3D Orientation-Preserving Variational Models for Accurate Image Registration



Daoping, Zhang and Chen, Ke ORCID: 0000-0002-6093-6623
(2020) 3D Orientation-Preserving Variational Models for Accurate Image Registration. SIAM Journal on Image Sciences, 13 (3). pp. 1653-1691.

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Abstract

The Beltrami coefficient from complex analysis has recently been found to provide a robust constraint for obtaining orientation-preserving and diffeomorphic transformations for registration of planar images. There exists no such concept of the Beltrami coefficient in three or higher dimensions, although a generalized theory of quasi-conformal maps in high dimensions exists. In this paper, we first propose a new algebraic measure in three dimensions (3D) that mimics the Beltrami concept in two dimensions (2D) and then propose a corresponding registration model based on it. We then establish the existence of solutions for the proposed model and further propose a converging generalized Gauss--Newton iterative method to solve the resulting nonlinear optimization problem. In addition, we also provide another two possible regularizers in 3D. Numerical experiments show that the new model can produce more accurate orientation-preserving transformations than competing state-of-the-art registration models.

Item Type: Article
Uncontrolled Keywords: orientation-preserving maps, variational model, 3D image registration, generalized Gauss-Newton method
Depositing User: Symplectic Admin
Date Deposited: 02 Jul 2020 09:43
Last Modified: 18 Jan 2023 23:47
DOI: 10.1137/20M1320006
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3092511