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 ov

er 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 dir

ection of mean. (Williams & Sekuler, 1984)– We can discriminate between these global percepts whe

n 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 redundanc

y in the sensory input. (Barlow, 1961)– Individual neurons rapidly adapt to changes in contrast a

nd 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 circl

es 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 1.25.– 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 c

ircles increase with delay.– The thresholds with heterogeneous are higher that homo

geneous displays.– The thresholds at 2 s are higher than at 100 ms or 0 ms de

lays.– 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 parall

el 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 wi

th 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 comp

arison 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.