ECVP 2011, August 28 – September 1, Toulouse, France
Models of substitution masking
Endel Põder
Institute of Psychology, University of Tartu, Estonia
E-mail: endel.poder@ut.ee
Background
The new model:
Substitution masking
Similar to CMOS, but with a more realistic mechanism of attention.
Enns and Di Lollo (1997) found that a visual target can be strongly masked by just
four dots presented after the target. A necessary precondition was unfocused
attention.
Di Lollo, Enns & Rensink (2000) demonstrated a similar type of masking when the
masking dots were turned on simultaneously with the target but remained visible for
some time after the target termination (common-onset masking). Unfocused attention
was warranted by distracting objects.
Two attentional episodes in each trial.
Computational Model of Object Substitution (CMOS)
2) Selective stage: d’ dependent on mask duration (function estimated from
the data), independent of set-size.
Di Lollo et al (2000) proposed that substitution masking reflects a reentrant
hypotheses-testing process in vision. They presented a quantitative model (CMOS)
that should simulate this reentrant hypotheses-testing.
At the beginning, attention is divided between all objects in a display.
The time of focusing of attention is independent of set-size.
1) Unselective stage: d’ dependent on set-size, independent on mask duration
du (n)  du (1)
n
d '  d ' d '
Total d’
2
u
2
s

pcn    x  d n   Φx 
m 1
This study
Probability correct
I evaluate the assumptions of the Di Lollo et al (2000) model and its supposed
relationship with reentrant processing, and test an alternative model for substitution
masking data.
Fit to the experimental data from Di Lollo et al (2000)
R2=0.99 (cf. CMOS, R2=0.93)
1. CMOS as an attentional gating model
There are two main equations for transformation of signals from target,
masker and noise:
W j k  

(1)
Pj k  1
j

P k  1
2
j
(2)
1 2
Substituting Wj(k-1) in equation (1) with equation (2) transforms this part of the
model into a single equation
Pj k  

Pj k  2
j

P k  2 
2
j
1 2
n=1
1
Proportion correct
Pj k   W j k  1  I j k  1

dx
n=2
0.9
n=4
0.8
n=8
0.7
n=16
0.6
MH
0.5
 I j k  1
0
100
200
300
400
Mask duration (ms)
This is just an integrating circuit (low-pass filter) applied to input signals!
Additional component: delay of focusing of attention, proportional to set-size
tc  S  n
Probability of correct recognition is determined by the target signal energy relative
to the total signal energy at the moment of arrival of attention.
The low-pass input filter together with the attentional delay form a simple
attentional gating model (Sperling & Weichselgartner, 1995).
Proportion correct
1
n=1
n=2
0.9
n=4
0.8
n=8
0.7
n=16
0.6
RG
0.5
0
Conclusion 1:
100
200
300
400
Mask duration (ms)
CMOS is a version of attentional gating model. It does not
contain anything related to reentrant hypotheses-testing.
Estimated d’ of selective stage
2. New model for substitution masking
A problem with CMOS
CMOS predicts a particular form of the mask duration and set-size interaction.
Because the time of deployment of attention is supposed to be proportional to the
set-size, the breakpoints of the masking curves should be shifted along the x-axis, in
proportion to the set-size. This is not observed in experimental data. Furthermore,
there is no good reason for the delay proportional to the set-size.
d' of selective stage
3
MH
RG
2
1
0
Typical CMOS predictions
100
200
300
400
Mask duration (ms)
1
Proportion correct
0
n=1
n=2
0.9
Conclusion 2:
n=4
The new attentional gating model fits the data better than CMOS.
n=8
0.8
0.7
n=16
References
0.6
Di Lollo, V., Enns, J.T., & Rensink, R.A. (2000). Competition for consciousness among visual events: The
psychophysics of reentrant visual processes. Journal of Experimental Psychology: General, 129 (4), 481-507.
0.5
Enns, J.T., & Di Lollo, V. (1997). Object substitution: A new form of visual masking in unattended visual locations.
Psychological Science, 8, 135-139.
0
100
200
Mask duration (ms)
300
400
Sperling, G., & Weichselgartner, E. (1995). Episodic theory of the dynamics of spatial attention. Psychological
Review, 102, 503-532.