  In this paper, we propose a unified energy minimization model for the
segmentation of non-smooth image structures. The energy of piecewise linear
patch reconstruction is considered as an objective measure of the quality of
the segmentation of non-smooth structures. The segmentation is achieved by
minimizing the single energy without any separate process of feature
extraction. We also prove that the error of segmentation is bounded by the
proposed energy functional, meaning that minimizing the proposed energy leads
to reducing the error of segmentation. As a by-product, our method produces a
dictionary of optimized orthonormal descriptors for each segmented region. The
unique feature of our method is that it achieves the simultaneous segmentation
and description for non-smooth image structures under the same optimization
framework. The experiments validate our theoretical claims and show the clear
superior performance of our methods over other related methods for segmentation
of various image textures. We show that our model can be coupled with the
piecewise smooth model to handle both smooth and non-smooth structures, and we
demonstrate that the proposed model is capable of coping with multiple
different regions through the one-against-all strategy.
