基于Nonlocal的MRI脑肿瘤图像分割方法的研究

The segmentation of Magnetic Resonance Imaging (MRI) brain tumor is an important task and is of great significance in clinical and scientific research. Accurate segmentation of brain tumor plays an important role in medical image analysis, which also becomes a hot point in medical, mathematical, computation science fields. Because of the special structures of brain tumor, which have complicated shape and vague edge, the most widely used image segmentation algorithms often fail to provide accurate segmentation results. The aim of this project is to develop a new model and design a fast calculation algorithm for the segmentation of MRI brain tumor. The main objects of this study are as follows: incorporating Nonlocal regularization mechanism to a variation model in order to improve the performance; analysis the existence and the convergence of stable solution of the given functional, then prove the consistency and study the numerical problems; designing a fast calculation algorithm based on the optimization theory to get better segmentation results. This project combines the characteristics of brain tumor, and fully uses the advantages of nonlocal regularization mechanism to avoid difficulties generated by blur edges in the traditional segmentation methods. Meanwhile, our model has many advantages, such as a small amount of calculation, fast convergence, also can be extended to other modalities segmentation. What’s more, it will promote the development of mathematic in medical image process and the fusion of different branching of science.

磁共振成像（MRI）脑肿瘤分割在临床诊断和科学研究中起着重要的作用。如何精确地分割MRI脑肿瘤是医学图像处理方面的重点和难点，也是医学、数学、计算机等领域的热点问题。本项目针对脑肿瘤形状复杂多变、边缘模糊等而难以实现精确分割的问题，构建了MRI脑肿瘤分割新模型并设计快速算法。主要研究内容包括：引入Nonlocal正则化方法，改进现有的MRI脑肿瘤图像分割模型，建立新型变分模型；对得到的变分模型稳定解的存在性以及收敛性做出分析，并进行相关的理论论证和数值研究；基于最优化理论，拟定出脑肿瘤分割的快速算法，取得更好的肿瘤边缘分割效果。本项目结合了肿瘤复杂性的特点，充分利用Nonlocal正则化的优势，避免了模糊边界难以分割的问题。同时具有运算量小，收敛快，便于推广到其他模态图像的分割等优点，将有力地推动数学在医学图像领域的发展，促进学科融合。

对磁共振成像(MRI)脑图进行快速精确分割，从而为脑肿瘤诊断提供良好的辅助，是医学上的一个热点和难点。本项目的研究基于Nonlocal图像分割最新技术，在已取得良好的工作基础上，进一步改进原有的分割算法，提出了更加快速高效的两步法算法模型。在模型的分析和快速求解中，我们将复杂的非线性非凸多变量泛函问题转变成由多个凸泛函迭代组成的优化问题，有效降低了模型求解的复杂度。该方法在模拟脑图上的分割结果显示，白质分割的精确度达94%以上，灰质分割的精确度接近90%。最后在真实脑图分割中也取得了很好的分割结果，尤其在结构保持方面效果显著，这为后续的MRI 脑肿瘤图像分割奠定了良好的基础。

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