This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.

The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new models, image analysis technique, fluid flow problems, etc. as applications of mathematical analysis and computational mathematics. The volume should bring forward new and emerging topics of mathematics and computing having potential applications and uses in other areas of sciences. It can serve as a valuable resource for graduate students, researchers and educators interested in mathematical tools and techniques for solving various problems arising in science and engineering.

This volume is a collection of chapters that present key ideas and theories, as well as their rigorous applications, required for the development of mathematical models in areas such as travelling waves, epidemiology, the chemotaxis system, atrial fibrillation, and vortex nerve complexes. The techniques, methodologies and approaches adopted in this book have relevance in several other fields including physics, biology, and sociology. Each chapter should also assist readers in comfortably comprehending the related and underlying ideas. The companion volume (Contemporary Mathematics, Volume 786) is devoted to principle and theory.

Zusammenfassung: This book offers a comprehensive and unbiased introduction to 3D Computer Vision, ranging from its foundations and essential principles to advanced methodologies and technologies. Divided into 11 chapters, it covers the main workflow of 3D computer vision as follows: camera imaging and calibration models; various modes and means of 3D image acquisition; binocular, trinocular and multi-ocular stereo vision matching techniques; monocular single-image and multi-image scene restoration methods; point cloud data processing and modeling; simultaneous location and mapping; generalized image and scene matching; and understanding spatial-temporal behavior. Each topic is addressed in a uniform manner: the dedicated chapter first covers the essential concepts and basic principles before presenting a selection of typical, specific methods and practical techniques. In turn, it introduces readers to the most important recent developments, especially in the last three years. This approach allows them to quickly familiarize themselves with the subject, implement the techniques discussed, and design or improve their own methods for specific applications. The book can be used as a textbook for graduate courses in computer science, computer engineering, electrical engineering, data science, and related subjects. It also offers a valuable reference guide for researchers and practitioners alike

Images or discrete objects, to be analyzed based on digital image data, need to be represented, analyzed, transformed, recovered etc. These problems have stimulated many interesting developments in theoretical foundations of image processing. This coherent anthology presents 27 state-of-the-art surveys and research papers on digital image geometry and topology. It is based on a winter school held at Dagstuhl Castle, Germany in December 2000 and offers topical sections on topology, representation, geometry, multigrid convergence, and shape similarity and simplification.

The 14th Iberoamerican Congress on Pattern Recognition (CIARP 2009, C- gresoIberoAmericanodeReconocimientodePatrones)formedthelatestofanow longseriesofsuccessfulmeetingsarrangedbytherapidlygrowingIberoamerican pattern recognition community. The conference was held in Guadalajara, Jalisco, Mexico and organized by the Mexican Association for Computer Vision, Neural Computing and Robotics (MACVNR). It was sponsodred by MACVNR and ?ve other Iberoamerican PR societies. CIARP 2009 was like the previous conferences in the series supported by the International Association for Pattern Recognition (IAPR). CIARP 2009 attracted participants from all over the world presenting sta- of-the-artresearchon mathematical methods and computing techniques for p- tern recognition, computer vision, image and signal analysis, robot vision, and speech recognition, as well as on a wide range of their applications. This time the conference attracted participants from 23 countries,9 in Ibe- america, and 14 from other parts of the world. The total number of submitted papers was 187, and after a serious review process 108 papers were accepted, all of them with a scienti?c quality above overall mean rating. Sixty-four were selected as oral presentations and 44 as posters. Since 2008 the conference is almost single track, and therefore there was no real grading in quality between oral and poster papers. As an acknowledgment that CIARP has established itself as a high-quality conference, its proceedings appear in the Lecture Notes in Computer Science series. Moreover, its visibility is further enhanced by a selection of a set of papers that will be published in a special issue of the journal Pattern Recognition Letters.

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

This book constitutes the refereed proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2009, held in Venice, Italy in May 2009. The 37 revised full papers presented were carefully reviewed and selected from 47 submissions. The papers are organized in topical sections on graph-based representation and recognition, graph matching, graph clustering and classification, pyramids, combinatorial maps, and homologies, as well as graph-based segmentation.

The subjects reviewed in the Advances in Imaging and Electron Physics series cover a broad range of themes including microscopy, electromagnetic fields and image coding. This book is essential reading for electrical engineers, applied mathematicians and robotics experts. - Emphasizes broad and in depth article collaborations between world-renowned scientists in the field of image and electron physics - Presents theory and it's application in a practical sense, providing long awaited solutions and new findings - Bridges the gap between academic researchers and R&D designers by addressing and solving daily issues