![]() ![]() Īndres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.A.: Probabilistic image segmentation with closedness constraints. We conduct initial experiments on synthetic images as well as real depth images, and discuss the advantages and drawbacks of the two models.Īmaldi, E., Coniglio, S., Taccari, L.: Discrete optimization methods to fit piecewise affine models to data points. We show that the MIP formulation on grid graphs is approximate, while on king’s graph, it is exact under certain circumstances. The other is to provide initial feasible solutions using a tailored heuristic algorithm. One is to adopt a cutting plane method to add the exponentially many multicut inequalities on-the-fly. The resulting problem is \(\mathcal \)-hard, and two techniques are introduced to improve the computation. To obtain a consistent partitioning (e.g., image segmentation), we include multicut constraints in the formulation. ![]() We propose a novel Mixed Integer Program (MIP) formulation for the piecewise affine fitting problem, where binary edge variables determine the boundary between two partitions of the function domain. This is useful for segmentation and denoising when the given function corresponds to a mapping from pixels of a bitmap image to their color depth values. In this paper, we investigate the problem of fitting a discontinuous piecewise affine function to a given function defined on an arbitrary subset of an integer lattice, where no restriction on the partition of the domain is enforced (i.e., its geometric shape can be nonconvex). However, most, if not all existing models, only deal with fitting a continuous function. Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions.
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