Abstract: To estimate mutual information of images rapidly and accurately is one of very important problem in image registration，which involves estimating joint probability density and marginal probability density of two images.Kernel Density Estimator（KDE），however，is computational expensive.This makes it very slow to compute mutual information.In this paper，a fast estimation algorithm is presented which takes advantage of the property of delta function and fast convolution based on fast Fourier transform.The proposed algorithm can estimate mutual information of images with linear time complexity.Experiments show the fast algorithm is very efficient.

Key words: mutual information, kernel density estimator, image registration, fast convolution

摘要： 快速、精确地估计图像互信息是图像配准中一个非常重要的课题，它涉及到两幅图像的联合概率密度和边缘概率密度的估计。针对核密度估计法运算量大而导致互信息估计速度慢的问题，提出了一种快速核密度估计法，并用它估计图像互信息。快速算法利用了单位冲激函数性质和基于快速傅立叶变换的快速卷积算法，能在线性时间复杂度内估计互信息。采用临床MRI图像的实验证实了快速算法的性能。

关键词: 互信息, 核密度估计, 图像配准, 快速卷积