Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic Distance Descriptors   The Gromov-Hausdorff (GH) distance is traditionally used for measuring
distances between metric spaces. It is defined as the minimal distortion of
embedding one surface into the other, while the optimal correspondence can be
described as the map that minimizes this distortion. Solving such a
minimization is a hard combinatorial problem that requires pre-computation and
storing of all pairwise geodesic distances for the matched surfaces. A popular
way for compact representation of functions on surfaces is by projecting them
into the leading eigenfunctions of the Laplace-Beltrami Operator (LBO). When
truncated, The basis of the LBO is known to be the optimal for representing
functions with bounded gradient in a min-max sense. Methods such as
Spectral-GMDS exploit this idea to simplify and efficiently approximate a
minimization related to the GH distance by operating in the truncated spectral
domain, and obtain state of the art results for matching of nearly isometric
shapes. However, when considering only a specific set of functions on the
surface, such as geodesic distances, an optimized basis could be considered as
an even better alternative. Here, we define the geodesic distance basis, which
is optimal for compact approximation of geodesic distances, in terms of
Frobenius norm. We use the suggested basis to extract the Geodesic Distance
Descriptor (GDD), which encodes the geodesic distances information as a linear
combination of the basis functions. We then show how these ideas can be used to
efficiently and accurately approximate the metric spaces matching problem with
almost no loss of information. These observations are used to construct a very
simple and efficient procedure for shape correspondence. Experimental results
show that the GDD improves both accuracy and efficiency of state of the art
shape matching procedures.

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The categories of this paper are: comp-gas
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio