Super-Resolution Surface Reconstruction from Few Low-Resolution Slices

Zhang, Yiyao ORCID: 0000-0003-1166-6935, Chen, Ke ORCID: 0000-0002-6093-6623 and Yang, Shang-Hua (2023) Super-Resolution Surface Reconstruction from Few Low-Resolution Slices. [Preprint]

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Official URL: http://dx.doi.org/10.3934/ipi.2023040

Abstract

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing the resolution of such surfaces becomes crucial. This paper proposes a new variational model for solving this problem, based on an Euler-Elastica-based regulariser. Further, we propose and implement two numerical algorithms for solving the model, a projected gradient descent method and the alternating direction method of multipliers. Numerical experiments using real-life examples (including two from outputs of another variational model) have been illustrated for effectiveness. The advantages of the new model are shown through quantitative comparisons by the standard deviation of Gaussian curvatures and mean curvatures from the viewpoint of discrete geometry.

Item Type:	Preprint
Additional Information:	33 pages, 25 figures
Uncontrolled Keywords:	math.AP, math.AP, cs.CV, 49Q20, 65K10, 65D18, 94A08, 68U10
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	19 Sep 2023 07:24
Last Modified:	15 Mar 2024 17:52
DOI:	10.48550/arxiv.2309.05071
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3172873