A computational model of mean size perception

인간의 시각 체계는 처리 용량의 한계를 극복하기 위해 복잡한 시각 자극의 중복되는 정보들을 요약해서 표상한다. 요약된 표상의 한 가지 예는 다양한 시각 자극의 평균 크기를 표상하는 것인데, 많은 선행 연구들을 통해 시각 체계의 평균 표상 능력은 매우 정확하다고 알려져 있다. 본 연구에서는 이와 같은 평균 크기 표상의 기제를 설명하는 계산 모형을 제안한다. 제시된 모형에서 시각 체계는 개별 자극들을 다소간의 잡음(초기 잡음)과 함께 부호화하고, 여러 자극들에서 부호화된 정보들을 통합한다. 시각 체계는 정보가 통합된 이후에도 의식 수준의 최종적인 표상이 형성되기 전까지 일정 수준의 잡음이 추가적으로 더해진다(후기 잡음). 본 모형의 타당도를 검증하기 위해 여러 크기의 자극들을 포함한 기준 자극 화면과 비교 자극 화면의 평균 크기를 비교하는 정신물리학 실험을 실시했다. 실험 결과, 크기 차이 변별의 민감도를 나타내는 역치는 자극 개수에 따라 감소했다. 다시 말해, 실험 참가자들은 자극 개수가 많아짐에 따라 그 자극들의 평균 크기를 더 정확하게 지각했는데, 이 결과는 후기 잡음을 포함한 모형으로 잘 설명된다. 본 모형은 개별 시각 정보들이 어떤 과정을 거쳐서 평균 표상을 형성하게 되는지를 보여주며, 본 연구에 사용된 실험 패러다임은 다양한 시각 속성의 평균 표상을 연구하는 데에 유용한 도구가 될 것으로 기대된다.

keywords: 평균 표상, 지각, 계산모형, 초기 소음, 후기 소음, 중심극한정리, 신호처리이론, mean size perception, computational model, noisy percept, early noise, late noise, central limit theorem, signal detection theory

Abstract

Human visual system represents a statistical summary of a complex visual input to overcome its limited capacity. An example of summary representation is the average size perception, which has been known to be accurate and precise. In the current study, we developed and validated a computational model of mean size perception. In this model, we assumed that the visual system encodes individual sizes with early noise, then integrates the noisy size information from multiple inputs. Finally, the integrated size information is added by late noise. The suggested model was validated with a psychophysical experiment, in which the standard and the test displays included multiple circles with different sizes and observers were asked to report which display had larger mean size. The psychophysical data was well accounted by the model with late noise: threshold for mean size discrimination was decreased with set-size, but the decrement of threshold was decelerated in large set-sizes. The proposed model allows us to understand underlying mechanism of mean size perception, and the experimental paradigm used in the current study is expected to be a useful tool for studying ensemble perception of various visual properties.

keywords: 평균 표상, 지각, 계산모형, 초기 소음, 후기 소음, 중심극한정리, 신호처리이론, mean size perception, computational model, noisy percept, early noise, late noise, central limit theorem, signal detection theory

참고문헌

Allik, J., Toom, M., Raidvee, A., Averin, K., & Kreegipuu, K. (2013). An almost general theory of mean size perception. Vision Research, 83, 25-39.

Alvarez, G. A. (2011). Representing multiple objects as an ensemble enhances visual cognition. Trends in Cognitive Sciences, 15(3), 122-31.

Ariely, D. (2001). Seeing Sets: Representation by Statistical Properties. Psychological Science, 12(2), 157-162.

Bauer, B. (2009). The danger of trial-by-trial knowledge of results in perceptual averaging studies. Attention, Perception & Psychophysics, 71(3), 655-65.

Brainard, D. H. (1997). The Psychophysics Toolbox. Spatial Vision, 10(4), 433-436.

Burgess, A. E., Wagner, R. F., Jennings, R. J., & Barlow, H. B. (1981). Efficiency of human visual signal discrimination. Science, 214(4516), 93-4.

Chong, S. C., & Treisman, A. (2003). Representation of statistical properties. Vision Research, 43(4), 393-404.

Chong, S. C., & Treisman, A. (2005a). Attentional spread in the statistical processing of visual displays. Perception & Psychophysics, 67(1), 1-13.

Chong, S. C., & Treisman, A. (2005b). Statistical processing: computing the average size in perceptual groups. Vision Research, 45(7), 891-900.

10.

Chong, S. C., Joo, S. J., Emmanouil, T.-A., & Treisman, A. (2008). Statistical processing: not so implausible after all. Perception & Psychophysics, 70(7), 1327-34.

11.

Dakin, S. C., &Watt, R. J. (1997). The computation of orientation statistics from visual texture. Vision Research, 37(22), 3181-3192.

12.

Eckstein, M. P., Ahumada, A. J., & Watson, A. B. (1997). Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14(9), 2406-19.

13.

Foley, J. M., & Legge, G. E. (1981). Contrast detection and near-threshold discrimination in human vision. Vision Research, 21(7), 1041-53.

14.

Fouriezos, G., Rubenfeld, S., & Capstick, G. (2008). Visual statistical decisions. Perception & Psychophysics, 70(3), 456-464.

15.

Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley.

16.

Haberman, J., &Whitney, D. (2007). Rapid extraction of mean emotion and gender from sets of faces. Current Biology : CB, 17(17), R751-3.

17.

Haberman, J., & Whitney, D. (2010). The visual system discounts emotional deviants when extracting average expression. Attention, Perception & Psychophysics, 72(7), 1825-38.

18.

Haberman, J., & Whitney, D. (2009). Seeing the mean: ensemble coding for sets of faces. Journal of Experimental Psychology: Human Perception and Performance, 35(3), 718-34.

19.

Heeley, D. W., & Buchanan-Smith, H. M. (1996). Mechanisms specialized for the perception of image geometry. Vision Research, 36(22), 3607-27.

20.

Klein, S. A. (2001). Measuring, estimating, and understanding the psychometric function: a commentary. Perception and Psychophysics, 63, 1421-1455.

21.

Lee, H., Baek, J., & Chong, S. C. (2016). Perceived magnitude of visual displays: Area, numerosity, and mean size. Journal of Vision, 16(3), 12.

22.

Leib, A. Y., Kosovicheva, A., & Whitney, D. (2016). Fast ensemble representations for abstract visual impressions. Nature Communications, 7, 13186.

23.

Lesmes, L. A., Lu, Z.-L., Baek, J., Tran, N., Dosher, B. A., & Albright, T. D. (2015). Developing Bayesian adaptive methods for estimating sensitivity thresholds (d’) in Yes-No and forced-choice tasks. Frontiers in Psychology, 6, 1070.

24.

Levitt, H. (1971). Transformed up-down methods in psychoacoustics. The Journal of the Acoustical Society of America, 49(2), 467-477.

25.

Lu, Z.-L., & Dosher, B. A. (1998). External noise distinguishes attention mechanisms. Vision Research, 38(9), 1183-98.

26.

Lu, Z.-L., & Dosher, B. A. (1999). Characterizing human perceptual inefficiencies with equivalent internal noise. Journal of the Optical Society of America A, 16(3), 764.

27.

Lu, Z.-L., & Dosher, B. A. (2008). Characterizing observers using external noise and observer models: assessing internal representations with external noise. Psychological Review, 115(1), 44-82.

28.

Lu, Z.-L., & Dosher, B. A. (2013). Visual Psychophysics: From Laboratory to Theory. Cambridge: The MIT Press.

29.

Macmillan, N. A., & Creelman, C. D. (1991). Detection Theory: A User’s Guide. New York: Cambridge Univesity Press.

30.

Maule, J., Witzel, C., & Franklin, A. (2014). Getting the gist of multiple hues: metric and categorical effects on ensemble perception of hue. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 31(4),A93-102.

31.

Morgan, M. J., Ward, R. M., & Hole, G. J. (1990). Evidence for positional coding in hyperacuity. Journal of the Optical Society of America. A, Optics and Image Science, 7(2), 297-304.

32.

Nachmias, J. (1981). On the psychometric function for contrast detection. Vision Research, 21(2), 215-23.

33.

Nachmias, J., & Sansbury, R. V. (1974). Grating contrast: discrimination may be better than detection. Vision Research, 14(10), 1039-42.

34.

Parkes, L., Lund, J., Angelucci, a, Solomon, J. A., & Morgan, M. J. (2001). Compulsory averaging of crowded orientation signals in human vision. Nature Neuroscience, 4(7), 739-44.

35.

Pelli, D. G. (1985). Uncertainty explains many aspects of visual contrast detection and discrimination. Journal of the Optical Society of America. A, Optics and Image Science, 2(9), 1508-32.

36.

Pelli, D. G., & Zhang, L. (1991). Accurate control of contrast on microcomputer displays. Vision Research, 31(7-8), 1337-50.

37.

Robitaille, N., & Harris, I. M. (2011). When more is less: extraction of summary statistics benefits from larger sets. Journal of Vision, 11(12), 1-8.

38.

Sweeny, T. D., & Whitney, D. (2014). Perceiving crowd attention: ensemble perception of a crowd’s gaze. Psychological Science, 25(10), 1903-13.

39.

Teghtsoonian, M. (1965). The Judgment of Size. The American Journal of Psychology, 78(3), 392.

40.

Wannacott, T. H., & Wonnacott, R. J. (1981). Regression a second course in statistics. New York: Wiley.

41.

Watamaniuk, S. N., & Duchon, A. (1992). The human visual system averages speed information. Vision Research, 32(5), 931-41.

42.

Williams, D. W., & Sekuler, R. (1984). Coherent global motion percepts from stochastic local motions. Vision Research, 24(1), 55-62.

43.

Yeshurun, Y., Carrasco, M., & Maloney, L. T. (2008). Bias and sensitivity in two-interval forced choice procedures: tests of the difference model. Vision Research, 48, 1837-1851.

바로가기메뉴

논문 상세

Vol.30 No.2

평균 크기 지각에 대한 계산 모형

A computational model of mean size perception

초록

Abstract

참고문헌

한국심리학회지: 인지 및 생물