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Computer vision is a rapidly growing field which aims to make computers 'see' as effectively as humans. In this book Dr Shapiro presents a new computer vision framework for interpreting time-varying imagery. This is an important task, since movement reveals valuable information about the environment. The fully-automated system operates on long, monocular image sequences containing multiple, independently-moving objects, and demonstrates the practical feasibility of recovering scene structure and motion in a bottom-up fashion. Real and synthetic examples are given throughout, with particular emphasis on image coding applications. Novel theory is derived in the context of the affine camera, a generalisation of the familiar scaled orthographic model. Analysis proceeds by tracking 'corner features' through successive frames and grouping the resulting trajectories into rigid objects using new clustering and outlier rejection techniques. The three-dimensional motion parameters are then computed via 'affine epipolar geometry', and 'affine structure' is used to generate alternative views of the object and fill in partial views. The use of all available features (over multiple frames) and the incorporation of statistical noise properties substantially improves existing algorithms, giving greater reliability and reduced noise sensitivity.

Image processing --- Geometry, Affine --- Mathematical models --- Data processing.

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Geometry, Affine. --- Geometry, Projective. --- Géométrie affine. --- Géométrie projective. --- Géométrie affine. --- Géométrie projective.

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This book provides a self-contained introduction to diagram geometry.  Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples.  Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry.  Group theorists will find examples of the use of diagram geometry.  Light on matroid theory is shed from the point of view of geometry with linear diagrams.  Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective.  Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.  .

geometrie --- wiskunde --- Geometry --- Mathematics --- Geometry, Projective --- Geometry, Affine --- Géométrie projective --- Géométrie affine --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Geometry, Projective. --- Geometry, Affine. --- Geometry. --- Euclid's Elements --- Finite geometries.

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Affine geometry and quadrics are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range of disciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstructing the author’s reasoning. The provision of a large number of exercises with hints will help students to develop their problem solving skills and will also be a useful resource for lecturers when setting work for independent study. Affinities, Euclidean Motions and Quadrics takes rudimentary, and often taken-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained book ideal for self-study that is not only foundational but unique in its approach.’ This text will be of use to lecturers in linear algebra and its applications to geometry as well as advanced undergraduate and beginning graduate students.

Geometry, Affine. --- Geometry, Plane. --- Quadrics. --- Geometry, Affine --- Geometry, Plane --- Quadrics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Geometry --- Surfaces, Conic --- Surfaces, Quadric --- Plane geometry --- Affine geometry --- Mathematics. --- Algebra. --- Mathematics, general. --- Paraboloid --- Surfaces --- Geometry, Modern --- Math --- Science --- Mathematical analysis

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Geometry, Affine --- Géométrie affine. --- Algèbre. --- Algebra --- Algèbre linéaire. --- Algebras, Linear. --- Géométrie affine. --- Algèbre. --- Algèbre linéaire.