Geometric Properties for Incomplete Data (eBook)

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2006 | 2006
XVI, 392 Seiten
Springer Netherland (Verlag)
978-1-4020-3858-7 (ISBN)

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Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area.

The book can be read both by specialists and graduate students in computer science, electrical engineering or mathematics who take an interest in data evaluations by approximation or interpolation, in particular data obtained in an image analysis context.


Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area. The book can be read both by specialists and graduate students in computer science, electrical engineering or mathematics who take an interest in data evaluations by approximation or interpolation, in particular data obtained in an image analysis context.

Contributors. Preface. I Continuous Geometry: Representation of Free-form Objects. Spheres and Conics. Algorithms for Spatial Pythagoreanhodograph Curves. Cumulative Chords, Piecewise-Quadratics and Piecewise-Cubics. Spherical Splines. Graph-Spectral Methods for Surface Height Recovery from Gauss Maps.- II Discrete Geometry: Segmentation of Boundaries into Convex and Concave Parts. Convex and Concave Parts of Digital Curves. Polygonalisation and Polyhedralisation by Optimisation. Binary Tomography by Iterating Linear Programs. Cascade of dual LDA Operators for Face Recognition. Precision of Geometric Moments in Picture Analysis. Shape-from-Shading by Iterative Fast Marching for Vertical and Oblique Light Sources. Shape from Shadows.- III Approximation and Regularization: A Confidence Measure for Variational Optic Flow Methods. Video Image Sequence Analysis: Estimating Missing Data and Segmenting Multiple Motions. Robust Local Approximation of Scattered Data. On Robust Estimation and Smoothing with Spatial and Tonal Kernels. Subspace Estimation with Uncertain and Correlated Data. On the use of Dual Norms in Bounded Variation Type Regularization.- Index.

Erscheint lt. Verlag 14.3.2006
Reihe/Serie Computational Imaging and Vision
Computational Imaging and Vision
Zusatzinfo XVI, 392 p.
Verlagsort Dordrecht
Sprache englisch
Themenwelt Informatik Grafik / Design Digitale Bildverarbeitung
Informatik Theorie / Studium Künstliche Intelligenz / Robotik
Mathematik / Informatik Mathematik Geometrie / Topologie
Technik
Schlagworte algorithms • Approximation • brandonwiskunde • computer vision • Discrete Geometry • Image Analysis • Interpolation • Moment • Shading
ISBN-10 1-4020-3858-5 / 1402038585
ISBN-13 978-1-4020-3858-7 / 9781402038587
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