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Based on the second Women in Shape (WiSH) workshop held in Sirince, Turkey in June 2016, these proceedings offer the latest research on shape modeling and analysis and their applications. The 10 peer-reviewed articles in this volume cover a broad range of topics, including shape representation, shape complexity, and characterization in solving image-processing problems. While the first six chapters establish understanding in the theoretical topics, the remaining chapters discuss important applications such as image segmentation, registration, image deblurring, and shape patterns in digital fabrication. The authors in this volume are members of the WiSH network and their colleagues, and most were involved in the research groups formed at the workshop. This volume sheds light on a variety of shape analysis methods and their applications, and researchers and graduate students will find it to be an invaluable resource for further research in the area.

Mathematics. --- Numerical analysis. --- Mathematical models. --- Mathematical Modeling and Industrial Mathematics. --- Numerical Analysis. --- Models, Mathematical --- Simulation methods --- Mathematical analysis --- Math --- Science --- Shape theory (Topology) --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces

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How do buildings store information and experience in their shape and form? Michael Leyton has attracted considerable attention with his interpretation of geometrical form as a medium for the storage of information and memory. In this publication he draws specific conclusions for the field of architecture and construction, attaching fundamental importance to the complex relationship between symmetry and asymmetry.

Geometry in architecture. --- Architectural design --- Shape theory (Topology) --- Memory (Philosophy) --- Symmetry (Art) --- Data processing. --- Form (Aesthetics) --- Proportion (Art) --- Philosophy --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Architecture --- Composition, proportion, etc. --- Geometry in architecture --- 72.012/013 --- 514 --- Data processing --- Architectonisch ontwerp --- Architectuurontwerp --- Ontwerp (architectuur) --- Geometrie --- Meetkunde --- Architectural History and Theory. --- History.

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Statistical models of shape, learnt from a set of examples, are a widely-used tool in image interpretation and shape analysis. Integral to this learning process is the establishment of a dense groupwise correspondence across the set of training examples. This book gives a comprehensive and up-to-date account of the optimisation approach to shape correspondence, and the question of evaluating the quality of the resulting model in the absence of ground-truth data. It begins with a complete account of the basics of statistical shape models, for both finite and infinite-dimensional representations of shape, and includes linear, non-linear, and kernel-based approaches to modelling distributions of shapes. The optimisation approach is then developed, with a detailed discussion of the various objective functions available for establishing correspondence, and a particular focus on the Minimum Description Length approach. Various methods for the manipulation of correspondence for shape curves and surfaces are dealt with in detail, including recent advances such as the application of fluid-based methods. This complete and self-contained account of the subject area brings together results from a fifteen-year program of research and development. It includes proofs of many of the basic results, as well as mathematical appendices covering areas which may not be totally familiar to some readers. Comprehensive implementation details are also included, along with extensive pseudo-code for the main algorithms. Graduate students, researchers, teachers, and professionals involved in either the development or the usage of statistical shape models will find this an essential resource.

Computer Science. --- Pattern Recognition. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Image Processing and Computer Vision. --- Computer science. --- Computer vision. --- Optical pattern recognition. --- Informatique --- Vision par ordinateur --- Reconnaissance optique des formes (Informatique) --- Mathematical optimization. --- Shape theory (Topology) --Statistical methods. --- Shape theory (Topology) --- Mathematical optimization --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Statistical methods --- Statistical methods. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Computer graphics. --- Image processing. --- Pattern recognition. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Optical data processing. --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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Presenting the latest research from the growing field of mathematical shape analysis, this volume is comprised of the collaborations of participants of the Women in Shape Modeling (WiSh) workshop, held at UCLA's Institute for Pure and Applied Mathematics in July 2013. Topics include: Simultaneous spectral and spatial analysis of shape Dimensionality reduction and visualization of data in tree-spaces, such as classes of anatomical trees like airways and blood vessels Geometric shape segmentation, exploring shape segmentation from a Gestalt perspective, using information from the Blum medial axis of edge fragments in an image Representing and editing self-similar details on 3D shapes, studying shape deformation and editing techniques Several chapters in the book directly address the problem of continuous measures of context-dependent nearness and right shape models. Medical and biological applications have been a major source of motivation in shape research, and key topics are examined here in detail. All together, the chapters in the book cover an entire spectrum in shape analysis starting from raw images and ending with shape-related decisions.

Mathematics. --- Visualization. --- Mathematical Applications in Computer Science. --- Physiological, Cellular and Medical Topics. --- Mathematical Modeling and Industrial Mathematics. --- Physiology --- Mathématiques --- Visualisation --- Physiology_xMathematics. --- Engineering & Applied Sciences --- Computer Science --- Shape theory (Topology) --- Shapes --- Forms (Shapes) --- Shape --- Computer science --- Computer mathematics. --- Mathematical models. --- Biomathematics. --- Geometry --- Surfaces --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Animal physiology --- Animals --- Biology --- Anatomy --- Imagination --- Visual perception --- Imagery (Psychology) --- Computer science—Mathematics. --- Models, Mathematical --- Simulation methods --- Mathematics --- Computer mathematics --- Electronic data processing --- Math --- Science

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The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.

Operating systems (Computers),. --- Shape theory (Topology) --- Asymptotic expansions --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Engineering. --- Mathematical physics. --- Computer mathematics. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Computational Science and Engineering. --- Mathematical Applications in the Physical Sciences. --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Mechanics, applied. --- Computer science. --- Informatics --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing --- Mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory