Geometric Deformations of Discriminants and Apparent Contours

• Verfasst von: Tari, Farid [VerfasserIn]
• Verfasst von: Salarinoghabi, Mostafa [VerfasserIn]
• Verfasst von: Hasegawa, Masaru [VerfasserIn]
• Titel: Geometric Deformations of Discriminants and Apparent Contours
• Verf.angabe: by Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa
• Ausgabe: 1st ed. 2025.
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Jahr: 2025
• Umfang: 1 Online-Ressource(X, 186 p. 60 illus., 51 illus. in color.)
• Gesamttitel/Reihe: Lecture Notes in Mathematics ; 2370
• ISBN: 978-3-031-87016-3
• DOI: doi:10.1007/978-3-031-87016-3
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Tari, Farid: Geometric deformations of discriminants and apparent contours. - Cham : Springer Nature, 2025. - x, 183 Seiten
• K10plus-PPN: 1924006901
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Chapter 1. Map-germs from the plane to the plane -- Chapter 2. Geometric deformations of discriminants -- Chapter 3. Geometric deformations of the fold and cusp -- Chapter 4. Ae-codimension 1 singularities -- Chapter 5. Ae-codimension 2 singularities -- Chapter 6. Apparent contours -- Chapter 7. Geometric invariants.

Abstract

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.