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Regularity Classes for Locally Orderless Images

机译:局部无序图像的正则类

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摘要

Gaussian scale space permits one to compute image derivatives. The limitation to some finite order is not inherent in the paradigm itself (Gaussian blurred functions are always smooth), but is caused by the interplay of (at least) two external factors. One is the ratio of the Gaussian scale parameter versus the atomic scale that limits physically or perceptually meaningful sizes (e.g. pixel size, or in general any scale at which the image is "locally orderless"). The second factor involved is the fiducial level of tolerance. Together these factors conspire to determine a maximal order beyond which differential structure becomes meaningless. Thus they give rise to the notion of regularity classes for images akin to the conceptual C~k-classification pertaining to mathematical functions. We study the relationship between the maximal differential order k, the ratio of inner scale to atomic scale, and the prescribed tolerance level, and draw several conclusions that are of practical interest when considering image derivatives.
机译:高斯比例空间允许计算图像导数。某些有限阶的限制并不是范式本身固有的(高斯模糊函数总是平滑的),而是由(至少)两个外部因素的相互作用引起的。一个是高斯比例参数与原子比例之比,该比例限制了物理或感知上有意义的尺寸(例如像素尺寸,或通常图像“局部无序”的任何比例)。涉及的第二个因素是基准的容忍度。这些因素共同决定了最大顺序,超过该最大顺序,差分结构变得毫无意义。因此,它们引起了图像的规则性类别的概念,类似于与数学函数有关的概念性Ck分类。我们研究了最大微分阶数k,内标与原子标之比和规定的公差水平之间的关系,并得出了一些在考虑图像导数时具有实际意义的结论。

著录项

  • 来源
    《》|2003年|p.255-265|共11页
  • 会议地点 Isle of Skye(GB);Isle of Skye(GB)
  • 作者

    Luc Florack; Remco Duits;

  • 作者单位

    Eindhoven University of Technology Department of Biomedical Engineering P.O. Box 512, NL-5600 MB Eindhoven, The Netherlands;

  • 会议组织
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 无线电电子学、电信技术;
  • 关键词

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