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Signal Processing for Computer Vision is a unique and thorough treatment of the signal processing aspects of filters and operators for low-level computer vision.
Computer vision has progressed considerably over recent years. From methods only applicable to simple images, it has developed to deal with increasingly complex scenes, volumes and time sequences. A substantial part of this book deals with the problem of designing models that can be used for several purposes within computer vision. These partial models have some general properties of invariance generation and generality in model generation.
Signal Processing for Computer Vision is the first book to give a unified treatment of representation and filtering of higher order data, such as vectors and tensors in multidimensional space. Included is a systematic organisation for the implementation of complex models in a hierarchical modular structure and novel material on adaptive filtering using tensor data representation.
Signal Processing for Computer Vision is intended for final year undergraduate and graduate students as well as engineers and researchers in the field of computer vision and image processing.


Signal Processing for Computer Vision is a unique and thorough treatment of the signal processing aspects of filters and operators for low-level computer vision.
Computer vision has progressed considerably over recent years. From methods only applicable to simple images, it has developed to deal with increasingly complex scenes, volumes and time sequences. A substantial part of this book deals with the problem of designing models that can be used for several purposes within computer vision. These partial models have some general properties of invariance generation and generality in model generation.
Signal Processing for Computer Vision is the first book to give a unified treatment of representation and filtering of higher order data, such as vectors and tensors in multidimensional space. Included is a systematic organisation for the implementation of complex models in a hierarchical modular structure and novel material on adaptive filtering using tensor data representation.
Signal Processing for Computer Vision is intended for final year undergraduate and graduate students as well as engineers and researchers in the field of computer vision and image processing.

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CONTENTS
PREFACE = ⅸ
1 INTRODUCTION AND OVERVIEW = 1
 1.1 Hierarchical Computing Structures = 3
 1.2 Low level representation and operations = 12
 1.3 Description in terms of symmetry = 20
 1.4 Cascading of operations = 24
 1.5 Compatibility representation = 25
 1.6 Description of size and scale = 27
 1.7 Model based processing = 33
 1.8 Representation of volumes and time sequences = 38
 1.9 Classification and response generation = 39
2 BIOLOGICAL VISION = 41
 2.1 Motivation = 41
 2.2 Overview of the visual system = 42
 2.3 Properties of neurons = 43
 2.4 The retina = 49
 2.5 Color vision = 59
 2.6 The visual pathways and the lateral geniculate nucleus = 67
 2.7 The primary visual cortex = 69
 2.8 Columnar organization and the layers of the cortex = 75
 2.9 Possible implementations of filters = 80
 2.10 Channel organization of features = 83
 2.11 The visual pathways beyond the primary visual cortex = 89
3 LOW LEVEL OPERATIONS = 97
 3.1 Information representation = 97
 3.2 Complex valued convolution functions = 102
 3.3 Compact representation = 105
 3.4 Examples of processing = 109
 3.5 More on compatibility representation = 112
 3.6 General properties of a useful information representation = 114
4 FOURIER TRANSFORMS = 117
 4.1 Introduction = 119
 4.2 Basics = 122
 4.3 Three aspects of the Fourier transform = 143
 4.4 Separability = 153
 4.5 Analytic signals = 164
 4.6 Examples of statistical calculations = 174
 4.7 Transform pairs = 177
 4.8 The fourier transform and discrete functions = 180
 4.9 The discrete Fourier transform = 192
5 KERNEL OPTIMIZATION = 199
 5.1 Spatial restrictions = 199
 5.2 Distance measure = 200
 5.3 Minimizing the distance = 201
 5.4 The weighting function = 201
 5.5 Optimization results = 203
 5.6 Kernel evaluation = 209
6 ORIENTATION AND VELOCITY = 219
 6.1 Tensors - A short introduction = 222
 6.2 Representing orientation = 224
 6.3 Orientation estimation = 230
 6.4 Tensor Construction = 239
 6.5 Interpretation of the orientation tensor = 249
 6.6 Time sequences - velocity = 253
 6.7 Performance measures = 257
7 LOCAL PHASE ESTIMATION = 259
 7.1 What is local phase? = 259
 7.2 Local Phase in Scale-space = 266
 7.3 Phase in higher dimensions = 271
 7.4 Applications using Local Phase Estimates = 275
8 LOCAL FREQUENCY = 279
 8.1 Frequency estimation = 281
 8.2 Wide range Frequency estimation = 288
 8.3 Experimental results = 290
9 REPRESENTATION AND AVERAGING = 297
 9.1 Background = 297
 9.2 Invariance and equivariance = 298
 9.3 Signals and certainties = 299
 9.4 Vector and tensor representation of local orientation = 310
 9.5 Averaging = 303
 9.6 Normalized averaging = 304
10 ADAPTIVE FILTERING = 309
 10.1 Adaptive filtering = 311
 10.2 Tensor controlled filter = 313
 10.3 The control tensor = 313
 10.4 Adaptive filter synthesis = 320
 10.5 Examples of filtering = 333
11 VECTOR AND TENSOR FIELD FILTERING = 343
 11.1 Introduction = 343
 11.2 Orientation in vector and tensor fields = 343
 11.3 Rotational symmetries = 350
 11.4 Curvature estimation = 361
12 CLASSIFICATION AND RESPONSE GENERATION = 367
 12.1 Information needed for classification = 368
 12.2 Linear discriminant functions = 371
 12.3 Minimum distance classification = 378
 12.4 Convolution operations = 380
 12.5 Generalized discriminant functions = 385
 12.6 Training of linear discriminant classifiers = 389
 12.7 Perceptrons and feedforward neural networks = 390
 12.8 Clustering and unsupervised classification = 396
13 TEXTURE ANALYSIS = 399
 13.1 Introduction = 399
 13.2 Issues in texture analysis = 401
 13.3 Human aspects of texture perception = 402
 13.4 Feature - based texture analysis = 405
 13.5 Structural approach using certainty gating = 412
REFERENCES = 419
INDEX = 433