离散莫尔斯函数与流域

IF 1.3 4区数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Mathematical Imaging and Vision Pub Date : 2023-08-10 DOI:10.1007/s10851-023-01157-8

Gilles Bertrand, Nicolas Boutry, Laurent Najman

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引用次数: 0

摘要

任何分水岭，当定义在维数d的正常伪流形上的堆栈上时，都是满足水滴原理的纯$$(d-1)$$ -子复形。本文引入了一类等价于离散莫尔斯函数的莫尔斯叠加函数。我们证明了正常伪流形上莫尔斯叠的分水岭是唯一定义的，并且可以用依赖于一系列坍缩的线性时间算法获得。最后，我们证明了这个分水岭是基于摩尔斯叠的最小值的伪泛褶面图的唯一最小生成森林的切割。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Discrete Morse Functions and Watersheds

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Discrete Morse Functions and Watersheds

Any watershed, when defined on a stack on a normal pseudomanifold of dimension d, is a pure $$(d-1)$$ -subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined and can be obtained with a linear-time algorithm relying on a sequence of collapses. Last, we prove that such a watershed is the cut of the unique minimum spanning forest, rooted in the minima of the Morse stack, of the facet graph of the pseudomanifold.

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来源期刊

Journal of Mathematical Imaging and Vision 工程技术-计算机：人工智能

CiteScore

4.30

自引率

5.00%

发文量

审稿时长

3.3 months

期刊介绍： The Journal of Mathematical Imaging and Vision is a technical journal publishing important new developments in mathematical imaging. The journal publishes research articles, invited papers, and expository articles. Current developments in new image processing hardware, the advent of multisensor data fusion, and rapid advances in vision research have led to an explosive growth in the interdisciplinary field of imaging science. This growth has resulted in the development of highly sophisticated mathematical models and theories. The journal emphasizes the role of mathematics as a rigorous basis for imaging science. This provides a sound alternative to present journals in this area. Contributions are judged on the basis of mathematical content. Articles may be physically speculative but need to be mathematically sound. Emphasis is placed on innovative or established mathematical techniques applied to vision and imaging problems in a novel way, as well as new developments and problems in mathematics arising from these applications. The scope of the journal includes: computational models of vision; imaging algebra and mathematical morphology mathematical methods in reconstruction, compactification, and coding filter theory probabilistic, statistical, geometric, topological, and fractal techniques and models in imaging science inverse optics wave theory. Specific application areas of interest include, but are not limited to: all aspects of image formation and representation medical, biological, industrial, geophysical, astronomical and military imaging image analysis and image understanding parallel and distributed computing computer vision architecture design.