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

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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