Local features in natural images via singularity theory / James Damon, Peter Giblin, Gareth Haslinger.

Format:

Book

Author/Creator:

Damon, James, 1945- author.

Giblin, P. J., author.

Haslinger, Gareth, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 2165.

Lecture notes in mathematics, 0075-8434 ; 2165

Language:

English

Subjects (All):

Singularities (Mathematics).

Physical Description:

x, 255 pages : illustrations (some color) ; 24 cm.

Place of Publication:

[Cham] Switzerland : Springer, [2016]

Summary:

This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer's eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the "apparent contours". We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the "stable configurations" for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.

Contents:

Introduction

Overview

Apparent Contours for Projections of Smooth Surfaces

Abstract Classification of Singularities Preserving Features

Singularity Equivalence Groups Capturing Interactions

Methods for Classification of Singularities

Methods for Topological Classification of Singularities

Stratifications of Generically Illuminated Surfaces with Geometric Features

Realizations of Abstract Mappings Representing Projection Singularities

Statements of the Main Classification Results

Stable View Projections and Transitions Involving Shade/Shadow Curves on a Smooth Surface (SC)

Transitions Involving Views of Geometric Features (FC)

Transitions Involving Geometric Features and Shade/Shadow Curves (SFC)

Classifications of Stable Multilocal Configurations and Their Generic Transitions.

Notes:

Includes bibliographical references.

ISBN:

9783319414706

3319414704

OCLC:

951761424