用于形状分析的多光谱几何方法

IF 1.3 4区 数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
David Bensaïd, Ron Kimmel
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引用次数: 0

摘要

(\mathbb{R}^3\)中的一个实体物体可以用它的光滑边界曲面来表示,该曲面可以配备一个内在度量,从而形成一个2-黎曼流形。在本文中,我们使用多重度量来分析这种曲面,从而产生了多光谱,通过这些光谱可以对给定曲面进行表征。它们对不同类型局部结构的相对敏感性使得每种度量都能提供独特的形状视角。大量实验表明,所提出的多度量方法显著改善了几何处理中的重要任务,如形状检索、查找非刚性物体的相似性和相应部分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A Multi-spectral Geometric Approach for Shape Analysis

A Multi-spectral Geometric Approach for Shape Analysis

A solid object in \(\mathbb {R}^3\) can be represented by its smooth boundary surface which can be equipped with an intrinsic metric to form a 2-Riemannian manifold. In this paper, we analyze such surfaces using multiple metrics that give birth to multi-spectra by which a given surface can be characterized. Their relative sensitivity to different types of local structures allows each metric to provide a distinct perspective of the shape. Extensive experiments show that the proposed multi-metric approach significantly improves important tasks in geometry processing such as shape retrieval and find similarity and corresponding parts of non-rigid objects.

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来源期刊
Journal of Mathematical Imaging and Vision
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
70
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.
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