Geometric Properties for Incomplete Data

by Klette, Reinhard; Kozera, Ryszard; Noakes, Lyle; Weickert, Joachim

• ISBN13: 9781402038570
• ISBN10: 1402038577
• Format: Hardcover
• Copyright: 2006-01-31
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

Contributors	vii
Preface	xiii
I. Continuous Geometry	1	(122)
The Twist Representation of Free-form Objects	3	(20)
G. Sommer
B. Rosenhahn
C. Perwass
Uncertain Geometry with Circles, Spheres and Conics	23	(20)
C. Perwass
W. Forstner
Algorithms for spatial Pythagorean-hodograph curves	43	(16)
R. T. Farouki
C. Y. Han
Cumulative Chords, Piecewise-Quadratics and Piecewise-Cubics	59	(18)
L. Noakes
R. Kozera
Spherical Splines	77	(26)
L. Noakes
Graph-Spectral Methods for Surface Height Recovery from Gauss Maps	103	(20)
A. Robles-Kelly
E. R. Hancock
II. Discrete Geometry	123	(158)
Segmentation of Boundaries into Convex and Concave Parts	125	(20)
U. Eckhardt
Convex and Concave Parts of Digital Curves	145	(16)
H. Dorksen-Reiter
I. Debled-Rennesson
Polygonalisation and Polyhedralisation by Optimisation	161	(22)
T. K. Linh
A. Imiya
A. Torii
Binary Tomography by Iterating Linear Programs	183	(16)
S. Weber
Ch. Schnorr
Th. Schule
J. Hornegger
Cascade of dual LDA operators for face recognition	199	(22)
W. Skarbek
K. Kucharski
M. Bober
Precision of Geometric Moments in Picture Analysis	221	(16)
M. N. Huxley
R. Klette
J. Zunic
Shape-from-Shading by Iterative Fast Marching for Vertical and Oblique Light Sources	237	(22)
A. Tankus
N. Sochen
Y. Yeshurun
Shape from Shadows	259	(22)
A. Imiya
III. Approximation and Regularization	281	(110)
A Confidence Measure for Variational Optic Flow Methods	283	(16)
A. Bruhn
J. Weickert
Video Image Sequence Analysis: Estimating Missing Data and Segmenting Multiple Motions	299	(18)
K. Kanatani
Y. Sugaya
Robust local approximation of scattered data	317	(18)
M. Fenn
G. Steidl
On Robust Estimation and Smoothing with Spatial and Tonal Kernels	335	(18)
P. Mrazek
J. Weickert
A. Bruhn
Subspace Estimation with Uncertain and Correlated Data	353	(20)
M. Muhlich
On the use of Dual Norms in Bounded Variation Type Regularization	373	(18)
A. Obereder
S. Osher
O. Scherzer
Index	391