Local Features in Natural Images via Singularity Theory

Description

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. Front Matter....Pages i-x Front Matter....Pages 1-1 Introduction....Pages 3-10 Overview....Pages 11-20 Front Matter....Pages 21-21 Apparent Contours for Projections of Smooth Surfaces....Pages 23-33 Abstract Classification of Singularities Preserving Features....Pages 35-39 Singularity Equivalence Groups Capturing Interactions....Pages 41-71 Methods for Classification of Singularities....Pages 73-99 Methods for Topological Classification of Singularities....Pages 101-114 Front Matter....Pages 115-115 Stratifications of Generically Illuminated Surfaces with Geometric Features....Pages 117-134 Realizations of Abstract Mappings Representing Projection Singularities....Pages 135-155 Statements of the Main Classification Results....Pages 157-177 Front Matter....Pages 179-179 Stable View Projections and Transitions Involving Shade/Shadow Curves on a Smooth Surface (SC)....Pages 181-191 Transitions Involving Views of Geometric Features (FC)....Pages 193-212 Front Matter....Pages 213-213 Transitions Involving Geometric Features and Shade/Shadow Curves (SFC)....Pages 215-241 Classifications of Stable Multilocal Configurations and Their Generic Transitions....Pages 243-252 Back Matter....Pages 253-257