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<p>The focus of this article is on exploring the concept of abstract homogeneity in relation to partially ordered sets. Our study delves into various properties of this notion, including self-homogeneity. We then apply these concepts to the practical area of image processing, demonstrating their relevance. Our application of abstract homogeneous functions in computer vision surpasses classical edge detection methods and approaches state-of-the-art results, highlighting their potential showing that a suitable family of functions for this task are the abstract homogeneous ones. Additionally, we improve these results by creating consensus feature images, which aggregate features to enhance the effect of abstract homogeneity. This method offers a subtle yet effective improvement in image processing tasks.</p>

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Abstract homogeneity on partially ordered Sets

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Ana Shirley Monteiro,
  • Regivan Santiago,
  • Martin Papčo,
  • Radko Mesiar,
  • Humberto Bustince,
  • Javier Fernandez,
  • Mikel Ferrero,
  • Cedric Marco-Detchart

摘要

The focus of this article is on exploring the concept of abstract homogeneity in relation to partially ordered sets. Our study delves into various properties of this notion, including self-homogeneity. We then apply these concepts to the practical area of image processing, demonstrating their relevance. Our application of abstract homogeneous functions in computer vision surpasses classical edge detection methods and approaches state-of-the-art results, highlighting their potential showing that a suitable family of functions for this task are the abstract homogeneous ones. Additionally, we improve these results by creating consensus feature images, which aggregate features to enhance the effect of abstract homogeneity. This method offers a subtle yet effective improvement in image processing tasks.