Vision with Direction

A Systematic Introduction to Image Processing and Computer Vision

By: Josef Bigun

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Hardcover | 9 February 2006

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416 Pages

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23.5 x 15.5 x 1.91

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Image analysis is a computational feat which humans show excellence in, in comp- ison with computers. Yet the list of applications that rely on automatic processing of images has been growing at a fast pace. Biometric authentication by face, ?ngerprint, and iris, online character recognition in cell phones as well as drug design tools are but a few of its benefactors appearing on the headlines. This is, of course, facilitated by the valuable output of the resarch community in the past 30 years. The pattern recognition and computer vision communities that study image analysis have large conferences, which regularly draw 1000 parti- pants. In a way this is not surprising, because much of the human-speci?c activities critically rely on intelligent use of vision. If routine parts of these activities can be automated, much is to be gained in comfort and sustainable development. The - search ?eld could equally be called visualintelligence because it concerns nearly all activities of awake humans. Humans use or rely on pictures or pictorial languages to represent, analyze, and develop abstract metaphors related to nearly every aspect of thinking and behaving, be it science, mathematics, philosopy, religion, music, or emotions. The present volume is an introductory textbook on signal analysis of visual c- putation for senior-level undergraduates or for graduate students in science and - gineering. My modest goal has been to present the frequently used techniques to analyze images in a common framework-directional image processing.

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Non-Fiction Computing & I.T.Computer Science Image Processing Artificial Intelligence Computer Vision Graphical & Digital Media Applications Engineering & Technology Energy Technology & Engineering Electrical Engineering Other Technologies & Applied Sciences Applied Optics

Mathematics Applied Mathematics

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Published: 12th February 2010

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

Vision with Direction

A Systematic Introduction to Image Processing and Computer Vision

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Hardcover

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