Abstract

© 1978 Optical Society of America

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  1. S. R. Purks and W. Richards, "Visual texture discrimination using random-dot patterns," J. Opt. Soc. Am. 67, 765–771 (1977).
  2. B. Julesz, "Visual pattern discrimination," IRE Trans. Inf. Theory IT-8, 84–92 (1962).
  3. B. Julesz, "Experiments in the visual perception of texture," Sci. Am. 232, 34–43 (April 1975).
  4. B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).
  5. I. Pollack, "Discrimination of third-order Markov constraints within visual displays," Percept. Psychophys. 13, 276–280 (1973).
  6. M. Rosenblatt and D. Slepian, "Nth order Markov chains with any set of N variables independent," J. Soc. Indus. Appl. Math. 10, 537–549 (1962).
  7. The n-gram transition probabilities (also called n-gram statistics) always refer to n adjacent samples (events) in a generalized discrete Markov processes of order n, while nth-order statistics are used in all discrete stochastic processes, and refer to any n samples, that in general are nonadjacent. These are old, accepted definitions found in advanced textbooks of probability theory, stochastic processes, and communication theory, and have nothing to do with Rosenblatt and Slepian, as Purks and Richards assume. What Rosenblatt and Slepian (Ref. 6) accomplished in 1962 was to provide for Julesz’ texture paradigm some very special Markov processes that satisfied the requirement of having identical nth-order statistics but different (n +1)th-order statistics. Obviously, both in the texture paradigm of Julesz (ref. 2) and in the work of Rosenblatt and Slepian (Ref. 6) nth-order statistics was used in the customary sense, that is the n samples of the statistics were non-adjacent.
  8. B. Julesz and N. Guttman, "High-order statistics and short-term auditory memory," in Proc. of the 5th International Congress on Acoustics, Liege, Vol. la, Report B 15 (1965).
  9. T. M. Caelli and B. Julesz, "On perceptual analyzers underlying visual texture discrimination: Part I," Biol. Cybernetics (in press).
  10. Dipole statistics (a term used in random geometry to denote second-order statistics) is obtained by randomly throwing needles (dipoles) on a texture, and measuring the frequencies that the two endpoints of a dipole of any given length and orientation fall on the same color of the texture (Refs. 3 and 4).

1977 (1)

1973 (2)

B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).

I. Pollack, "Discrimination of third-order Markov constraints within visual displays," Percept. Psychophys. 13, 276–280 (1973).

1965 (1)

B. Julesz and N. Guttman, "High-order statistics and short-term auditory memory," in Proc. of the 5th International Congress on Acoustics, Liege, Vol. la, Report B 15 (1965).

1962 (2)

B. Julesz, "Visual pattern discrimination," IRE Trans. Inf. Theory IT-8, 84–92 (1962).

M. Rosenblatt and D. Slepian, "Nth order Markov chains with any set of N variables independent," J. Soc. Indus. Appl. Math. 10, 537–549 (1962).

Caelli, T. M.

T. M. Caelli and B. Julesz, "On perceptual analyzers underlying visual texture discrimination: Part I," Biol. Cybernetics (in press).

Frisch, H. L.

B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).

Gilbert, E. N.

B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).

Guttman, N.

B. Julesz and N. Guttman, "High-order statistics and short-term auditory memory," in Proc. of the 5th International Congress on Acoustics, Liege, Vol. la, Report B 15 (1965).

Julesz, B.

B. Julesz, "Experiments in the visual perception of texture," Sci. Am. 232, 34–43 (April 1975).

B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).

B. Julesz and N. Guttman, "High-order statistics and short-term auditory memory," in Proc. of the 5th International Congress on Acoustics, Liege, Vol. la, Report B 15 (1965).

B. Julesz, "Visual pattern discrimination," IRE Trans. Inf. Theory IT-8, 84–92 (1962).

T. M. Caelli and B. Julesz, "On perceptual analyzers underlying visual texture discrimination: Part I," Biol. Cybernetics (in press).

Pollack, I.

I. Pollack, "Discrimination of third-order Markov constraints within visual displays," Percept. Psychophys. 13, 276–280 (1973).

Purks, S. R.

Richards, W.

Rosenblatt, M.

M. Rosenblatt and D. Slepian, "Nth order Markov chains with any set of N variables independent," J. Soc. Indus. Appl. Math. 10, 537–549 (1962).

Shepp, L. A.

B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).

Slepian, D.

M. Rosenblatt and D. Slepian, "Nth order Markov chains with any set of N variables independent," J. Soc. Indus. Appl. Math. 10, 537–549 (1962).

IRE Trans. Inf. Theory (1)

B. Julesz, "Visual pattern discrimination," IRE Trans. Inf. Theory IT-8, 84–92 (1962).

J. Opt. Soc. Am. (1)

J. Soc. Indus. Appl. Math. (1)

M. Rosenblatt and D. Slepian, "Nth order Markov chains with any set of N variables independent," J. Soc. Indus. Appl. Math. 10, 537–549 (1962).

Percept. Psychophys. (1)

I. Pollack, "Discrimination of third-order Markov constraints within visual displays," Percept. Psychophys. 13, 276–280 (1973).

Perception (1)

B. Julesz, E. N. Gilbert, L. A. Shepp, and H. L. Frisch, "Inability of humans to discriminate between visual textures that agree in sec-ond-order statistics—revisited," Perception 2, 391–405 (1973).

Sci. Am. (1)

B. Julesz, "Experiments in the visual perception of texture," Sci. Am. 232, 34–43 (April 1975).

Other (4)

The n-gram transition probabilities (also called n-gram statistics) always refer to n adjacent samples (events) in a generalized discrete Markov processes of order n, while nth-order statistics are used in all discrete stochastic processes, and refer to any n samples, that in general are nonadjacent. These are old, accepted definitions found in advanced textbooks of probability theory, stochastic processes, and communication theory, and have nothing to do with Rosenblatt and Slepian, as Purks and Richards assume. What Rosenblatt and Slepian (Ref. 6) accomplished in 1962 was to provide for Julesz’ texture paradigm some very special Markov processes that satisfied the requirement of having identical nth-order statistics but different (n +1)th-order statistics. Obviously, both in the texture paradigm of Julesz (ref. 2) and in the work of Rosenblatt and Slepian (Ref. 6) nth-order statistics was used in the customary sense, that is the n samples of the statistics were non-adjacent.

B. Julesz and N. Guttman, "High-order statistics and short-term auditory memory," in Proc. of the 5th International Congress on Acoustics, Liege, Vol. la, Report B 15 (1965).

T. M. Caelli and B. Julesz, "On perceptual analyzers underlying visual texture discrimination: Part I," Biol. Cybernetics (in press).

Dipole statistics (a term used in random geometry to denote second-order statistics) is obtained by randomly throwing needles (dipoles) on a texture, and measuring the frequencies that the two endpoints of a dipole of any given length and orientation fall on the same color of the texture (Refs. 3 and 4).

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