图像边缘的数学结构剖析
首发时间:2011-03-30
摘要:本文从二维流形角度剖析了图像边缘的数学结构,认为边缘点存在于非光滑流形与光滑流形的差集之中;探索性地讨论了图像边缘点邻域内的反演流形、非光滑点、陡变点、马赫点和反演结构点概念,由此讨论了边缘点存在的必要条件,给出了基于流形的图像边缘点定义、边缘点的活动标架,指出图像边缘的几何意义是:由边缘点活动标架中的4个维度参数构成的4维空间中的一条连续曲线。
关键词: 图像边缘 数学结构 非光滑流形 反演集合 活动标架
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Analysis on Mathematical Structure of Image Edge
Abstract:This paper analyzes the mathematical structure of the image edge from the two-manifold angle, Thought that the edge point exists in the non-smooth manifold and in smooth manifold's difference set; Exploratory discussed in the image edge point neighborhood inversion manifold, non-smooth points, sudden change points, the Mach points and the inversion structure points,from this discussed the edge point existence essential condition, has given based on manifold's image edge point definition, the moving frame of edge point, pointed out that the image edge the geometry significance is: moving frame by the edge points in the four dimensions of parameters consisting of 4-dimensional space in a continuous curve.
Keywords: Image edge mathematical structure Non-smooth manifold Inversion set Moving frame
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