3D Shape

Its Unique Place in Visual Perception

The uniqueness of shape as a perceptual property lies in the fact that it is both complex and structured. Shapes are perceived veridically—perceived as they really are in the physical world, regardless of the orientation from which they are viewed. The constancy of the shape percept is the sine qua non of shape perception; you are not actually studying shape if constancy cannot be achieved with the stimulus you are using. Shape is the only perceptual attribute of an object that allows unambiguous identification. In this first book devoted exclusively to the perception of shape by humans and machines, Zygmunt Pizlo describes how we perceive shapes and how to design machines that can see shapes as we do. He reviews the long history of the subject, allowing the reader to understand why it has taken so long to understand shape perception, and offers a new theory of shape.

Until recently, shape was treated in combination with such other perceptual properties as depth, motion, speed, and color. This resulted in apparently contradictory findings, which made a coherent theoretical treatment of shape impossible. Pizlo argues that once shape is understood to be unique among visual attributes and the perceptual mechanisms underlying shape are seen to be different from other perceptual mechanisms, the research on shape becomes coherent and experimental findings no longer seem to contradict each other. A single theory of shape perception is thus possible, and Pizlo offers a theoretical treatment that explains how a three-dimensional shape percept is produced from a two-dimensional retinal image, assuming only that the image has been organized into two-dimensional shapes. Pizlo focuses on discussion of the main concepts, telling the story of shape without interruption. Appendixes provide the basic mathematical and computational information necessary for a technical understanding of the argument. References point the way to more in-depth reading in geometry and computational vision.

Table of Contents

  1. Contents
  2. Preface
  3. 1. Early Theories of Shape and the First Experiments on Shape Constancy
  4. 2. The Cognitive Revolution Leads to Neo-Gestaltism and Neo-Empiricism
  5. 3. Machine Vision
  6. 4. Formalisms Enter into the Study of Shape Perception
  7. 5. A New Paradigm for Studying Shape Perception
  8. Appendix A 2D Perspective and Projective Transformation
  9. Appendix B Perkins' Laws
  10. Appendix C Projective Geometry in Computational Models
  11. Appendix D Shape Constraints in Reconstruction of Polyhedra
  12. Notes
  13. References
  14. Index