Local Features in Natural Images via Singularity Theory

• Main Authors: Damon, James (Author), Giblin, Peter (Author), Haslinger, Gareth (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Lecture Notes in Mathematics, 2165
• Subjects: Mathematics.; Computer graphics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Computer science > Mathematics.; Computer mathematics.; Global Analysis and Analysis on Manifolds.; Mathematical Applications in Computer Science.; Computer Imaging, Vision, Pattern Recognition and Graphics.

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 wit...

Table of Contents:

• Introduction
• Overview
• Part I-Mathematical Basis for Analysis of Feature-Shade/Shadow- Contours
• Abstract Classification of Singularities Preserving Features
• Singularity Equivalence Groups Capturing Interactions
• Methods for Classification of Singularities
• Methods for Topological Classification of Singularities
• Part II-The Classification of Interactions Involving Feature– Shade/Shadow–Contours
• Stratifications of Generically Illuminated Surfaces with Geometric Features
• Realizations of Abstract Mappings Representing Projection Singularities
• Statements of the Main Classification Results
• Part III-Classifications of Interactions of Pairs of Feature– Shade/Shadow–Contours
• Stable View Projections and Transitions involving Shade/Shadow Curves on a Smooth Surface (SC)
• Transitions involving Views of Geometric Features (FC)
• Part IV-Classifications of Multiple Interactions
• Transitions involving Geometric Features and Shade/Shadow Curves (SFC)
• Classifications of Stable Multilocal Configurations and Their Generic Transitions
• Bibliography.