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Mathematical Morphology: 40 Years On
Mathematical Morphology is a speciality in Image Processing and Analysis, which considers images as geometrical objects, to be analyzed through their interactions with other geometrical objects. It relies on several branches of mathematics, such as discrete geometry, topology, lattice theory, partial differential equations, integral geometry and geometrical probability. It has produced fast and efficient algorithms for computer analysis of images, and has found applications in bio-medical imaging, materials science, geoscience, remote sensing, quality control, document processing and data analysis. This book contains the 43 papers presented at the 7th International Symposium on Mathematical Morphology, held in Paris on April 18-20, 2005. It gives a lively state of the art of current research topics in this field. It also marks a milestone, the 40 years of uninterrupted development of this ever-expanding domain.
Topographical Tools for Filtering and Segmentation 2
Mathematical morphology has developed a powerful methodology for segmenting images, based on connected filters and watersheds. We have chosen the abstract framework of node- or edge-weighted graphs for an extensive mathematical and algorithmic description of these tools. Volume 2 proposes two physical models for describing valid flooding on a node- or edge-weighted graph, and establishes how to pass from one to another. Many new flooding algorithms are derived, allowing parallel and local flooding of graphs. Watersheds and flooding are then combined for solving real problems. Their ability to model a real hydrographic basin represented by its digital elevation model constitutes a good validity check of the underlying physical models. The last part of Volume 2 explains why so many different watershed partitions exist for the same graph. Marker-based segmentation is the method of choice for curbing this proliferation. This book proposes new algorithms combining the advantages of the previous methods which treated node- and edge-weighted graphs differently.
Topographical Tools for Filtering and Segmentation 1
Mathematical morphology has developed a powerful methodology for segmenting images, based on connected filters and watersheds. We have chosen the abstract framework of node- or edge-weighted graphs for an extensive mathematical and algorithmic description of these tools. Volume 1 is devoted to watersheds. The topography of a graph appears by observing the evolution of a drop of water moving from node to node on a weighted graph, along flowing paths, until it reaches regional minima. The upstream nodes of a regional minimum constitute its catchment zone. The catchment zones may be constructed independently of each other and locally, in contrast with the traditional approach where the catchment basins have to be constructed all at the same time. Catchment zones may overlap, and thus, a new segmentation paradigm is proposed in which catchment zones cover each other according to a priority order. The resulting partition may then be corrected, by local and parallel treatments, in order to achieve the desired precision.
Knowledge and Context in Tibetan Medicine
Knowledge and Context in Tibetan Medicine is a collection of essays dedicated to the description and interpretation of Tibetan medical knowledge across different historical, cultural, and intellectual contexts.
Current Catalog
First multi-year cumulation covers six years: 1965-70.
Mathematical Morphology and its Applications to Image and Signal Processing
This book contains the proceedings of the International Symposium on Mathematical Morphology and its Applications to Image and Signal Processing IV, held June 3-5, 1998, in Amsterdam, The Netherlands. The purpose of the work is to provide the image analysis community with a sampling of recent developments in theoretical and practical aspects of mathematical morphology and its applications to image and signal processing. Among the areas covered are: digitization and connectivity, skeletonization, multivariate morphology, morphological segmentation, color image processing, filter design, gray-scale morphology, fuzzy morphology, decomposition of morphological operators, random sets and statistical inference, differential morphology and scale-space, morphological algorithms and applications. Audience: This volume will be of interest to research mathematicians and computer scientists whose work involves mathematical morphology, image and signal processing.
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