Morphological methods in 3D image fusion and sequence analysis in medical imaging

神经外科手术计划需要强大的和有效的分割和分类结果和大脑结构的时间变化的分析。这只能在多模态3D数据集（即，来自不同医学图像采集设备的数据）可以彼此匹配并且3D图像序列中的对应结构可以经由适当变形的计算来拟合的情况下实现。特别地，计算医学图像序列的不同帧之间的变形允许对疾病以及诸如肿瘤的结构的生长和变化进行详细的和空间分辨的研究。而不是匹配图像强度，我们只考虑图像形态，并试图匹配它们之间的图像序列的不同模态或不同的时间步长。这些形态分别由水平集的实体和它们的高斯映射唯一地表征。我们的模型将基于要最小化的成本泛函，该成本泛函分为测量高斯映射变形的匹配成本泛函和确保该逆问题适定性的正则化成本泛函。后者的功能允许通过一个各向异性的二次形式，这取决于水平集的形状算子的水平集上的水平集和边缘的变形的局部大的变化。这种方法的几个推广建议。基于匹配结果，我们将改进自动分割方法，该方法现在可以依赖于多种图像模态，并且有助于在时间序列内进行相关性。我们将开发的工具应用于典型的医学图像，并根据临床专业知识广泛验证所获得的结果

Neurosurgery planning requires robust and valid segmentation and classification results and an analysis of the temporal change of brain structures. This can only be achieved, if multi-modal 3D datasets (i.e. data from different medical image acquisition devices) can be matched to each other and corresponding structures in 3D image sequences can be correlatd via the computation of a appropriate deformation. Especially, the calculation of deformations inbetween different frames of a medical image sequence allows a detailed and spatially resolved study of diseases and the growth and change of structures such as tumors. Instead of matching image intensity we consider image morphologies only and try to match them between images of different modality or different time steps from a sequence of images. The morphologies are characterized uniquely by the entity of level sets and their Gauss maps respectively. Our model will be based on a cost functional to be minimized which splits into a matching cost functional measuring the deformation of Gauss maps and a regularization cost functional ensuring well-posedness of this inverse problem. The latter functional allows for locally large variations of the deformation across level sets and edges on level sets via an anisotropic quadratic form which depends on the shape operator of the level sets. Several generalization of this approach are proposed. Based on the matching results we will improve automatic segmentation methods, which now can rely on multiple image modalities and are helpful for correlations within a time sequence. We will apply the developed tools to typical medical images and extensively validate the obtained results based on clinical expertise