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Geometric deformations of discriminants and apparent contours

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric deformations of discriminants and apparent contours/ by Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa.
Author:	Tari, F.
other author:	Salarinoghabi, Mostafa.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	x, 186 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Geometry, Differential. -
Online resource:	https://doi.org/10.1007/978-3-031-87016-3
ISBN:	9783031870163

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 ;v. 2370..

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

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

523835
Geometry, Differential.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Geometric deformations of discriminants and apparent contours
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245 1 0 $a Geometric deformations of discriminants and apparent contours $h [electronic resource] / $c by Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a x, 186 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2370
505 0 $a 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.
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.
650 0 $a Geometry, Differential. $3 523835
650 0 $a Deformations of singularities. $3 735156
650 1 4 $a Differential Geometry. $3 891003
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
700 1 $a Salarinoghabi, Mostafa. $3 3784362
700 1 $a Hasegawa, Masaru. $3 3784363
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2370. $3 3784364
856 4 0 $u https://doi.org/10.1007/978-3-031-87016-3
950 $a Mathematics and Statistics (SpringerNature-11649)