The fields of image analysis, computer vision, and artificial intelligence all make use of descriptions of shape in grey-level images. Most existing algorithms for the automatic recognition and classification of particular shapes have been devel­ oped for specific purposes, with the result that these methods are often restricted in their application. The use of advanced and theoretically well-founded math­ ematical methods should lead to the construction of robust shape descriptors having more general application. Shape description can be regarded as a meeting point of vision research, mathematics, computing science, and the application fields of image analy­ sis, computer vision, and artificial intelligence. The NATO Advanced Research Workshop "Shape in Picture" was organised with a twofold objective: first, it should provide all participants with an overview of relevant developments in these different disciplines; second, it should stimulate researchers to exchange original results and ideas across the boundaries of these disciplines. This book comprises a widely drawn selection of papers presented at the workshop, and many contributions have been revised to reflect further progress in the field. The focus of this collection is on mathematical approaches to the construction of shape descriptions from grey-level images. The book is divided into five parts, each devoted to a different discipline. Each part contains papers that have tutorial sections; these are intended to assist the reader in becoming acquainted with the variety of approaches to the problem.

Inhalt

The Khalimsky Line as a Foundation for Digital Topology.- Topological Foundations of Shape Analysis.- A New Concept for Digital Geometry.- Theoretical Approaches to N-Dimensional Digital Objects.- On Boundaries and Boundary Crack-Codes of Multidimensional Digital Images.- Studying Shape Through Size Functions.- to Categorical Shape Theory, with Applications in Mathematical Morphology.- Shape Theory: an ANR-Sequence Approach.- Can Categorical Shape Theory Handle Grey-level Images?.- Mathematical Morphology as a Tool for Shape Description.- On Information Contained in the Erosion Curve.- Morphological Area Openings and Closings for Grey-scale Images.- Manifold Shape: from Differential Geometry to Mathematical Morphology.- On Negative Shape.- An Overview of the Theory and Applications of Wavelets.- Fractal Surfaces, Multiresolution Analyses, and Wavelet Transforms.- Interpolation in Multiscale Representations.- Discrete Stochastic Growth Models for Two-Dimensional Shapes.- Classical and Fuzzy Differential Methods in Shape Analysis.- Elements of a Fuzzy Geometry for Visual Space.- On the Relationship Between Surface Covariance and Differential Geometry.- Image Representation Using Affine Covariant Coordinates.- Equivariant Dynamical Systems: a Formal Model for the Generation of Arbitrary Shapes.- Neural Processing of Overlapping Shapes.- Contour Texture and Frame Curves for the Recognition of Non-Rigid Objects.- Conic Primitives for Projectively Invariant Representation of Planar Curves.- Blind Approximation of Planar Convex Shapes.- Recognition of Affine Planar Curves Using Geometric Properties.- Recognizing 3-D Curves from a Stereo Pair of Images: a Semi-differential Approach.- Statistical Shape Methodology in Image Analysis.- Recognition of Shapes from a Finite Series of Plane Figures.- Polygonal Harmonic Shape Characterization.- Shape Description and Classification Using the Interrelationship of Structures at Multiple Scales.- Learning Shape Classes.- Inference of Stochastic Graph Models for 2-D and 3-D Shapes.- Hierarchical Shape Analysis in Grey-level Images.- Irregular Curve Pyramids.- Multiresolution Shape Description by Corners.- Model-based Bottom-Up Grouping of Geometric Image Primitives.- Hierarchical Shape Representation for Image Analysis.- Scale-Space for N-dimensional Discrete Signals.- Scale-Space Behaviour and Invariance Properties of Differential Singularities.- Exploring the Shape Manifold: the Role of Conservation Laws.- Performance in Noise of a Diffusion-based Shape Descriptor.- Towards a Morphological Scale-Space Theory.- Geometry-based Image Segmentation Using Anisotropic Diffusion.- Images: Regular Tempered Distributions.- Local and Multilocal Scale-Space Description.- List of Authors.