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We consider textured images, where the textures are composed of different numbers of additively superimposed oriented patterns. Our aim is to develop an energy minimization approach to segment these images into regions according to the number of patterns superimposed. The number of superimposed patterns can be inferred by testing orientation tensors for rank deficiency. In particular, the hypothesis that a local image patch exhibits a given number of superimposed oriented patterns holds if the corresponding orientation tensor is rank deficient by one. The tests can be carried out based on quantities computed from the eigenvalues of the orientation tensors, or equivalently from invariants such as determinant, minors and trace. Direct thresholding of these quantities leads, however, to non-robust segmentation results. We therefore develop energy functions which consist of a data term evaluating tensor rank, and a smoothness term which assesses smoothness of the segmentation results. As the orientation tensors and thus the data term depend on the number of orientations tested for, we derive a hierarchical algorithm for approximate energy minimization using graph cuts. We show the robustness of the approach using both synthetic and real image data.

ORIENTATION-BASED SEGMENTATION OF TEXTURED IMAGES BY ENERGY MINIMIZATION