变分能量方法及其在医学图像处理中的应用

【作者】 彭佳林；

【导师】 丘成栋； 孔德兴；

【作者基本信息】 浙江大学 ， 数学， 2013， 博士

【摘要】 图像处理分析要解决的两个核心问题是：1)如何提高图像的质量和信息量；2)如何从大量的图像数据信息中快速地获取人们真正关心的信息。变分能量方法是应用数学领域中的一个重要方法,近三十年来在图像处理中得到广泛的应用和发展。图像超分辨和分割是(医学)图像处理中的两类典型问题,前者着眼于增大图像包含的信息量,后者主要是定量的提取目标物体的轮廓。本文主要是从这两类问题出发展开研究,利用医学数据特征、凸优化和低秩矩阵恢复的理论,建立了一系列高效的变分能量泛函,并提出了相应的快速求解算法。我们试图通过这些方法的建立作为搭建医学图像处理和临床医学之间桥梁的一个新的尝试。主要工作包括：首先,针对医学图像中分割中的一类典型问题——肝脏CT图像分割,本文建立了一个基于图像表征的自适应混合变分模型。受到模糊的边界、复杂的背景、低对比度、组织间灰度重叠等因素的影响,肝脏CT图像分割是一个具有挑战性的问题。此外图像中有识别力的特征如灰度、边界等分布的不均匀性进一步增加了分割的难度。提出的模型在不同的图像区域有选择性地根据灰度、边界及局部上下文信息确定目标区域。针对周围组织粘连及模糊边界难于识别的问题,我们引入了一个基于整体和局部区域表征的势能场函数,它能够利用局部“上下文”信息有效地识别弱边界。实验表明通过有机的结合不同的图像信息,提出的模型能够很好地处理带有复杂背景、灰度重叠以及弱边界的医学分割问题。提出的模型具备较高的分割精度和较短的处理时间,能够很好地满足医学的实际需求。其次,本文建立了一个带约束的凸的肝脏分割模型,并提出了一个改进的原始对偶算法。非凸模型由于一般只能局部求解,因此对初值有很大的依赖性。凸模型能够从任意初值出发得到全局解,但是很多模型的全局解缺少实际意义。对于带有复杂背景及灰度重叠的两区域肝脏分割问题,使得其全局最优解对应想要的分割。这需要有效地去除复杂背景的干扰,将全局解限制在目标分割上。对此我们提出了一个灰度-边界变分能量项,并结合了区域表征约束以及初始交互约束。我们给出了带交互约束的凸模型的解的松弛-阀值最优性。针对提出的非严格凸非光滑模型,我们提出了一个加速的原始对偶算法。大量的数据实验表明提出的模型能够有效地分割肝脏,而且仅仅需要很简单的交互初始化。最后,本文提出了基于矩阵结构低秩正则化的单张图像超分辨能量模型。众所周知,由于大量的细节缺失,单张图像超分辨问题是一个严重不适定的反问题。为了得到稳定的解,人们往往引入正则化方法。一般的基于数据学习的超分辨模型的重建结果,不仅因训练集合和模型参数的不同而不同,而且存在很多异值(Outlier)噪声误差或不适当重建。本文中提出了一种基于重建矩阵结构低秩正则化的超分辨方法。该方法通过融合不同的粗糙超分辨结果得到干净的超分辨。在异值噪声随机、稀疏的假设下,我们提出的方法在保持图像结构的同时,能够有效地去除异值噪声误差。实验表明,提出的方法的结果不仅远远好于输入的粗糙超分辨结果,而且要优于当前主流的算法。更多还原

【Abstract】 Image process and analysis aim to improve the image quality through post-processing and rapidly extract the information that the specific application needs from huge mount of image data. Variational energy method is one of the most important methods in applied mathematics. In the last few decades have seen a great many applications and developments of variational methods in image pro-cessing. Super-resolution and segmentation are two typical problems in (medical) image processing. The first task targets to increase the amount of information and the second is to extract the boundary the specific object. Focussing on these two problems, we present here several efficient formulations of these problems based the variational method, relaxation, convex optimization and the theory of low rank matrix recovery, while also taking account of the features of specific data and the needs of their applications. Several efficient computational schemes and algorithms are also developed for the corresponding energies. With these new models and algorithms, we are trying to build a bridge for the daily clinical practice and the image processing techniques. Main research includes:Firstly, A region appearance based adaptive variational model is proposed for the liver segmentation from CT image, which is a typical problem in medical image processing. Due to intensity overlapping, ambiguous edges and complex backgrounds, liver segmentation is a difficult task.the non-uniform distributions of discriminative image features pose further challenges. In view of this, a spa-tially varying weight is incorporated by the proposed hybrid model such that the model can locate liver regions and edges selectively according to intensity, gradient and local context. Given the adhering tissues and weak edges, a novel potential field based on global and local region appearance is introduced to re-solve ambiguity. The experiments on standard data sets show that through the adaptive integration of different image cues, the proposed model can efficiently address complex background, intensity overlapping and weak edges. Moreover, it is robust to initialization and data quality. Quantitative validations and com- parative results demonstrate the accuracy, efficiency and robustness of the model and thus can well satisfy the clinical requirement.Secondly, we propose a constrained convex model with an efficient algo-rithm for liver segmentation problem, which is complicated by complex back-ground and intensity overlapping. Nonconvex models are prone to get stuck in local minima and thus sensitive to initialization. While convex models can be minimized globally with any initialization, one of the biggest challenges is to define an energy with meaningful global minimizer, especially for problems with complex background and ambiguous edges. In this paper we proposed a model which combined a novel intensity-edge term, a region appearance term and user specified constrains in initial stage,which can maximally restrict the solution space to target segmentation. Also we prove the optimal property thresholded solution of the convex model. Moreover, we proposed an accelerated primal-dual algorithm.Finally, we propose a structural low rank regularization method for the sin-gle image super-resolution. As is well known, single image super-resolution is a highly ill-posed problem due to the large amount of missing information in reg-ular positions. To obtain stable and reasonable solution, the general approach is to introduce regularization terms. One popular method is the learning based approach which can be adaptive to data structure. However, the results are heav-ily affected by the content of training data and learning algorithms. Moreover, they are plagued by artifacts such as inconsistent reconstructions and outliers which usually have significantly different values than neighborhoods. To address these problems, we propose a new variational energy with a structural low rank regularization, which produces clear reconstruction by fusing different coarse re-constructions. With the assumption of randomness and sparsity of the outliers, the proposed model can simultaneously remove the artifacts and keep the image structures.更多还原