Shape in Picture: Mathematical Description of Shape in Grey-level Images

Front Matter....Pages i-x
Introduction....Pages 1-2
The Khalimsky Line as a Foundation for Digital Topology....Pages 3-20
Topological Foundations of Shape Analysis....Pages 21-36
A New Concept for Digital Geometry....Pages 37-51
Theoretical Approaches to N -Dimensional Digital Objects....Pages 53-70
On Boundaries and Boundary Crack-Codes of Multidimensional Digital Images....Pages 71-80
Studying Shape Through Size Functions....Pages 81-90
Introduction to Categorical Shape Theory, with Applications in Mathematical Morphology....Pages 91-110
Shape Theory: An ANR-Sequence Approach....Pages 111-125
Can Categorical Shape Theory Handle Grey-level Images?....Pages 127-146
Mathematical Morphology as a Tool for Shape Description....Pages 147-176
On Information Contained in the Erosion Curve....Pages 177-195
Morphological Area Openings and Closings for Grey-scale Images....Pages 197-208
Manifold Shape: from Differential Geometry to Mathematical Morphology....Pages 209-223
On Negative Shape....Pages 225-247
An Overview of the Theory and Applications of Wavelets....Pages 249-274
Fractal Surfaces, Multiresolution Analyses and Wavelet Transforms....Pages 275-290
Interpolation in Multiscale Representations....Pages 291-300
Discrete Stochastic Growth Models for Two-Dimensional Shapes....Pages 301-318
Classical and Fuzzy Differential Methods in Shape Analysis....Pages 319-332
Elements of a Fuzzy Geometry for Visual Space....Pages 333-342
On the Relationship Between Surface Covariance and Differential Geometry....Pages 343-352
Image Representation Using Affine Covariant Coordinates....Pages 353-362
Equivariant Dynamical Systems: a Formal Model for the Generation of Arbitrary Shapes....Pages 363-382
Neural Processing of Overlapping Shapes....Pages 383-392
Contour Texture and Frame Curves for the Recognition of Non-Rigid Objects....Pages 393-402
Conic Primitives for Projectively Invariant Representation of Planar Curves....Pages 403-414
Blind Approximation of Planar Convex Shapes....Pages 415-422
Recognition of Affine Planar Curves Using Geometric Properties....Pages 423-432
Recognizing 3-D Curves from a Stereo Pair of Images: a Semi-differential Approach....Pages 433-442
Statistical Shape Methodology in Image Analysis....Pages 443-452
Recognition of Shapes from a Finite Series of Plane Figures....Pages 453-462
Polygonal Harmonic Shape Characterization....Pages 463-472
Shape Description and Classification Using the Interrelationship of Structures at Multiple Scales....Pages 473-482
Learning Shape Classes....Pages 483-492
Inference of Stochastic Graph Models for 2-D and 3-D Shapes....Pages 493-510
Hierarchical Shape Analysis in Grey-level Images....Pages 511-524
Irregular Curve Pyramids....Pages 525-537
Multiresolution Shape Description by Corners....Pages 539-548
Model-based Bottom-Up Grouping of Geometric Image Primitives....Pages 549-558
Hierarchical Shape Representation for Image Analysis....Pages 559-570
Scale-Space for N -Dimensional Discrete Signals....Pages 571-590
Scale-Space Behaviour and Invariance Properties of Differential Singularities....Pages 591-600
Exploring the Shape Manifold: the Role of Conservation Laws....Pages 601-620
Performance in Noise of a Diffusion-based Shape Descriptor....Pages 621-630
Towards a Morphological Scale-Space Theory....Pages 631-640
Geometry-based Image Segmentation Using Anisotropic Diffusion....Pages 641-650
Images: Regular Tempered Distributions....Pages 651-659
Local and Multilocal Scale-Space Description....Pages 661-670
Back Matter....Pages 671-682