肝脏磁共振图像分割的可计算变分模型

Image segmentation is an important branch of image processing, accuracy and efficiency are two most important requirements of medical image segmentation. Medical imaging is the technique and process of creating visual representations of the interior of a body for clinical analysis and medical intervention. Where medical image processing plays an important role in improving medical diagnosis and treatment. This project will study liver MRI segmentation, existing segmentation models and methods are not ideal for liver MRI segmentations. This project consider the noise of liver MRI, plans to study more appropriate new segmentation models for liver segmentation, convexification of non-convex segmentation models, efficient and effective algorithms. Firstly, since variational models have the advantage of flexibility and intuition, we focus on models based on calculus of variation. Use information theory and nonlocal operators, which are very effective methods for inhomogeneous images, meanwhile, we will do study on convexification of non-convex segmentation models by the functional lifting method. Moreover, due to the two demands on medical image segmentations and the huge data of medical images, we will design fast and effective numerical algorithms using calculus of variation, optimization theory, operator splitting technique, and so on. Finally, we apply our models and algorithms to practical problems to show their advantages.

图像分割是图像处理的一个重要分支，准确度和分割速度是医学图像分割最重要的两个需求。医学影像是为了临床分析和医疗干预获取并处理内部组织影像的可视化技术与过程。其中医学图像处理对提高医生诊断和治疗水平具有十分重要的作用。本项目对肝脏 MRI 分割问题进行研究，已有的分割模型和方法，对有些肝脏MRI分割效果和速度并不理想。本项目考虑肝脏MRI带噪情况，计划研究更加适合肝脏分割的新模型、非凸分割模型的凸化方法以及快速有效的求解算法。首先，鉴于变分模型具有灵活性和直观性等优点，我们将重点研究以变分方法为基础的模型。结合信息论、非局部算子等对非均匀图像非常有效的方法，同时利用泛函提升的方法深入研究非凸模型的凸化方法。其次，针对医学图像分割的两个需求与医学图像数据量大的特点，我们将综合利用变分理论、优化理论、算子分裂等技巧设计快速、有效的算法。最后，我们将得到的模型和算法应用到实际问题中来验证其优点。

对于灰度覆盖、边界模糊、背景复杂，但灰度和纹理信息相对简单的图像分割一直以来是个热门却困难的问题。针对这类图像，特别是肝脏MRI图像分割，这篇文章给出了一个基于非局部信息的正则化混合分割模型。通过水平集方法，利用变分理论和优化算法，给出了该模型的数值解。并通过实验，与已有模型分割结果进行定性、定量对比，说明我们的模型在我们感兴趣的这类图像上能得到相对理想的分割结果。