Mathematical Morphology on Directional Data

IF 1.3 4区数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Mathematical Imaging and Vision Pub Date : 2024-09-06 DOI:10.1007/s10851-024-01210-0

Konstantin Hauch, Claudia Redenbach

引用次数: 0

Abstract

We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.

Abstract Image

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定向数据的数学形态学

我们为像素值为单位向量的定向图像定义形态运算符和滤波器。这就需要使用深度函数来获得单位向量的排序关系。它们提供了相对于指定中心向量的中心向外排序。我们在合成方向图像上应用了我们的算子，并将它们与灰度图像的经典形态学算子进行了比较。作为应用实例，我们增强了压缩玻璃泡沫的断层区域，并分割了玻璃纤维增强聚合物的错位纤维区域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.