Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Vector Heat Method   This paper describes a method for efficiently computing parallel transport of
tangent vectors on curved surfaces, or more generally, any vector-valued data
on a curved manifold. More precisely, it extends a vector field defined over
any region to the rest of the domain via parallel transport along shortest
geodesics. This basic operation enables fast, robust algorithms for
extrapolating level set velocities, inverting the exponential map, computing
geometric medians and Karcher/Fr\'{e}chet means of arbitrary distributions,
constructing centroidal Voronoi diagrams, and finding consistently ordered
landmarks. Rather than evaluate parallel transport by explicitly tracing
geodesics, we show that it can be computed via a short-time heat flow involving
the connection Laplacian. As a result, transport can be achieved by solving
three prefactored linear systems, each akin to a standard Poisson problem. To
implement the method we need only a discrete connection Laplacian, which we
describe for a variety of geometric data structures (point clouds, polygon
meshes, etc). We also study the numerical behavior of our method, showing
empirically that it converges under refinement, and augment the construction of
intrinsic Delaunay triangulations (iDT) so that they can be used in the context
of tangent vector field processing.

25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex