Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shortest Paths in Graphs with Matrix-Valued Edges: Concepts, Algorithm
  and Application to 3D Multi-Shape Analysis   Finding shortest paths in a graph is relevant for numerous problems in
computer vision and graphics, including image segmentation, shape matching, or
the computation of geodesic distances on discrete surfaces. Traditionally, the
concept of a shortest path is considered for graphs with scalar edge weights,
which makes it possible to compute the length of a path by adding up the
individual edge weights. Yet, graphs with scalar edge weights are severely
limited in their expressivity, since oftentimes edges are used to encode
significantly more complex interrelations. In this work we compensate for this
modelling limitation and introduce the novel graph-theoretic concept of a
shortest path in a graph with matrix-valued edges. To this end, we define a
meaningful way for quantifying the path length for matrix-valued edges, and we
propose a simple yet effective algorithm to compute the respective shortest
path. While our formalism is universal and thus applicable to a wide range of
settings in vision, graphics and beyond, we focus on demonstrating its merits
in the context of 3D multi-shape analysis.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an