Copyright © 2008 The Institute of Electronics, Information and Communication Engineers
Regular Section -- Papers -- Biological Engineering |
Parzen-Window Based Normalized Mutual Information for Medical Image Registration
1 The authors are with the Graduate School of Engeneering and Science, Ritsumeikan University, Kusatsu-shi, 525–8577 Japan. E-mail: qdxurui{at}hotmail.com, 2 The author is also presently with School of Electronic and Information Engineering, Dalian University of Technology, P.R. China., 3 The author is with the Department of Opto-electronic Engineering, Beijing Institute of Technology, P.R. China., 4 The author is with the Biomedical MR Science Center, Shiga University of Medical Science, Otsu-shi, 520–2192 Japan., 5 The author is with the Department of Surgery, Shiga University of Medical Science, Otsu-shi, 520–2192 Japan.
Image Registration can be seen as an optimization problem to find a cost function and then use an optimization method to get its minimum. Normalized mutual information is a widely-used robust method to design a cost function in medical image registration. Its calculation is based on the joint histogram of the fixed and transformed moving images. Usually, only a discrete joint histogram is considered in the calculation of normalized mutual information. The discrete joint histogram does not allow the cost function to be explicitly differentiated, so it can only use non-gradient based optimization methods, such as Powell's method, to seek the minimum. In this paper, a parzen-window based method is proposed to estimate the continuous joint histogram in order to make it possible to derive the close form solution for the derivative of the cost function. With this help, we successfully apply the gradient-based optimization method in registration. We also design a new kernel for the parzen-window based method. Our designed kernel is a second order polynomial kernel with the width of two. Because of good theoretical characteristics, this kernel works better than other kernels, such as a cubic B-spline kernel and a first order B-spline kernel, which are widely used in the parzen-window based estimation. Both rigid and non-rigid registration experiments are done to show improved behavior of our designed kernel. Additionally, the proposed method is successfully applied to a clinical CT-MR non-rigid registration which is able to assist a magnetic resonance (MR) guided microwave thermocoagulation of liver tumors.
Key Words: parzen-window method, normalized mutual information, medical image registration, optimization
Manuscript received February 1, 2007. Manuscript revised July 13, 2007.
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