MR图像分割问题基于变分方法的泛化统计模型（英文）

Generalized statistical model based on variational method for MR image segmentation

为解决灰度不均的医学图像分割现存问题,提出了基于变分方法的泛化统计模型,该模型可以同时得到偏移场和分割结果。在传统的灰度不均匀图像模型中,MR图像经常被分解为以下三部分:真实图像、偏移场以及服从零均值正态分布的噪声。该假设虽然可以简化运算,但在求解实际问题时仍存在一定的局限性,因为零均值的正态分布并不能适应噪声的复杂多样性。因此本文利用变分方法对噪声的敏感特性,同时松弛假设条件,即假设该噪声符合一般正态分布,经过严密的理论推导及高效的模型求解提出了GMLTD方法。并与两种具有代表性的算法:MLTD和MICO进行了多角度的对比实验,实验证明了该方法在算法鲁棒性、分割精度和收敛速度方面均有可喜表现。该算法可应用于医学图像的分割问题,希望能起到抛砖引玉的作用,获得更多的关注与更深入的研究。

A novel generalized statistic model, GMLTD （generalized maximum likelihood in transformed domain）, which simultaneously works out the bias field and segmentation result of magnetic resonance （MR） images with intensity inhomogeneities is proposed in this paper. Based on the classical model of images in the presence of intensity inhomogeneities, the MR image is decomposed into three components, namely the real image, bias field, and noises specially assumed to be Gaussian distributed with the zero means and different variances. In the hypothesis of zero-mean noise, it＇s beneficial for simple computation, but not comprehensive for the description of noise regularity. Therefore, we soften the restriction by generalizing the means of noises. That is to say, the noises of different objects are subject to Gaussian distribution with different means and variances, which is more in line with the law of noise in natural images. Experiments, on either synthetic or real images, show that the proposed method achieves similar algorithm robustness to the MLTD （maximum likelihood in transformed domain）, but performs better not only in segmentation accuracy but also in convergence rate. Moreover, quantitative evaluations and comparisons with another representative approach MICO （multiplicative instrinsic component optimization） have demonstrated the superior performance of GMLTD in terms of computational accuracy and efficiency.