A Unifying Framework for $n$-Dimensional Quasi-Conformal Mappings
| Autor: | Lok Ming Lui, Gary Choi, Daoping Zhang, Jianping Zhang |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Differential Geometry
Computational Geometry (cs.CG) FOS: Computer and information sciences Computer Vision and Pattern Recognition (cs.CV) Applied Mathematics General Mathematics Computer Science - Computer Vision and Pattern Recognition Numerical Analysis (math.NA) Graphics (cs.GR) Computer Science - Graphics Differential Geometry (math.DG) FOS: Mathematics Computer Science - Computational Geometry Mathematics - Numerical Analysis |
| Zdroj: | SIAM Journal on Imaging Sciences. 15:960-988 |
| ISSN: | 1936-4954 |
| DOI: | 10.1137/21m1457497 |
| Popis: | With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal theory can be utilized for ensuring the bijectivity of the mappings. In addition, it is often desirable for the mappings to satisfy certain prescribed geometric constraints and possess low distortion in conformality or volume. In this work, we develop a unifying framework for computing $n$-dimensional quasi-conformal mappings. More specifically, we propose a variational model that integrates quasi-conformal distortion, volumetric distortion, landmark correspondence, intensity mismatch and volume prior information to handle a large variety of deformation problems. We further prove the existence of a minimizer for the proposed model and devise efficient numerical methods to solve the optimization problem. We demonstrate the effectiveness of the proposed framework using various experiments in two- and three-dimensions, with applications to medical image registration, adaptive remeshing and shape modeling. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|