Tensor Field Segmentation Using Region Based Active Contour Model

Abstract

Tensor fields (matrix valued data sets) have recently attracted 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 effective region-based active contour model for tensor field segmentation and show its application to diffusion 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 difference 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 contour 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 diffusion tensor MRI as well as structure tensors obtained from real texture data are shown to depict the performance of the proposed model.