Local Features in Natural Images via Singularity Theory

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.