期刊
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
卷 43, 期 11, 页码 4177-4188出版社
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2020.2993500
关键词
Mathematical model; Complexity theory; Two dimensional displays; Three-dimensional displays; Computational efficiency; Computer vision; Computational modeling; Fast marching; eikonal equation; static hamilton-jacobi; isotropic; anisotropic
资金
- Spanish Ministerio de Economia y Competitividad [TIN2015-65069-C2-1-R]
- Xunta de Galicia [ED431C 2018/34]
- European Union (European Regional Development Fund)
- Centro Singular de Investigacion de Galicia, accreditation 2016-2019)
This paper introduces a unified propagation method for handling both the classic Eikonal equation and the more general static Hamilton-Jacobi equations. The method maintains low complexity while increasing accuracy by creating 'mini wave-fronts' to minimize discretization error. Experimental results demonstrate superior precision and computational efficiency compared to state-of-the-art techniques.
This paper presents a unified propagation method for dealing with both the classic Eikonal equation, where the motion direction does not affect the propagation, and the more general static Hamilton-Jacobi equations, where it does. While classic Fast Marching Method (FMM) techniques achieve the solution to the Eikonal equation with a O(M log M) (or O(M) assuming some modifications), solving the more general static Hamilton-Jacobi equation requires a higher complexity. The proposed framework maintains the O(M log M) complexity for both problems, while achieving higher accuracy than available state-of-the-art. The key idea behind the proposed method is the creation of 'mini wave-fronts', where the solution is interpolated to minimize the discretization error. Experimental results show how our algorithm can outperform the state-of-the-art both in precision and computational cost.
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