Authors: James Damon, Peter Giblin, Gareth Haslinger
Includes geometric features of objects, shade/shadow features, and apparent contours
Analyzes generic changes under viewer movement
Amply illustrated with computer generated images
Yields approach for edge detection where multiple curves meet
Employs singularity theory on semi-analytic stratified spaces
Combines singularity methods with geometry of surfaces
Builds on earlier results in singularity theory and shows necessity of topological methods
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.
Table of contents
Front Matter
Preliminaries
Front Matter
Introduction
Overview
Mathematical Basis for Analysis of Feature-Shade/Shadow-Contours
Front Matter
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
The Classification of Interactions Involving Feature-Shade/Shadow-Contours
Front Matter
Stratifications of Generically Illuminated Surfaces with Geometric Features
Realizations of Abstract Mappings Representing Projection Singularities
Statements of the Main Classification Results
Classifications of Interactions of Pairs of Feature-Shade/Shadow-Contours
Front Matter
Stable View Projections and Transitions Involving Shade/Shadow Curves on a Smooth Surface (SC)
Transitions Involving Views of Geometric Features (FC)
Classifications of Multiple Interactions
Front Matter
Transitions Involving Geometric Features and Shade/Shadow Curves (SFC)
Classifications of Stable Multilocal Configurations and Their Generic Transitions
Back Matter