Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess