Representation of statistical properties 作 者： Sang Chul Chong, Anne Treisman 報告者：李正彥 日 期： 2006/3/23

Outline Introduction Experiment 1 Experiment 2 Experiment 3 General discussion

Introduction The representations of daily similar objects is summarized with statistical descriptors. Task: judge the mean with arrays of 12 circles of heterogeneous sizes. – Exposure duration, and memory delays. – The accuracy within the same distribution, and across different distributions (normal, uniform, two-peaks, and homogeneous).

Composite image hypothesis (Davidson, Fox, & Dick, 1973) – Visual system builds up a composite perceptual image over consecutive fixations by overlapping successive perceptual image in a system that maps a retinal reference frame onto a spatiotopic reference frame. People abstract a schematic representation of a scene from several successive fixations. (Hochberg, 1978; Hock & Schmelzkopf, 1980)

In change detection experiments, observers have considerable difficulty in detecting task due to the blank screen in alternation. (Rensink, O’Regan, & Clark, 1997) Statistical properties may play a part in forming schematic perceptual representations. Visual system represents overall statistical properties when sets of similar objects are present. (Ariely, 2001; Ariely & Burbeck,1995)

Statistical Process Motion perception – People form a unified global percept of motion in the direction of mean. (Williams & Sekuler, 1984) – We can discriminate between these global percepts when they differ by as 1°~2° for distribution containing up to about 45 different directions. (Watamaniuk et al., 1989) – The average speed-discrimination thresholds ranging from 5~10%.

Orientation – 1.5° for line textures. – 2.5 ° for Glass patterns. – 1.2 °~2.5 ° for Gaussian distributed orientations. Neuron level – Early sensory neurons is to remove statistical redundancy in the sensory input. (Barlow, 1961) – Individual neurons rapidly adapt to changes in contrast and spatial scale (Smirnakis et al., 1997), orientation (Muller et al., 1999), variance of velocity (Brenner et al., 2000).

Size – People are better at judging the mean size of a set of circles than at judging any randomly selected ones. (Ariely, 2001) The mean judgment task: followed by a single probe circle, then, is it larger or smaller? Depended on immediate memory. – Modification Target and probe are present together with successive presentation at ISIs of 100 ms or 2 s. 3 kinds of size judgments: mean size in heterogeneous displays, same-sized items in homogeneous displays, and size of single items presented alone.

Experiment 1 Method – 5 participants from Princeton University, all had normal or corrected-to-normal vision. – Participants viewed the screen with both eyes, and were seated approximately 66 cm from the screen. – The mixture sizes were equally spaced on a log scale separated by a factor of – In each trial the circles are scaled by factors – 0.7, 0.8, 0.9, 1.

Design – Independent variables The type of size comparison to be made. Either the mean sizes of the heterogeneous arrays, or the sizes of the circles in the 2 homogeneous arrays. Presentation mode. Simultaneous, or successive (2 ISIs: 100 ms and 2 s). – Each participant served in at least 4 sessions containing six blocks ([heterogeneous, homogeneous, and single] x [simultaneous or successive]) each. – The circles on each side differed by a constant (2%, 4%, 6%, 8%, 10%, and 12%) difference in diameter withing any given display. – Threshold was defined as the percent diameter difference between the 2 displays that gave 75% accuracy in this graph.

Procedure

Results and discussion – Thresholds were low for all 3 types of size judgments. – Thresholds for the heterogeneous arrays and the single circles increase with delay. – The thresholds with heterogeneous are higher that homogeneous displays. – The thresholds at 2 s are higher than at 100 ms or 0 ms delays. – At 2 s ISI, homogeneous condition was different from the mean and single item conditions. – The process of extracting the mean size might be a parallel preattentive process. → Experiment 2

Experiment 2 How the exposure duration affected judgments. Design – Independent variables The type of size comparison (heterogeneous, homogeneous, and single). Exposure duration time (50 ms, 100 ms, 1s). – 2 sessions consisting of 3 blocks each. – The estimate method of threshold is the same as experiment 1 (except the 14% step). Procedure is the same as the simultaneous condition in Experiment 1.

Results and discussion – Overall thresholds differed significantly across the size judgment condition. – Threshold in heterogeneous mean condition is higher than in homogenous condition. – Thresholds at 50/100 ms durations are higher that those at 1 s duration. – The interaction between the type of size judgment and the presentation duration was not significant. – Thresholds for mean size were higher than for those for homogeneous and single condition at 1 s duration. – Participants are capable of extracting the mean size quite accurately in as little as 50 ms.

Experiment 3 4 different distributions of sizes – Uniform: equal numbers of each of 4 different sizes. – Two-peak: equal numbers of 2 different sizes. – Normal: unequal numbers of four different sizes. – Homogeneous: only one size.

Design – All possible pairs of the distributions type were tested with the 5 experienced participants. The 2 new participants were tested on the 6 possible pairs among 3 distributions. – The order of blocks are random selected. And the order for the next participant was the reverse of the previous one. – The estimation of threshold is the same as Experiment 2, except 2 naïve participants had a 3% step. 3 of the experienced participants redid 3 / 4 pair-wise comparison with a step size of 3%/4% diameter differents.

Results and discussion – The threshold across different distributions is higher that within the same distributions. – Overall effect of distribution type is significant. – Threshold of pairs from 2 homogeneous distributions is lower than pairs drawn from 2 normal distributions. – Judgment on two-peak and a homogeneous pair has the highest threshold. – When the distributions are different, participants are forced to compare the means rather that any single items. – Participants are able to respond to the mean of 2 sizes, almost as accurately as to a single size. – Thresholds for the naïve participants did not differ from the experienced ones.

General Discussion The mean judgments with heterogeneous displays were as accurate as the single item judgments. (Ex 1) Thresholds rise significantly with delay (only to 10%), and with decreased presentation time (only to 8%). In brief exposures and long delays, the homogeneous displays have the best performance. Thus the redundant presentation is helpful in processing. In long exposures and no delays, the single item displays have better performance than the heterogeneous displays. (maybe the ceiling effect caused by internal noise) The mean size judgment is a separate parallel mechanism. Participants really were averaging sizes when the made the judgments. (Experiment 3)

Statistical processing does not depend on conscious process. Perception of the mean depends on first registering all the individual elements. The function of statistical properties of a display in everyday life. – Help us to distinguish different surfaces by different texture. – Facilitate detection of an odd objects in a scene. – Economize on the limited capacity of the visual system.