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Geometric deformations of discriminants and apparent contours

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric deformations of discriminants and apparent contoursby Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa.
作者:	Tari, F.
其他作者:	Salarinoghabi, Mostafa.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	x, 186 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Geometry, Differential.
電子資源:	https://doi.org/10.1007/978-3-031-87016-3
ISBN:	9783031870163$q(electronic bk.)

Geometric deformations of discriminants and apparent contours
Tari, F.

Geometric deformations of discriminants and apparent contours[electronic resource] /by Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa. - Cham :Springer Nature Switzerland :2025. - x, 186 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,v. 23701617-9692 ;. - Lecture notes in mathematics ;2035..

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.

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.

ISBN: 9783031870163$q(electronic bk.)

Standard No.: 10.1007/978-3-031-87016-3doiSubjects--Topical Terms:

182610
Geometry, Differential.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Geometric deformations of discriminants and apparent contours
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520 $a 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.
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