{"title":"A Multi-spectral Geometric Approach for Shape Analysis","authors":"David Bensaïd, Ron Kimmel","doi":"10.1007/s10851-024-01192-z","DOIUrl":null,"url":null,"abstract":"<p>A solid object in <span>\\(\\mathbb {R}^3\\)</span> 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.\n</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Imaging and Vision","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10851-024-01192-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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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