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1 Received January 8, 010; Revised August 4, 010; Accepted September 30, , The Effects of Stimulus Size and Retinal Position on Depth Perception from Binocular Disparity Masayuki SATO and Shoji SUNAGA Department of Information and Media Engineering, University of Kitakyushu, 1 1 Hibikino, Wakamatsu-ku, Kitakyushu, Department of Human Science, Kyushu University, Shiobaru, Minami-ku, Fukuoka, The effects of stimulus size and retinal position on apparent depth from binocular disparity were measured using a random-dot stereogram with one dimensional DoG difference of Gaussian disparity modulation along either horizontal or vertical direction. The standard deviations of two Gaussians were 1 deg and 1.5 deg respectively, corresponding to 0.18 cpd peak spatial frequency. The stimulus subtended 10 deg to the direction with disparity modulation and the size perpendicular to that direction was varied from 0.5 deg to 0 deg in Experiment 1. The central area of, 6, 10, or 14 deg was blanked in the 0-deg test stimulus in Experiment. The results showed that stimulus size larger than 6 deg was necessary to detect disparity modulation along the horizontal direction, whereas to detect vertical modulation much smaller stimulus size was enough. Further analysis indicated that the cooperative interaction between the central and peripheral visual field in stereopsis was well explained by probability summation of outputs from insensitive local disparity detectors. Key words: binocular disparity, depth perception, stimulus size, retinal eccentricity, anisotropy Rogers Graham 1 Craik-O Brien- Cornsweet Bradshaw Rogers Hibbard Gillam msato@env.kitakyu-u.ac.jp

2 Cambridge Research Systems VSG /5 CRT RDFH StereoGraphics Crystal- Eyes 3 57 cm CRT arc min 0 /deg Hz cd/m 0.0 cd/m Fig. 1 Random dot stereogram illustrating an example of test stimulus used in A the vertical modulation condition and B the horizontal modulation condition in Exp Fig. 1 1 Fig. 1 A y x, y d DoG y y d A 3exp exp σ 15. σ A 3.3 arc sec 1790 arc sec d s 1 deg Fig. 1 B x cd/m 6.1 cd/m 1.0 cd/m cd/m 0.44 cd/m cd/m

3 10 deg s 0.5 deg 0 deg s 1 A log A 34 s 0.5 deg deg 6 deg 3 deg 6 deg 10 deg 14 deg 0 deg Fig. SS A s 0.5 deg 6 deg deg 0 deg deg 6 deg Fig. Fig. Probability of correct response, opposite response, flat response, not fused response, and false match response for observer SS. 1 7 s 0.5 deg s deg s s 0 deg Fig. 0 deg 0 deg.4 deg

4 Fig. 3 Probability of correct response, opposite response, and flat response for four observers s 0.5 deg, vertical modulation condition. Fig. s Fig. 3 s 0.5 deg 4 SS YT MS Fig. 4 Effects of stimulus size s on the probability of detection. p d p nd p nd p d p nd/ p nd/ p d

5 Fig. 4 4 Fig. 4 MS s deg SS YS s Fig. 5 Random dot stereogram illustrating an example of test stimulus used in the horizontal modulation condition of Exp Fig. 6 Effects of gap size g on the probability of detection Fig. 5 1 g deg 6 deg 10 deg 14 deg Fig. 6 4 Fig. 4 g g g 14 deg

6 Fig. 7 Stereo thresholds as a function of eccentricity. 1 deg 6 deg g 1 10 deg 10 deg 8 9 Fig Fig. 7 stereo threshold g Prince Rogers 8 DoG 0.18 cpd Prince Rogers Fig. 7 Prince Rogers Prince Rogers Fig. 8 A Probability to detect horizontal depth modulation for the central stimulus Exp. 1. B That for the peripheral stimulus Exp.. C Probability of depth detection predicted by the probability summation model. N 4. Rawlings Shipley 9 1 deg 5. 1 s 0 deg

7 1 s 6 deg g 6 deg 1 s 0 deg s a deg g a deg s 0 deg 1 1 s 0 deg s 0 deg Fig. 8 Fig. 8 A 1 4 Fig. 8 B 4 Fig. 8 C 1 s 0 deg s g s g 6. 1 deg 0 deg 3 0 deg 1 B. J. Rogers and M. E. Graham: Anisotropies in the perception of three-dimensional surfaces, Science, M. F. Bradshaw and B. J. Rogers: Sensitivity to horizontal and vertical corrugations defined by binocular disparity, Vision Res., P. B. Hibbard, M. F. Bradshaw, K. Langley and B. J. Rogers: The stereoscopic anisotropy: Individual differences and underlying mechanisms, J. Exp. Psychol. Hum. Percept. Perform., Cornsweet Cornsweet B. Gillam, D. Chambers and T. Russo: Postfusional latency in stereoscopic slant perception and the primitives of stereopsis, J. Exp. Psychol. Hum. Percept. Perform., S. J. D. Prince and B. J. Rogers: Sensitivity to disparity corrugations in peripheral vision, Vision Res., S. C. Rawlings and T. Shipley: Stereoscopic acuity and horizontal angular distance from fixation, J. Opt. Soc. Am.,

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