Level-Set Methods for Tensor-Valued Images

Tensor-valued data are becoming more and more important as input for todays image analysis problems. This has been caused by a number of applications including diffusion tensor (DT-) MRI and physical measurements of anisotropic behaviour such as stress-strain relationships, interia and permittivity tensors. Consequently, there arises the need to filter and segment such tensor fields. In this paper we extend three important level set methods to tensor-valued data. To this end we first generalise Di Zenzo’s concept of a structure tensor for vector-valued images to tensor-valued data. This allows us to derive formulations of mean curvature motion and self-snakes in the case of tensor-valued images. We prove that these processes maintain positive semidefiniteness if the initial matrix data are positive semidefinite. Finally we present a geodesic active contour model for segmenting tensor fields. Since it incorporates information from all channels, it gives a contour representation that is highly robust under noise.

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