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Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. Th...
This book is a concise but thorough introduction to the tools commonly used in pattern recognition and machine learning, including classification, dimensionality reduction, regression, and clustering, as well as recent popular topics such as deep neural networks and Gaussian process regression. The Second Edition is thoroughly revised, featuring a new chapter on the emerging topic of physics-informed machine learning and additional material on deep neural networks. Combining theory and practice, this book is suitable for the graduate or advanced undergraduate level classroom and self-study. It fills the need of a mathematically-rigorous text that is relevant to the practitioner as well, with datasets from applications in bioinformatics and materials informatics used throughout to illustrate the theory. These datasets are available from the book website to be used in end-of-chapter coding assignments based on python and Keras/Tensorflow. All plots in the text were generated using python scripts and jupyter notebooks, which can be downloaded from the book website.
The refereed proceedings of the 4th International Conference on Scale Space Methods in Computer Vision, Scale-Space 2003, held at Isle of Skye, UK in June 2003. The 56 revised full papers presented were carefully reviewed and selected from 101 submissions. The book offers topical sections on deep structure representations, scale space mathematics, equivalences, implementing scale spaces, minimal approaches, evolution equations, local structure, image models, morphological scale spaces, temporal scale spaces, shape, and motion and stereo.
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.
This book explains the state-of-the-art algorithms used to simulate biological dynamics. Each technique is theoretically introduced and applied to a set of modeling cases. Starting from basic simulation algorithms, the book also introduces more advanced techniques that support delays, diffusion in space, or that are based on hybrid simulation strategies. This is a valuable self-contained resource for graduate students and practitioners in computer science, biology and bioinformatics. An appendix covers the mathematical background, and the authors include further reading sections in each chapter.
Mathematical Nonlinear Image Processing deals with a fast growing research area. The development of the subject springs from two factors: (1) the great expansion of nonlinear methods applied to problems in imaging and vision, and (2) the degree to which nonlinear approaches are both using and fostering new developments in diverse areas of mathematics. Mathematical Nonlinear Image Processing will be of interest to people working in the areas of applied mathematics as well as researchers in computer vision. Mathematical Nonlinear Image Processing is an edited volume of original research. It has also been published as a special issue of the Journal of Mathematical Imaging and Vision. (Volume 2, Issue 2/3).
Provides a broad sampling of the most recent theoretical and practical developments in applications to image processing and analysis.