Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps
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 conf...
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| Format: | Article |
| Language: | English |
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Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/105421 https://orcid.org/0000-0002-4692-5442 |
| _version_ | 1826212167991427072 |
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| author | Lee, Yin Tat Lam, Ka Chun Lui, Lok Ming |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lee, Yin Tat Lam, Ka Chun Lui, Lok Ming |
| author_sort | Lee, Yin Tat |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:17:07Z |
| format | Article |
| id | mit-1721.1/105421 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:17:07Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1054212022-10-02T01:57:36Z Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps Lee, Yin Tat Lam, Ka Chun Lui, Lok Ming Massachusetts Institute of Technology. Department of Mathematics Lee, Yin Tat 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. 2016-11-22T18:50:36Z 2016-11-22T18:50:36Z 2015-09 2015-09 2016-08-18T15:42:49Z Article http://purl.org/eprint/type/JournalArticle 0885-7474 1573-7691 http://hdl.handle.net/1721.1/105421 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. https://orcid.org/0000-0002-4692-5442 en http://dx.doi.org/10.1007/s10915-015-0113-5 Journal of Scientific Computing 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. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Lee, Yin Tat Lam, Ka Chun Lui, Lok Ming Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps |
| title | Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps |
| title_full | Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps |
| title_fullStr | Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps |
| title_full_unstemmed | Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps |
| title_short | Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps |
| title_sort | landmark matching transformation with large deformation via n dimensional quasi conformal maps |
| url | http://hdl.handle.net/1721.1/105421 https://orcid.org/0000-0002-4692-5442 |
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