Abstract

Tensor fields (matrix valued data sets) have recently at- tracted increased attention in the fields of image processing, computer vision, visualization and medical imaging. Tensor field segmentation is an important problem in tensor field analysis and has not been addressed adequately in the past. In this paper, we present an e?ective region-based active contour model for tensor field segmentation and show its applica- tion to difiusion tensor magnetic resonance images (MRI) as well as for the texture segmentation problem in computer vision. Specifically, we present a variational principle for an active contour using the Euclidean difierence of tensors as a discriminant. The variational formulation is valid for piecewise smooth regions, however, for the sake of simplicity of exposition, we present the piecewise constant region model in detail. This variational principle is a generalization of the region-based active con- tour to matrix valued functions. It naturally leads to a curve evolution equation for tensor field segmentation, which is subsequently expressed in a level set framework and solved numerically. Synthetic and real data experiments involving the segmentation of difiusion tensor MRI as well as structure tensors obtained from real texture data are shown to depict the performance of the proposed model.