Skip to main content

Mereology of Visual Form

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2059))

Abstract

Visual forms come in countless varieties, from the simpli- city of a sphere, to the geometric complexity of a face, to the fractal complexity of a rugged coast. These varieties have been studied with mathematical tools such as topology, differential geometry and fractal geometry. They have also been examined, largely in the last three decades, in terms of mereology, the study of part-whole relationships. The result is a fascinating body of theoretical and empirical results. In this paper I review these results, and describe a new development that applies them to the problem of learning names for visual forms and their parts.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tyler, C.W.: Analysis of Human Receptor Density. In: Lakshminarayanan, V. (ed.): Basic and Clinical Applications of Vision Science. Kluwer Academic, Norwell, Massachusetts (1997) 63–71

    Google Scholar 

  2. Bower, G.H., Glass, A.L.: Structural Units and the Redintegrative Power of Picture Fragments. J. Exper. Psych. 2 (1976) 456–466

    Google Scholar 

  3. Braunstein, M.L., Hoffman, D.D., Saidpour, A.: Parts of Visual Objects: An Experimental Test of the Minima Rule. Perception 18 (1989) 817–826

    Article  Google Scholar 

  4. Palmer, S.E.: Hierarchical Structure in Perceptual Representation. Cognit. Psychol. 9 (1977) 441–474

    Article  MathSciNet  Google Scholar 

  5. Hoffman, D.D., Richards, W.A.: Parts of Recognition. Cognition 18 (1984) 65–96

    Article  Google Scholar 

  6. Hoffman, D.D.: The Interpretation of Visual Illusions. Sci. Am. 249 6 (1983) 154–162

    Article  Google Scholar 

  7. Hoffman, D.D., Singh, M.: Salience of Visual Parts. Cognition 63 (1997) 29–78

    Article  Google Scholar 

  8. Singh, M., Hoffman, D.D.: Part Boundaries Alter the Perception of Transparency. Psych. Sci. 9 (1998) 370–378

    Article  Google Scholar 

  9. Baylis, G.C., Driver, J.: Obligatory Edge Assignment in Vision: The Role of Figure and Part Segmentation in Symmetry Detection. J. Exp. Psych.: Hum. Percept. Perform. 21 (1995) 1323–1342

    Article  Google Scholar 

  10. Bruce, V., Morgan, M.J.: Violations of Symmetry and Repetitions in Visual Patterns. Perception 4 (1975) 239–249

    Article  Google Scholar 

  11. Hoffman, D.D.: Visual Intelligence: How We Create What We See. W.W. Norton, New York (1998)

    Google Scholar 

  12. Mach, E.: The Analysis of Sensations, and the Relation of the Physical to the Psychical. Dover, New York (1885/1959) (Translated by Williams, C.M.)

    Google Scholar 

  13. Hulleman, J., te Winkel, W., Boselie, F.: Concavities as Basic Features in Visual Search: Evidence from Search Asymmetries. Percept. Psychophys. 62 (2000) 162–174

    Google Scholar 

  14. Wolfe, J.M., Bennett, S.C.: Preattentive Object Files: Shapeless Bundles of Basic Features. Vis. Res. 37 (1997) 24–43

    Google Scholar 

  15. Singh, M., Seyranian, G., Hoffman, D.D.: Parsing Silhouettes: The Short-Cut Rule. Percept. Psychophys. 61 (1999) 636–660

    Google Scholar 

  16. Marr, D., Nishihara, H.K.: Representation and Recognition of Three-Dimensional Shapes. Proc. Roy. Soc. Lond. B, 200 (1978) 269–294

    Article  Google Scholar 

  17. Roberts, L.G.: Machine Perception of Three-Dimensional Solids. In: Tippett, J.T. et al. (eds.): Optical and Electrooptical Information Processing. MIT Press, Cambridge, Massachusetts (1965) 211–277

    Google Scholar 

  18. Waltz, D.: Generating Semantic Descriptions from Drawings of Scenes with Shadows. In: Winston, P. (ed.): The Psychology of Computer Vision. McGraw-Hill, New York (1975) 19–91

    Google Scholar 

  19. Winston, P.A.: Learning Structural Descriptions from Examples. In: Winston, P. (ed.): The Psychology of Computer Vision. McGraw-Hill, New York (1975) 157–209

    Google Scholar 

  20. Brooks, R.A.: Symbolic Reasoning among 3-D Models and 2-D Images. Artific. Intell. 17 (1981) 205–244

    Article  Google Scholar 

  21. Biederman, I.: Recognition-By-Components: A Theory of Human Image Understanding. Psych. Rev. 94 (1987) 115–147

    Article  Google Scholar 

  22. Biederman, I.: Higher Level Vision. In: Osherson, D., Kosslyn, S., Hollerbach, J. (eds.) An Invitation to Cognitive Science, Volume 2. MIT Press, Cambridge, Massachusetts (1990) 41–72

    Google Scholar 

  23. Pentland, A.P.: Perceptual Organization and the Representation of Natural Form. Artific. Intell. 28 (1986) 293–331

    Article  MathSciNet  Google Scholar 

  24. Lowe, D.: Perceptual Organization and Visual Recognition. Kluwer, Amsterdam (1985)

    Google Scholar 

  25. Witkin, A.P., Tenenbaum, J.M.: On the Role of Structure in Vision. In: Beck, J., Hope, B., Rosenfeld, A. (eds.) Human and Machine Vision. Academic Press, New York (1983) 481–543

    Google Scholar 

  26. Tarr, M.J., Williams, P., Hayward, W.G. Gauthier, I.: Three-Dimensional Object Recognition Is Viewpoint Dependent. Nature Neurosci. 1 (1998) 275–277

    Article  Google Scholar 

  27. Siddiqi, K., Kimia, B.B.: Parts of Visual Form: Computational Aspects. IEEE PAMI 17 (1995) 239–251

    Google Scholar 

  28. Kimia, B.B., Tannenbaum, A.R., Zucker, S.W.: Entropy Scale-Space. Plenum Press, New York (1991) 333–344

    Google Scholar 

  29. Parent, P., Zucker, S.W.: Trace Inference, Curvature Consistency, and Curve Detection. IEEE PAMI 11 (1989) 823–839

    Google Scholar 

  30. Hayward, W.G., Tarr, M.J., Corderoy, A.K.: Recognizing Silhouettes and Shaded Images Across Depth Rotation. Perception 28 (1999) 1197–1215

    Article  Google Scholar 

  31. Rodriguez, T., Nilson, C., Singh, M., Hoffman, D.D.: Word and Part. (under review).

    Google Scholar 

  32. Imai, M., Gentner, D.: A Cross-Linguistic Study of EarlyWord Meaning: Universal Ontology and Linguistic Influence. Cognition 62 (1997) 169–200

    Article  Google Scholar 

  33. Landau, B., Smith, L.B., Jones, S.: Syntactic Context and the Shape Bias in Children’s and Adults’ Lexical Learning. J. Mem. Lang. 31 (1992) 807–825

    Article  Google Scholar 

  34. Soja, N.N., Carey, S., Spelke, E.S.: Ontological Categories Guide Young Children’s Inductions of Word Meanings: Object Terms and Substance Terms. Cognition 38 (1990) 179–211

    Article  Google Scholar 

  35. Subrahmanyam, K., Landau, B., Gelman, R. Shape, Material, and Syntax: Interacting Forces in Children’s Learning in Novel Words for Objects and Substances. Lang. Cognit. Proc. 14 (1999) 249–281

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hoffman, D.D. (2001). Mereology of Visual Form. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form 2001. IWVF 2001. Lecture Notes in Computer Science, vol 2059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45129-3_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-45129-3_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42120-7

  • Online ISBN: 978-3-540-45129-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics