Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward Designing Intelligent PDEs for Computer Vision: An Optimal
  Control Approach   Many computer vision and image processing problems can be posed as solving
partial differential equations (PDEs). However, designing PDE system usually
requires high mathematical skills and good insight into the problems. In this
paper, we consider designing PDEs for various problems arising in computer
vision and image processing in a lazy manner: \emph{learning PDEs from real
data via data-based optimal control}. We first propose a general intelligent
PDE system which holds the basic translational and rotational invariance rule
for most vision problems. By introducing a PDE-constrained optimal control
framework, it is possible to use the training data resulting from multiple ways
(ground truth, results from other methods, and manual results from humans) to
learn PDEs for different computer vision tasks. The proposed optimal control
based training framework aims at learning a PDE-based regressor to approximate
the unknown (and usually nonlinear) mapping of different vision tasks. The
experimental results show that the learnt PDEs can solve different vision
problems reasonably well. In particular, we can obtain PDEs not only for
problems that traditional PDEs work well but also for problems that PDE-based
methods have never been tried before, due to the difficulty in describing those
problems in a mathematical way.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol