Vision With Direction

by Bigun, Josef

• ISBN13: 9783540273226
• ISBN10: 3540273220
• Format: Hardcover
• Copyright: 2006-04-30
• Publisher: Springer-Verlag New York Inc

Summary

This introductory textbook presents the modern signal processing concepts used in computer vision and image analysis in a systematic and mathematically coherent way. For the first time in a textbook on image processing, single direction, group direction, corners and edges, Hough transform, and motion estimation are developed in a principled way using direction tensors as the unifying concept. The topics presented include Hilbert spaces, the Fourier transform, scale analysis, direction fields, structure tensors, motion tensors, the Hough transform, grouping, and segmentation. Directional signal processing, an increasingly crucial element of computer vision for which neural circuits exist in human vision, is dealt with in depth by use of tensors. All chapters are richly illustrated, with color graphics from cover to cover; applications are studied in various fields, including biometric person authentication, texture analysis, optical character recognition, and motion estimation and tracking; and exercises help the sudent verify progress.Developed out of courses given by the author, this introductory textbook addresses advanced undergarduates as well as master and PhD students in computer science, engineering, mathematics, and in other disciplines where techniques from computer vision, image processing, visual computation and signal analysis are applied.

Author Biography

A fellow of the Institute of Electrical and Electronic Engineering (IEEE) and the International Association for Pattern Recognition (IAPR), Josef Bigun obtained his Ms and Ph.D. degrees from Linkoping University, Sweden, in 1983 and 1988 respectively. In 1988, he joined the Swiss Federal Institute of Technology in Lausanne where he worked as Adjoint Scientifique until 1998 with the exception that in 1997 he was a visiting professor at the Royal Institute of Technology, (KTH) Stockholm. He has been elected professor to the Signal Analysis Chair, his current position, at Halmstad University and Chalmers Institute of Technology in 1998. He has been in technical and organizational committees of numerous national and international conferences. In particular, he co-chaired the First International Conference on Audio and Video Based Person Authentication in 1997. He has been contributing as a referee or as an editorial board member of international journals including Pattern Recognition Letters and IEEE Image Processing. He has contributed to the initiation and progress of several national and international research projects in computer vision, in particular in biometric person authentication, e.g. the EU projects IT-VIRSBS, ACTS-M2VTS, NOE-BIOSECURE.

Table of Contents

Part I Human and Computer Vision
Neuronal Pathways of Vision	3	(18)
Optics and Visual Fields of the Eye	3	(2)
Photoreceptors of the Retina	5	(2)
Ganglion Cells of the Retina and Receptive Fields	7	(2)
The Optic Chiasm	9	(1)
Lateral Geniculate Nucleus (LGN)	10	(1)
The Primary Visual Cortex	11	(2)
Spatial Direction, Velocity, and Frequency Preference	13	(4)
Face Recognition in Humans	17	(2)
Further Reading	19	(2)
Color	21	(14)
Lens and Color	21	(1)
Retina and Color	22	(2)
Neuronal Operations and Color	24	(2)
The 1931 CIE Chromaticity Diagram and Colorimetry	26	(4)
RGB: Red, Green, Blue Color Space	30	(1)
HSB: Hue, Saturation, Brightness Color Space	31	(4)
Part II Linear Tools of Vision
Discrete Images and Hilbert Spaces	35	(22)
Vector Spaces	35	(2)
Discrete Image Types, Examples	37	(3)
Norms of Vectors and Distances Between Points	40	(4)
Scalar Products	44	(2)
Orthogonal Expansion	46	(2)
Tensors as Hilbert Spaces	48	(5)
Schwartz Inequality, Angles and Similarity of Images	53	(4)
Continuous Functions and Hilbert Spaces	57	(4)
Functions as a Vector Space	57	(1)
Addition and Scaling in Vector Spaces of Functions	58	(1)
A Scalar Product for Vector Spaces of Functions	59	(1)
Orthogonality	59	(1)
Schwartz Inequality for Functions, Angles	60	(1)
Finite Extension or Periodic Functions---Fourier Coefficients	61	(8)
The Finite Extension Functions Versus Periodic Functions	61	(1)
Fourier Coefficients (FC)	62	(3)
(Parseval--Plancherel) Conservation of the Scalar Product	65	(2)
Hermitian Symmetry of the Fourier Coefficients	67	(2)
Fourier Transform---Infinite Extension Functions	69	(16)
The Fourier Transform (FT)	69	(3)
Sampled Functions and the Fourier Transform	72	(7)
Discrete Fourier Transform (DFT)	79	(3)
Circular Topology of DFT	82	(3)
Properties of the Fourier Transform	85	(18)
The Dirac Distribution	85	(3)
Conservation of the Scalar Product	88	(2)
Convolution, FT, and the δ	90	(4)
Convolution with Separable Filters	94	(1)
Poisson Summation Formula, the Comb	95	(3)
Hermitian Symmetry of the FT	98	(1)
Correspondences Between FC, DFT, and FT	99	(4)
Reconstruction and Approximation	103	(16)
Characteristic and Interpolation Functions in N Dimensions	103	(6)
Sampling Band-Preserving Linear Operators	109	(5)
Sampling Band-Enlarging Operators	114	(5)
Scales and Frequency Channels	119	(34)
Spectral Effects of Down-and Up-Sampling	119	(6)
The Gaussian as Interpolator	125	(2)
Optimizing the Gaussian Interpolator	127	(3)
Extending Gaussians to Higher Dimensions	130	(4)
Gaussian and Laplacian Pyramids	134	(2)
Discrete Local Spectrum, Gabor Filters	136	(6)
Design of Gabor Filters on Nonregular Grids	142	(4)
Face Recognition by Gabor Filters, an Application	146	(7)
Part III Vision of Single Direction
Direction in 2D	153	(56)
Linearly Symmetric Images	153	(10)
Real and Complex Moments in 2D	163	(1)
The Structure Tensor in 2D	164	(4)
The Complex Representation of the Structure Tensor	168	(3)
Linear Symmetry Tensor: Directional Dominance	171	(1)
Balanced Direction Tensor: Directional Equilibrium	171	(2)
Decomposing the Complex Structure Tensor	173	(2)
Decomposing the Real-Valued Structure Tensor	175	(1)
Conventional Corners and Balanced Directions	176	(1)
The Total Least Squares Direction and Tensors	177	(3)
Discrete Structure Tensor by Direct Tensor Sampling	180	(6)
Application Examples	186	(1)
Discrete Structure Tensor by Spectrum Sampling (Gabor)	187	(9)
Relationship of the Two Discrete Structure Tensors	196	(3)
Hough Transform of Lines	199	(3)
The Structure Tensor and the Hough Transform	202	(3)
Appendix	205	(4)
Direction in Curvilinear Coordinates	209	(36)
Curvilinear Coordinates by Harmonic Functions	209	(4)
Lie Operators and Coordinate Transformations	213	(2)
The Generalized Structure Tensor (GST)	215	(6)
Discrete Approximation of GST	221	(3)
The Generalized Hough Transform (GHT)	224	(2)
Voting in GST and GHT	226	(2)
Harmonic Monomials	228	(2)
``Steerability'' of Harmonic Monomials	230	(1)
Symmetry Derivatives and Gaussians	231	(2)
Discrete GST for Harmonic Monomials	233	(3)
Examples of GST Applications	236	(2)
Further Reading	238	(2)
Appendix	240	(5)
Direction in ND, Motion as Direction	245	(32)
The Direction of Hyperplanes and the Inertia Tensor	245	(4)
The Direction of Lines and the Structure Tensor	249	(3)
The Decomposition of the Structure Tensor	252	(3)
Basic Concepts of Image Motion	255	(3)
Translating Lines	258	(1)
Translating Points	259	(4)
Discrete Structure Tensor by Tensor Sampling in ND	263	(4)
Affine Motion by the Structure Tensor in 7D	267	(3)
Motion Estimation by Differentials in Two Frames	270	(2)
Motion Estimation by Spatial Correlation	272	(2)
Further Reading	274	(1)
Appendix	275	(2)
World Geometry by Direction in N Dimensions	277	(34)
Camera Coordinates and Intrinsic Parameters	277	(6)
World Coordinates	283	(4)
Intrinsic and Extrinsic Matrices by Correspondence	287	(6)
Reconstructing 3D by Stereo, Triangulation	293	(7)
Searching for Corresponding Points in Stereo	300	(5)
The Fundamental Matrix by Correspondence	305	(2)
Further Reading	307	(1)
Appendix	308	(3)
Part IV Vision of Multiple Directions
Group Direction and N-Folded Symmetry	311	(18)
Group Direction of Repeating Line Patterns	311	(3)
Test Images by Logarithmic Spirals	314	(1)
Group Direction Tensor by Complex Moments	315	(3)
Group Direction and the Power Spectrum	318	(2)
Discrete Group Direction Tensor by Tensor Sampling	320	(4)
Group Direction Tensors as Texture Features	324	(2)
Further Reading	326	(3)
Part V Grouping, Segmentation, and Region Description
Reducing the Dimension of Features	329	(12)
Principal Component Analysis (PCA)	329	(6)
PCA for Rare Observations in Large Dimensions	335	(3)
Singular Value Decomposition (SVD)	338	(3)
Grouping and Unsupervised Region Segregation	341	(18)
The Uncertainty Principle and Segmentation	341	(3)
Pyramid Building	344	(1)
Clustering Image Features---Perceptual Grouping	345	(2)
Fuzzy C-Means Clustering Algorithm	347	(1)
Establishing the Spatial Continuity	348	(3)
Boundary Refinement by Oriented Butterfly Filters	351	(3)
Texture Grouping and Boundary Estimation Integration	354	(2)
Further Reading	356	(3)
Region and Boundary Descriptors	359	(18)
Morphological Filtering of Regions	359	(5)
Connected Component Labelling	364	(2)
Elementary Shape Features	366	(2)
Moment-Based Description of Shape	368	(3)
Fourier Descriptors and Shape of a Region	371	(6)
Concluding Remarks	377	(2)
References	379	(12)
Index	391