Scholarlink

<p class="MsoNormal" style="margin-bottom: .0001pt; line-height: normal; background: white;"><span lang="EN-GB">This book presents new and original results on the deformations of apparent contours of surfaces in Euclidean 3-space and the discriminants of plane-to-plane map-germs.&#xa0;Given a viewing direction, the apparent contour (also called the profile or outline) is the projection of the set of points on the surface where the viewing direction is tangent to the surface. Apparent contours are extensively used in computer vision and image analysis and pose significant mathematical challenges.&#xa0;</span></p><p class="MsoNormal" style="margin-bottom: .0001pt; line-height: normal; background: white;"><span lang="EN-GB">&#xa0;</span><span lang="EN-GB">As the viewing direction varies, the apparent contour deforms, with emerging and vanishing inflections and vertices. The book provides a complete catalog of these bifurcations for generic surfaces as the viewing direction changes. Additionally, it explores geometric invariants that determine the maximum number of inflections and vertices that may appear in such deformations of an apparent contour. Aimed at researchers working in differential geometry, singularity theory, computer vision, and related areas, the text can also serve as material for an undergraduate reading course.</span></p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Geometric Deformations of Discriminants and Apparent Contours

  • 书籍

  • 发表日期：

    2025年

查看全文
  • Farid Tari,
  • Mostafa Salarinoghabi,
  • Masaru Hasegawa

摘要

This book presents new and original results on the deformations of apparent contours of surfaces in Euclidean 3-space and the discriminants of plane-to-plane map-germs. Given a viewing direction, the apparent contour (also called the profile or outline) is the projection of the set of points on the surface where the viewing direction is tangent to the surface. Apparent contours are extensively used in computer vision and image analysis and pose significant mathematical challenges. 

 As the viewing direction varies, the apparent contour deforms, with emerging and vanishing inflections and vertices. The book provides a complete catalog of these bifurcations for generic surfaces as the viewing direction changes. Additionally, it explores geometric invariants that determine the maximum number of inflections and vertices that may appear in such deformations of an apparent contour. Aimed at researchers working in differential geometry, singularity theory, computer vision, and related areas, the text can also serve as material for an undergraduate reading course.