstitute of Biomedical Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
Received 19 December 2005;
accepted 16 August 2006.
Available online 2 October 2006.
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Abstract
Image registration methods based on mutual information criteria, including mutual information and normalized mutual information, have been widely used in 3-D multimodal medical image registration and have shown promising results. Although they are also used in monomodal image registration, their performance is not as excellent as that in multimodal registration. There are many fluctuations in the registration function, which hinder the optimization procedure and lead to registration failure. This paper discusses this problem and ascribes it to interpolation artefacts and the variability of entropy. We implement experiments to evaluate the performance of the two similarity measures for 2-D and 3-D monomodal registration. To avoid the interpolation artefacts, we use pixels or voxels as the translation metric; to diminish the influence of entropy variability, we use normalized mutual information. The results show that, both for standard and normalized mutual information, the fluctuations caused by interpolation are fewer in the function of the registration without interpolation. Normalized mutual information has some similar properties to mutual information, but is almost invariant to the changing of entropy and appears to be more stable and robust than standard mutual information. These differences seem to indicate a preference for the normalized mutual information in monomodal registration.
Keywords: Image registration; Mutual information; Normalized mutual information; Interpolation artefact
Fig. 1. Local maxima caused by interpolation in the registration function MI for 2-D MR-T2 images with translation along x axis (left), y axis (middle) and in-plane rotation (right). The translation metric is mm.
Fig. 2. The registration function MI for 2-D MR-T2 images without interpolation while with translation along x axis (left) and y axis (right). The translation metric is pixel.
Fig. 3. The responses of entropies to the translation. The changes of entropies of floating image and reference image (left and middle) and joint entropy (right) are similar, maximal values compose a vicinity with translation around 100 pixels.
Fig. 4. Registration function Y with interpolation (the top) and without interpolation (the bottom), the left column is with translation along x axis and the right is with the translation along y axis.
Fig. 5. The registration functions of 2-D CT images. Registration function Y and MI with interpolation (the top) and without interpolation (the bottom), the left column is with translation along x axis and the right is with the translation along y axis.
Fig. 6. The registration functions of 2-D PET images. Registration function Y and MI with interpolation (the top) and without interpolation (the bottom), the left column is with translation along x axis and the right is with the translation along y axis.
Fig. 7. The registration functions of 3-D CT images. Registration function Y and MI with interpolation (the top) and without interpolation (the bottom), the left column is with translation along x axis, the middle is with the translation along y axis, and the right is with the translation along z axis.
Fig. 8. The registration functions of 3-D MR-T2 images. Registration function Y and MI with interpolation (the top) and without interpolation (the bottom), the left column is with translation along x axis, the middle is with the translation along y axis, and the right is with the translation along z axis.
Fig. 9. The registration functions of 3-D PET images. Registration function Y and MI with interpolation (the top) and without interpolation (the bottom), the left column is with translation along x axis, the middle is with the translation along y axis, and the right is with the translation along z axis.
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