Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps
Name
10915_2015_Article_113.pdf
Size
7.28 MB
Format
Adobe PDF
Checksum (MD5)
f3357eecfb7401295d24ec81c926f339
Author(s)
Lee, Yin Tat
Lam, Ka Chun
Lui, Lok Ming
Date Issued
September 2015
Journal
Journal of Scientific Computing
Publisher
Springer US
Citation
Lee, Yin Tat, Ka Chun Lam, and Lok Ming Lui. “Landmark-Matching Transformation with Large Deformation Via N-Dimensional Quasi-Conformal Maps.” Journal of Scientific Computing 67.3 (2016): 926–954.
Version
Author's final manuscript
Abstract
We propose a new method to obtain landmark-matching transformations between n-dimensional Euclidean spaces with large deformations. Given a set of feature correspondences, our algorithm searches for an optimal folding-free mapping that satisfies the prescribed landmark constraints. The standard conformality distortion defined for mappings between 2-dimensional spaces is first generalized to the n-dimensional conformality distortion K(f) for a mapping f between n-dimensional Euclidean spaces (n ≥ 3). We then propose a variational model involving K(f) to tackle the landmark-matching problem in higher dimensional spaces. The generalized conformality term K(f) enforces the bijectivity of the optimized mapping and minimizes its local geometric distortions even with large deformations. Another challenge is the high computational cost of the proposed model. To tackle this, we have also proposed a numerical method to solve the optimization problem more efficiently. Alternating direction method with multiplier is applied to split the optimization problem into two subproblems. Preconditioned conjugate gradient method with multi-grid preconditioner is applied to solve one of the sub-problems, while a fixed-point iteration is proposed to solve another subproblem. Experiments have been carried out on both synthetic examples and lung CT images to compute the diffeomorphic landmark-matching transformation with different landmark constraints. Results show the efficacy of our proposed model to obtain a folding-free landmark-matching transformation between n-dimensional spaces with large deformations.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10915-015-0113-5
