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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.

Inhaltsverzeichnis

Frontmatter

Preliminaries

Frontmatter

2016 | OriginalPaper | Buchkapitel

Chapter 1. Introduction

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 2. Overview

James Damon, Peter Giblin, Gareth Haslinger

Mathematical Basis for Analysis of Feature-Shade/Shadow-Contours

Frontmatter

2016 | OriginalPaper | Buchkapitel

Chapter 3. Apparent Contours for Projections of Smooth Surfaces

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 4. Abstract Classification of Singularities Preserving Features

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 5. Singularity Equivalence Groups Capturing Interactions

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 6. Methods for Classification of Singularities

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 7. Methods for Topological Classification of Singularities

James Damon, Peter Giblin, Gareth Haslinger

The Classification of Interactions Involving Feature-Shade/Shadow-Contours

Frontmatter

2016 | OriginalPaper | Buchkapitel

Chapter 8. Stratifications of Generically Illuminated Surfaces with Geometric Features

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 9. Realizations of Abstract Mappings Representing Projection Singularities

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 10. Statements of the Main Classification Results

James Damon, Peter Giblin, Gareth Haslinger

Classifications of Interactions of Pairs of Feature-Shade/Shadow-Contours

Frontmatter

2016 | OriginalPaper | Buchkapitel

Chapter 11. Stable View Projections and Transitions Involving Shade/Shadow Curves on a Smooth Surface (SC)

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 12. Transitions Involving Views of Geometric Features (FC)

James Damon, Peter Giblin, Gareth Haslinger

Classifications of Multiple Interactions

Frontmatter

2016 | OriginalPaper | Buchkapitel

Chapter 13. Transitions Involving Geometric Features and Shade/Shadow Curves (SFC)

James Damon, Peter Giblin, Gareth Haslinger

2016 | OriginalPaper | Buchkapitel

Chapter 14. Classifications of Stable Multilocal Configurations and Their Generic Transitions

James Damon, Peter Giblin, Gareth Haslinger

Backmatter

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