Advances in Computer Vision - Vol. 2

By Christopher Brown | Go to book overview

1
THE USE OF THE FACET MODEL AND THE TOPOGRAPHIC PRIMAL SKETCH IN IMAGE ANALYSIS

LINDA G. SHAPIRO
ROBERT M. HARALICK
University of Washington

TING-CHUEN PONG
University of Minnesota


INTRODUCTION

The facet model states that all processing of digital-image data has its final authoritative interpretation relative to what the processing does to the underlying gray-tone intensity surface. The digital image's pixel values are noisy sampled observations of the underlying surface. Thus, in order to do any processing, we must estimate this underlying surface at each pixel position. This requires a model that describes what the general form of the surface would be in the neighborhood of any pixel if there were no noise. To estimate the surface from the neighborhood around a pixel, then, amounts to estimating the free parameters of the general form. The processing that takes place is then defined in terms of the estimated parameters.

The topographic primal sketch ( Haralick, Watson, & Laffey, 1983) is one possible way of representing the fundamental structure of a digital image in a rich and robust way. The basis of the topographic primal sketch is the classification and grouping of the underlying image-intensity surface patches according to the categories defined by monotonic, gray-tone invariant functions of directional derivatives. Examples of such categories are peak, pit, ridge, ravine, saddle, flat, and hillside. From this initial classification, categories can be grouped to obtain a rich, hierarchical, and structurally complete representation of the fundamental image structure. By contrast, representations of the fundamental image structure only involving edges or the primal sketch as described by Marr ( 1976) are impoverished in the sense that they are insufficient for unambiguous matching. They also do not have the required invariance with respect to monotonically increasing gray-tone transformations.

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Advances in Computer Vision - Vol. 2
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • Contributors vii
  • Introduction ix
  • References xiv
  • 1: The Use of the Facet Model and the Topographic Primal Sketch in Image Analysis 1
  • Introduction 1
  • Summary 45
  • References 45
  • 2: Scaling and Fingerprint Theorems for Zero-Crossings 47
  • Introduction 47
  • Appendix A 74
  • Appendix B 74
  • Appendix B 77
  • Appendix B 77
  • 3: Form Perception Using Transformation Networks: Polyhedra 79
  • 3: Form Perception Using Transformation Networks 79
  • Acknowledgements 116
  • 4: The Parts of Perception 121
  • Summary 139
  • Summary 171
  • References 174
  • Author Index 177
  • Subject Index 180
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