Abstract
Recently the concept of a proximity measure has emerged as a computational cornerstone for modelling human perception. In particular, for visual perception a proximity measure is an index defined over pairs of images that quantifies the degree to which the two objects are alike as perceived by a respondent at the particular time of measurement. Analyses of these proximity measures have been done almost solely under the purview of the multidimensional scaling (MDS) technique.
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References
Bourbaki, N., Integration, Hermann, Paris, 1965.
Bourbaki, N., Topologie Generale, Hermann, Paris, 1974.
Beals, R. and D. Krantz, “Metrics and geodesies induced by order relations,” Mathematische Zeitschrift, 1012, 258–298, 1967.
Dugundgi, J. and R. Arens, “Topologies for function spaces,” Pacific J. of Math., 1, 5–31, 1951.
Falmagne, J., “Psychometric function theory,” J. of Math. Psyc., 25, 1–50, 1982.
Lew, J., “Some counterexamples in multidimensional scaling,” J. Math. Psyc., 17, 247–254, 1978.
Mackey, G., “Borel structures in groups and their duals,” Trans. Amer. Math. Soc., 85, 134–165, 1957.
Manicke, R., “On the stochastic geometrical foundations of metric multidimensional scaling,” J. Math. Soc. Sci., 9, 53–62, 1985.
Manicke, R., “The unique existence of a probability measure for human pattern recognition,” submitted to the J. of Math. Psyc., 1986.
Mattenklott, A., J. Sehr and K. Miescke, “A stochastic model for paired comparisons of social stimuli,” J. of Math. Pscy 26, 149–168, 1982.
Menger, K., “Statistical metrics,” Proc. Nat Acad Sci U.S.A., 28, 535–537.
Serstnev, A., “Random normed spaces,” Kazan. Gos. Univ. Ucen. Zap, 122, 3–20.
Shepard, R., “Attention and the metric structure of the stimulus space,” J. of Math. Psyc., 1, 54–87, 1964.
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© 1987 Springer-Verlag Berlin Heidelberg
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Manicke, R.L. (1987). Stochastic Geometry and Perception. In: Devijver, P.A., Kittler, J. (eds) Pattern Recognition Theory and Applications. NATO ASI Series, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83069-3_23
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DOI: https://doi.org/10.1007/978-3-642-83069-3_23
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