Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Teichm\"uller extremal mapping and its applications to landmark matching
  registration   Registration, which aims to find an optimal 1-1 correspondence between
shapes, is an important process in different research areas. Conformal mappings
have been widely used to obtain a diffeomorphism between shapes that minimizes
angular distortion. Conformal registrations are beneficial since it preserves
the local geometry well. However, when landmark constraints are enforced,
conformal mappings generally do not exist. This motivates us to look for a
unique landmark matching quasi-conformal registration, which minimizes the
conformality distortion. Under suitable condition on the landmark constraints,
a unique diffeomporphism, called the Teichm\"uller extremal mapping between two
surfaces can be obtained, which minimizes the maximal conformality distortion.
In this paper, we propose an efficient iterative algorithm, called the
Quasi-conformal (QC) iterations, to compute the Teichm\"uller mapping. The
basic idea is to represent the set of diffeomorphisms using Beltrami
coefficients (BCs), and look for an optimal BC associated to the desired
Teichm\"uller mapping. The associated diffeomorphism can be efficiently
reconstructed from the optimal BC using the Linear Beltrami Solver(LBS). Using
BCs to represent diffeomorphisms guarantees the diffeomorphic property of the
registration. Using our proposed method, the Teichm\"uller mapping can be
accurately and efficiently computed within 10 seconds. The obtained
registration is guaranteed to be bijective. The proposed algorithm can also be
extended to compute Teichm\"uller mapping with soft landmark constraints. We
applied the proposed algorithm to real applications, such as brain landmark
matching registration, constrained texture mapping and human face registration.
Experimental results shows that our method is both effective and efficient in
computing a non-overlap landmark matching registration with least amount of
conformality distortion.

34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex