多元Chebyshev正交多项式混合模型及其在医学图像分割中的应用

针对原有一元正交多项式混合模型只能根据灰度特征分割图像的问题,提出一种基于多元Chebyshev正交 多项式混合模型的多维特征的医学图像分割方法。首先,根据Fouricr分析方法与张量积理论推导出图像的多元 Chcbyshcv正交多项式,并构建多元正交多项式的非参数混合模型,用最小均方差(MISE)估计每一个模型的平滑参 数;然后,用EM算法求解正交多项式系数和模型的混合比。此方法不需要对模型作任何假设,可以有效克服“模型失 配”问题。通过实验,表明了该分割方法的有效性。

Medical Image Segmentation Based on Finite Mixture Models of Non-parametric Multivariate Chebyshev Orthogonal Polynomials

To solve the problem of over reliance on priori assumptions of the parameter methods for finite mixture mo dcls and the problem that monk Chebyshev orthogonal polynomials can only process the gray images, a segmentation method of mixture models of multivariate Chebyshev orthogonal polynomials for color image was proposed in this pa- per. First, the multivariate Chebyshev orthogonal polynomials was derived by the Fourier analysis and the tensor pro- duct theory, and the nonparametric mixture model of multivariate orthogonal polynomials was proposed. And the mean integrated squared error(MISE) was used to estimate the smoothing parameter for each model. Second, the expectation maximum(EM) algorithm was used to estimate the orthogonal polynomial coefficients and the model of the weight. hhis method does not require any prior assumptions on the model, and it can effectively overcome the "model mismatch" problem. hhe experimental results with the images show that this method can achieve better segmentation results than the mean-shift method.