We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.
We propose new dense descriptors for texture segmentation. Given a region of arbitrary shape in an image, these descriptors are formed from shape-dependent scale spaces of oriented gradients. These scale spaces are defined by Poisson-like partial differential equations. A key property of our new descriptors is that they do not aggregate image data across the boundary of the region, in contrast to existing descriptors based on aggregation of oriented gradients. As an example, we show how the descriptor can be incorporated in a Mumford-Shah energy for texture segmentation. We test our method on several challenging datasets for texture segmentation and textured object tracking. Experiments indicate that our descriptors lead to more accurate segmentation than non-shape dependent descriptors and the state-of-the-art in texture segmentation.