A Differential Geometric Description of the Relationships among Perceptions

Journal of Mathematical Psychology

Volumn 44, Issue 2, 2000, Pages 241-284

  Levin, David N ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000577253     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmps.1999.1240     Document Type: Article

References (37)

1. Baird J. C. Sensation and judgment: complementarity theory of psychophysics. 1997;Erlbaum, Mahwah. p. 216-235.
2. Baird J. C., Noma E. Fundamentals of scaling and psychophysics. 1978;Wiley, New York.
3. Beals R., Krantz D. H., Tversky A. Foundations of multidimensional scaling. Psychological Review. 75:1968;127-142.
4. Carroll J. D., Arabie P. Multidimensional scaling. Annual Reviews of Psychology. 31:1980;607-649.
5. Deutsch D. The psychology of music. 1982;Academic Press, New York.
6. Dzhafarov E. D., Colonius H. Fechnerian metrics in unidimensional and multidimensional stimulus spaces. Psychological Bulletin and Review. 6:1999;239-268.
7. Farah M. J. Visual agnosia: disorders of object recognition and what they tell us about normal vision. 1990;MIT Press, Cambridge.
8. Fechner G. T. Elemente der Psychophysik. 1860;Breitkopf and Hartel, Leipzig.
9. Hoffman W. C. The Lie transformation group approach to visual neuropsychology. Leeuwenberg E. L. J., Buffart H. F. J. M. Formal theories of visual perception. 1978;27-66 Wiley, New York.
10. Holman E. W. Completely nonmetric multidimensional scaling. Journal of Mathematical Psychology. 18:1978;39-51.
11. Levin D. N. A relativistic description of perception. Journal of Mathematical Psychology. 40:1996a;348.
12. Levin D. N. A relativistic description of perception. Proceedings of the 26th Annual Meeting of the Society for Neuroscience. 1:1996b;270.
13. Levin, D. N. 1997, A differential geometric description of the perception of color mixtures, Proceedings of the 30th Annual Meeting of the Society for Mathematical Psychology, July 31-August 3, 1997, Bloomington, Indiana, p, 13.
14. Levin, D. N. 1998a, A differential geometric description of perceptual experience: simplified methodology for flat spaces, Proceedings of the 31st Annual Meeting of the Society for Mathematical Psychology, August 6-9, 1998, Nashville, TN, p, 7.
15. Levin, D. N. 1998b, Using affine-connected differential geometry to generalize Fechnerian psychophysics to n-dimensional stimulus manifolds, Proceedings of the 31st Annual Meeting of the Society for Mathematical Psychology, August 6-9, 1998, Nashville, TN, p, 33.
16. Levin, D. N. 1999a, Method and apparatus for measurement, analysis, characterization, emulation, and translation of perception. US patent #5,860,936, January 19, 1999.
17. Levin, D. N.1999b. Psychophysical scales derived from perceptual analogies: A multidimensional generalization of Fechnerian psychophysics. Proceedings of the 15th Annual Meeting of the International Society for Psychophysics, October 21-24, 1999, Tempe, AZ, pp. 123-128.
18. Lindman H., Caelli T. Constant curvature Riemannian scaling. Journal of Mathematical Psychology. 17:1978;89-109.
19. Luce R. D., Edwards W. The derivation of subjective scales from just noticeable differences. Psychological Review. 65:1958;222-237.
20. Luce R. D., Galanter E. Discrimination. Luce R. D., Bush R. R., Galanter E. Handbook of mathematical psychology. 1963;191-244 Wiley, New York.
21. Mandriota F. J., Mintz D. E., Notterman J. M. Visual velocity discrimination: effects of spatial and temporal cues. Science. 138:1962;437-438.
22. Marks L. E. Sensory processes: the new psychophysics. 1974;Academic Press, New York.
23. Naito S., Cole J. B. The gravity lens illusion and its mathematical model. Fischer G. H., Laming D. Contributions to mathematical psychology, psychometrics, and methodology. 1994;39-50 Springer-Verlag, Berlin.
24. Rumelhart D. E., Abrahamson A. A. A model for analogical reasoning. Cognitive Psychology. 5:1973;1-28.
25. Sacks O. The man who mistook his wife for a hat. 1985;HarperCollins, New York.
26. Sacks O. An anthropologist on Mars: Seven paradoxical tales. 1995;Knopf, New York.
27. Schrodinger E. Space-time structure. 1963;Cambridge University Press, Cambridge.
28. Shepard R. N. Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology. 1:1964;54-87.
29. Shepard R. N. The circumplex and related topological manifolds in the study of perception. Shye S. Theory construction and data analysis in the behavioral sciences. 1978;29-80 Jossey-Bass, San Francisco.
30. Shepard R. N. Structural representations of musical pitch. Deutsch D. The psychology of music. 1982;343-390 Academic Press, New York.
31. Spillmann L., Werner J. S. Visual perception: the neurophysiological foundations. 1990;Academic Press, San Diego. p. 301.
32. Stevens S. S. Psychophysics: introduction to its perceptual, neural, and social prospects. 1975;Wiley, New York. p. 99-133.
33. Townsend J. T., Thomas R. D. On the need for a general quantitative theory of pattern similarity. Masin S. C. Foundations of perceptual theory. 1993;297-368 Elsevier, Amsterdam.
34. Watson A. A Riemann geometric explanation of the visual illusions and figural after-effects. Leeuwenberg E. L. J., Buffart H. F. J. M. Formal theories of visual perception. 1978;139-169 Wiley, New York.
35. Weinberg S. Gravitation and cosmology: principles and applications of the general theory of relativity. 1972;Wiley, New York.
36. Yamazaki T. Non-Riemannian approach to geometry of visual space: an application of affinely connected geometry to visual alleys and horopter. Journal of Mathematical Psychology. 31:1987;270-298.
37. Zhang J., Wu S. Structure of visual perception. Proceedings of the National Academy of Sciences. 87:1990;7819-7823.