Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonparametric Continuous Sensor Registration   This paper develops a new mathematical framework that enables nonparametric
joint semantic and geometric representation of continuous functions using data.
The joint embedding is modeled by representing the processes in a reproducing
kernel Hilbert space. The functions can be defined on arbitrary smooth
manifolds where the action of a Lie group aligns them. The continuous functions
allow the registration to be independent of a specific signal resolution. The
framework is fully analytical with a closed-form derivation of the Riemannian
gradient and Hessian. We study a more specialized but widely used case where
the Lie group acts on functions isometrically. We solve the problem by
maximizing the inner product between two functions defined over data, while the
continuous action of the rigid body motion Lie group is captured through the
integration of the flow in the corresponding Lie algebra. Low-dimensional cases
are derived with numerical examples to show the generality of the proposed
framework. The high-dimensional derivation for the special Euclidean group
acting on the Euclidean space showcases the point cloud registration and
bird's-eye view map registration abilities. An implementation of this framework
for RGB-D cameras outperforms the state-of-the-art robust visual odometry and
performs well in texture and structure-scarce environments.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn