Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order Shape Optimization for Geometric Inverse Problems in Vision   We develop a method for optimization in shape spaces, i.e., sets of surfaces
modulo re-parametrization. Unlike previously proposed gradient flows, we
achieve superlinear convergence rates through a subtle approximation of the
shape Hessian, which is generally hard to compute and suffers from a series of
degeneracies. Our analysis highlights the role of mean curvature motion in
comparison with first-order schemes: instead of surface area, our approach
penalizes deformation, either by its Dirichlet energy or total variation.
Latter regularizer sparks the development of an alternating direction method of
multipliers on triangular meshes. Therein, a conjugate-gradients solver enables
us to bypass formation of the Gaussian normal equations appearing in the course
of the overall optimization. We combine all of the aforementioned ideas in a
versatile geometric variation-regularized Levenberg-Marquardt-type method
applicable to a variety of shape functionals, depending on intrinsic properties
of the surface such as normal field and curvature as well as its embedding into
space. Promising experimental results are reported.

7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas