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Geometric Deformations of Discriminants and Apparent Contours / by Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Lecture Notes in Mathematics ; 2370Publisher: Cham : Springer Nature Switzerland, 2025Edition: 1st ed. 2025Description: 1 Online-Ressource(X, 186 p. 60 illus., 51 illus. in color.)ISBN:
  • 9783031870163
Subject(s): Additional physical formats: 9783031870156 | 9783031870170 | Erscheint auch als: 9783031870156 Druck-Ausgabe | Erscheint auch als: 9783031870170 Druck-Ausgabe | Erscheint auch als: Geometric deformations of discriminants and apparent contours. Druck-Ausgabe Cham : Springer Nature, 2025. x, 183 SeitenDDC classification:
  • 516.36 23
DOI: DOI: 10.1007/978-3-031-87016-3Online resources: Summary: 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.Summary: 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.PPN: PPN: 1924006901Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS | ZDB-2-LNM
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