Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applying Lie Groups Approaches for Rigid Registration of Point Clouds   In the last decades, some literature appeared using the Lie groups theory to
solve problems in computer vision. On the other hand, Lie algebraic
representations of the transformations therein were introduced to overcome the
difficulties behind group structure by mapping the transformation groups to
linear spaces. In this paper we focus on application of Lie groups and Lie
algebras to find the rigid transformation that best register two surfaces
represented by point clouds. The so called pairwise rigid registration can be
formulated by comparing intrinsic second-order orientation tensors that encode
local geometry. These tensors can be (locally) represented by symmetric
non-negative definite matrices. In this paper we interpret the obtained tensor
field as a multivariate normal model. So, we start with the fact that the space
of Gaussians can be equipped with a Lie group structure, that is isomorphic to
a subgroup of the upper triangular matrices. Consequently, the associated Lie
algebra structure enables us to handle Gaussians, and consequently, to compare
orientation tensors, with Euclidean operations. We apply this methodology to
variants of the Iterative Closest Point (ICP), a known technique for pairwise
registration. We compare the obtained results with the original implementations
that apply the comparative tensor shape factor (CTSF), which is a similarity
notion based on the eigenvalues of the orientation tensors. We notice that the
similarity measure in tensor spaces directly derived from Lie's approach is not
invariant under rotations, which is a problem in terms of rigid registration.
Despite of this, the performed computational experiments show promising results
when embedding orientation tensor fields in Lie algebras.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg