Geometric deformations of discriminants and apparent contours / Farid Tari, Mostafa Salarinoghabi, Masaru Hasegawa.

Format:

Book

Author/Creator:

Tari, F. (Farid), author.

Salarinoghabi, Mostafa, author.

Hasegawa, Masaru, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2370 ;.

Lecture notes in mathematics, 0075-8434 ; volume 2370

Language:

English

Subjects (All):

Geometry, Differential.

Deformations of singularities.

Physical Description:

x, 183 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2025]

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"--Publisher's description.

Contents:

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.

Notes:

Includes bibliographical references (pages 177-180) and index.

ISBN:

9783031870156

3031870158

OCLC:

1521554541