Detailed Contents
         Foreword by Shimon Ullman xvii
         Preface xxiii
         PART I
         INTRODUCTION AND
         PHILOSOPHICAL PRELIMINARIES
         GENERAL INTRODUCTION 3
         Chapter 1
         The Philosophy and the Approach 8
         Background 8
         Understanding Complex Information-Processing Systems 19
         Representation and description 20
         Process 22
         The three levels 24
         Importance of computational theory 27
         The approach of J. J. Gibson 29
         A Representational Framework for Vision 31
         The purpose of vision 32
         Advanced vision 34
         To the desirable via the possible 36
         PART II
         VISION
         Chapter 2
         Representing the Image 41
         Physical Background of Early Vision 41
         Representing the image 44
         Underlying physical assumptions 44
         Existence of surfaces 44
         Hierarchical organization 44
         Similarity 47
         Spatial continuity 49
         Continuity of discontinuities 49
         Continuity of fl ow 50
         General nature of the representation 51
         Zero-Crossings and the Raw Primal Sketch 54
         Zero-Crossings 54
         Biological implications 61
         The psychophysics of early vision 61
         The physiological realization of the ▽2G filters 64
         The physiological detection of zero crossings 64
         The fi rst complete symbolic representation of the image 67
         The raw primal sketch 68
         Philosophical aside 75
         Spatial Arrangement of an Image 79
         Light Sources and Transparency 86
         Other light source effects 88
         Transparency 89
         Conclusions 90
         Grouping Processes and the Full Primal Sketch 91
         Main points in the argument 96
         The computational approach and the psychophysics of texture discrimination 96
         Chapter 3
         From Images to Surfaces 99
         Modular Organization of the Human Visual Processor 99
         Processes, Constraints, and the Available Representations of an Image 103
         Stereopsis 111
         Measuring stereo disparity 111
         Computational theory 111
         Algorithms for stereo matching 116
         A cooperative algorithm 116
         Cooperative algorithms and the stereo matching problem 122
         Biological evidence 125
         A second algorithm 127
         Uniqueness, cooperativity, and the pulling effect 140
         Panum’s fusional area 144
         Impressions of depth from larger disparities 144
         Have we solved the right problem? 148
         Vergence movements and the 2½-D sketch 149
         Neural implementation of stereo fusion 152
         Computing distance and surface orientation from disparity 155
         Computational theory 155
         Distance from the viewer to the surface 155
         Surface orientation from disparity change 156
         Algorithm and implementation 159
         Directional Selectivity 159
         Introduction to visual motion 159
         Computational theory 165
         An algorithm 167
         Neural implementation 169
         Using directional selectivity to separate independently moving surfaces 175
         Computational theory 175
         Algorithm and implementation 177
         Looming 182
         Apparent Motion 182
         Why apparent motion? 183
         The two halves of the problem 184
         The correspondence problem 188
         Empirical fi ndings 188
         What is the input representation? 188
         Two dimensionality of the correspondence process 193
         Ullman’s theory of the correspondence process 196
         A critique of Ullman’s theory 199
         A new look at the correspondence problem 202
         One problem or two? 202
         Separate systems for structure and object constancy 204
         Structure from Motion 205
         The problem 205
         A previous approach 207
         The rigidity constraint 209
         The rigidity assumption 210
         A note about the perspective projection 211
         Optical flow 212
         The input representation 212
         Mathematical results 213
         Shape Contours 215
         Some examples 216
         Occluding contours 218
         Constraining assumptions 219
         Implications of the assumptions 222
         Surface orientation discontinuities 225
         Surface contours 226
         The puzzle and diffi culty of surface contours 228
         Determining the shape of the contour generator 229
         The effects of more than one contour 230
         Surface Texture 233
         The isolation of texture elements 234
         Surface parameters 234
         Possible measurements 234
         Estimating scaled distance directly 238
         Summary 239
         Shading and Photometric Stereo 239
         Gradient space 240
         Surface illumination, surface refl ectance, and image intensity 243
         The refl ectance map 245
         Recovery of shape from shading 248
         Photometric stereo 249
         Brightness, Lightness, and Color 250
         The Helson–Judd approach 252
         Retinex theory of lightness and color 253
         Algorithms 255
         Extension to color vision 256
         Comments on the retinex theory 257
         Some physical reasons for the importance of simultaneous contrast 259
         Hypothesis of the superfi cial origin of nonlinear changes in intensity 26
         Implications for measurements on a trichromatic image 262
         Summary of the approach 264
         Summary 264
         Chapter 4
         The Immediate Representation of Visible Surfaces 268
         Introduction 268
         Image Segmentation 270
         Reformulating the Problem 272
         The Information to be Represented 275
         General Form of the 2½-D Sketch 277
         Possible Forms for the Representation 279
         Possible Coordinate Systems 283
         Interpolation, Continuation, and Discontinuities 285
         Computational Aspects of the Interpolation Problem 288
         Discontinuities 289
         Interpolation methods 290
         Other Internal Computations 291
         Chapter 5
         Representing Shapes for Recognition 295
         Introduction 295
         Issues Raised by the Representation of Shape 296
         Criteria for judging the effectiveness of a shape representation 296
         Accessibility 297
         Scope and uniqueness 297
         Stability and sensitivity 298
         Choices in the design of a shape representation 298
         Coordinate systems 298
         Primitives 300
         Organization 302
         The 3-D Model Representation 302
         Natural coordinate systems 303
         Axis-based descriptions 304
         Modular organization of the 3-D model representation 305
         Coordinate system of the 3-D model 307
         Natural Extensions 309
         Deriving and Using the 3-D Model Representation 313
         Deriving a 3-D model description 313
         Relating viewer-centered to object-centered coordinates 317
         Indexing and the catalogue of 3-D models 318
         Interaction between derivation and recognition 321
         Finding the correspondence between image and catalogued model 322
         Constraint analysis 322
         Psychological Considerations 325
         Chapter 6
         Synopsis 329
         PART III
         EPILOGUE
         Chapter 7
         In Defense of the Approach 335
         Introduction 335
         A Conversation 336
         Afterword by Tomaso Poggio 362
         Glossary 368
         Bibliography 375
         Index 393
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