Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning Spectral Unions of Partial Deformable 3D Shapes   Spectral geometric methods have brought revolutionary changes to the field of
geometry processing. Of particular interest is the study of the Laplacian
spectrum as a compact, isometry and permutation-invariant representation of a
shape. Some recent works show how the intrinsic geometry of a full shape can be
recovered from its spectrum, but there are approaches that consider the more
challenging problem of recovering the geometry from the spectral information of
partial shapes. In this paper, we propose a possible way to fill this gap. We
introduce a learning-based method to estimate the Laplacian spectrum of the
union of partial non-rigid 3D shapes, without actually computing the 3D
geometry of the union or any correspondence between those partial shapes. We do
so by operating purely in the spectral domain and by defining the union
operation between short sequences of eigenvalues. We show that the approximated
union spectrum can be used as-is to reconstruct the complete geometry [MRC*19],
perform region localization on a template [RTO*19] and retrieve shapes from a
database, generalizing ShapeDNA [RWP06] to work with partialities. Working with
eigenvalues allows us to deal with unknown correspondence, different sampling,
and different discretizations (point clouds and meshes alike), making this
operation especially robust and general. Our approach is data-driven and can
generalize to isometric and non-isometric deformations of the surface, as long
as these stay within the same semantic class (e.g., human bodies or horses), as
well as to partiality artifacts not seen at training time.

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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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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: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an