Mathematical Morphology and Its Applications to Image Processing: (2 Computational Imaging and Vision)

Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analysing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, etc. MM is not only a theory, but also a powerful image analysis technique. The purpose of the present book is to provide the image analysis community with a snapshot of current theoretical and applied developments of MM. The book consists of forty-five contributions classified by subject. It demonstrates a wide range of topics suited to the morphological approach.

Table of Contents:
Theory.- Set operator decomposition and conditionally translation invariant elementary operators.- Mutational equations of morphological dilation tubes.- Thresholdings, umbrae, residuals, and surpluses of l-images.- Filtering.- Adaptive parameterized openings.- Synthesis of adaptive weighted order statistic filters with gradient algorithms.- A spatially variant, locally adaptive, background normalization operator.- Using genetic algorithms in the design of morphological filters.- Minimal generator basis of a finite structural opening.- Segmentation.- Watershed, hierarchical segmentation and waterfall algorithm.- Minimum spanning forests for morphological segmentation.- The flat zone approach and color images.- Joint region and motion estimation with morphological tools.- Morphological segmentation of image sequences.- Sampling.- Critical morphological sampling and applications to image coding.- A sampling approach based on equicontinuity.- Coding.- Application of morphological filters for contour image sequence coding.- The geodesic morphological skeleton and fast transformation algorithms.- Multi—parameter skeleton decomposition.- Representations and slope transform.- Morphological systems theory: slope transforms, Max—Min differential equations, envelope filters, and sampling.- Two dual representations of morphology based on the parallel normal transport property.- Dominance and incidence structures with applications to stochastic geometry and mathematical morphology.- Granulometries and shape description.- The multiscale morphology decomposition theorem.- Statistical pattern spectrum for binary pattern recognition.- Generalized geodesic distances applied to interpolation and shape description.- Random models and tessellations.- Performance analysis of amorphological Voronoï tessellation algorithm.- Optimization in Voronoï diagrams.- A stochastic tessellation of digital space.- Liquid phase sintered materials modelling by random closed sets.- Monte-Carlo estimation of morphological granulometric discrete size distributions.- Algorithmic techniques.- On the implementation of morphological operations.- An evaluation of priority queues for mathematical morphology.- One pixel thick skeletons.- Fast grayscale granulometry algorithms.- An efficient implementation technique of adaptive morphological operations.- Implementation of a distributed watershed algorithm.- Visualization of Minkowski operations by computer graphics techniques.- Morphogenesis simulations with lattice gas.- Biological applications.- Single object geometry — the stereology of registered serial sections.- Texture classification using neural networks and local granulometries.- Fusion of MR and CT images of the human brain using multiresolution morphology.- Morphological scheme for morphometric analysis of epidermal biopsy images.- Automatic quantification of spine parameters from X—ray images by means of morphological tools.- Industrial and remote sensing applications.- Image Processing: a key to success in industrial applications.- Radar images analysis using morphological filters.- Application of morphological operators to supervised multidimensional data classification.- Appendix A.- The “Centre de Morphologie Mathémathique”: an overview.- Appendix B.- List of posters contributions presented at ISMM’94.- Author Index.