Department of Electrical and Computer Engineering, University of Windsor, Windsor, ON, N9B-3P4, Canada.
IEEE Trans Med Imaging. 2012 Jan;31(1):103-16. doi: 10.1109/TMI.2011.2165342. Epub 2011 Aug 18.
Finite mixture model based on the Student's-t distribution, which is heavily tailed and more robust than Gaussian, has recently received great attention for image segmentation. A new finite Student's-t mixture model (SMM) is proposed in this paper. Existing models do not explicitly incorporate the spatial relationships between pixels. First, our model exploits Dirichlet distribution and Dirichlet law to incorporate the local spatial constrains in an image. Secondly, we directly deal with the Student's-t distribution in order to estimate the model parameters, whereas, the Student's-t distributions in previous models are represented as an infinite mixture of scaled Gaussians that lead to an increase in complexity. Finally, instead of using expectation maximization (EM) algorithm, the proposed method adopts the gradient method to minimize the higher bound on the data negative log-likelihood and to optimize the parameters. The proposed model is successfully compared to the state-of-the-art finite mixture models. Numerical experiments are presented where the proposed model is tested on various simulated and real medical images.
基于学生 t 分布的有限混合模型具有重尾性和比高斯分布更稳健的特点，最近在图像分割中受到了广泛关注。本文提出了一种新的有限学生 t 混合模型（SMM）。现有模型并没有明确地将像素之间的空间关系纳入其中。首先，我们的模型利用狄利克雷分布和狄利克雷定律来整合图像中的局部空间约束。其次，我们直接处理学生 t 分布，以估计模型参数，而之前的模型中的学生 t 分布则表示为缩放高斯分布的无限混合，从而增加了复杂性。最后，我们采用梯度法来最小化数据负对数似然的上限，并优化参数，而不是使用期望最大化（EM）算法。所提出的方法成功地与最先进的有限混合模型进行了比较。在各种模拟和真实医学图像上进行了数值实验，以验证所提出模型的有效性。
