Discrete Potts Model for Generating Superpixels on Noisy Images

Many computer vision applications, such as object recognition and segmentation, increasingly build on superpixels. However, there have been so far few superpixel algorithms that systematically deal with noisy images. We propose to first decompose the image into equal-sized rectangular patches, which also sets the maximum superpixel size. Within each patch, a Potts model for simultaneous segmentation and denoising is applied, that guarantees connected and non-overlapping superpixels and also produces a denoised image. The corresponding optimization problem is formulated as a mixed integer linear program (MILP), and solved by a commercial solver. Extensive experiments on the BSDS500 dataset images with noises are compared with other state-of-the-art superpixel methods. Our method achieves the best result in terms of a combined score (OP) composed of the under-segmentation error, boundary recall and compactness.Comment: 23 page

Learning Discontinuous Piecewise Affine Fitting Functions using Mixed Integer Programming for Segmentation and Denoising

Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a discontinuous piecewise affine function to given data that lie in an orthogonal grid, where no restriction on the partition is enforced (i.e., its geometric shape can be nonconvex). This is useful for segmentation and denoising when data corresponding to images. We propose a novel Mixed Integer Program (MIP) formulation for the piecewise affine fitting problem, where binary variables determine the location of break-points. To obtain consistent partitions (i.e. image segmentation), we include multi-cut constraints in the formulation. Since the resulting problem is $\mathcal{NP}$-hard, two techniques are introduced to improve the computation. One is to add facet-defining inequalities to the formulation and the other to provide initial integer solutions using a special heuristic algorithm. We conduct extensive experiments by some synthetic images as well as real depth images, and the results demonstrate the feasibility of our model.Comment: 20page