Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second order elastic metrics on the shape space of curves   Second order Sobolev metrics on the space of regular unparametrized planar
curves have several desirable completeness properties not present in lower
order metrics, but numerics are still largely missing. In this paper, we
present algorithms to numerically solve the initial and boundary value problems
for geodesics. The combination of these algorithms allows to compute Karcher
means in a Riemannian gradient-based optimization scheme. Our framework has the
advantage that the constants determining the weights of the zero, first, and
second order terms of the metric can be chosen freely. Moreover, due to its
generality, it could be applied to more general spaces of mapping. We
demonstrate the effectiveness of our approach by analyzing a collection of
shapes representing physical objects.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph