Geometric Properties for Incomplete Data

ISBN-13: 9789048169825 / Angielski / Miękka / 2010 / 392 str.

Reinhard Klette;Ryszard Kozera;Lyle Noakes

Opis

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.

Recenzje

From the reviews:

"This compendium should be treated as a higher-level text with the target audience being computer scientists, electrical engineers, and mathematician, both in the research and industrial settings. Graduate-level students interested in pursuing advanced treatments of the topic can benefit from reading this book as well. ... This text is an important and worthwhile contribution to the computational imaging and vision literature; it is easy to read and rigorous in its mathematical development." (R. Goldberg, ACM Computing Reviews, Vol. 49 (4), April, 2008)

Spis treści

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.

O autorze

Joachim Weickert is Full Professor of Mathematics and Computer Science at Saarland University (Saarbrücken, Germany) where he heads the Mathematical Image Analysis Group. He performs research in image processing, computer vision and scientific computing, focusing on techniques based on partial differential equations and variational methods.