Temporal dynamics of perceptual decision

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Content TEMPORAL DYNAMICS OF PERCEPTUAL DECISION

by

Wilson Chu

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PYSCHOLOGY)

May 2008

Copyright 2008 Wilson Chu

ii
DEDICATION

To My Family

iii

ACKNOWLEDGEMENTS

To Prof. Bosco Tjan, an endless source of information and
humor. Always willing to drop everything to help you when you
have questions, whether it be about calibrating eye-trackers,
building a TTL trigger, or where to get the best coffee beans.
To Prof. Joseph Hellige, Prof. Frank Manis, and Prof.
Judith Hirsch, for generously providing their time and endless
patience. All the members of LOBES, both past and present, for
their countless hours of support and enduring friendships.
Last, but certainly not least. My advisor, Prof. Zhong-Lin
Lu. From the first time we met in his Psych 274 class, he has
continually inspired, challenged and motivated me. His
determination, contagious, his intelligence, is unwavering. If
it were not for his persistent support and guidance I would not
be where I am today. It has been both a great privilege and a
great honor to have studied under such a brilliant man. Thank
you.

iv
TABLE OF CONTENTS
Dedication ii
Acknowledgement iii
List of Tables vi
List of Figures vii
Abstract viii
Chapter I. Introduction 3
1.1 Previous Attempts to Integrate Perception and
Reaction Time 4
1.2 Reaction Time Models 11
1.2.1.1 Criterion Models 11
1.2.1.2 Relative Criterion Models 11
1.2.2 Sequential Sampling Framework 11
1.2.2.1 Random-Walk Models 12
1.2.2.2 Weiner Diffusion 12
1.2.2.3 Ornstein-Uhlenbeck Diffusion 13
1.2.2.4 Accumulator Models and Counter
Models 13
1.2.2.5 Leaky Competing Accumulator Model 14
1.3 Sensory Analysis - A Signal Detection
Approach 16
1.3.1 Signal Detection Theory 16
1.3.2 External Noise Method 18
1.3.3 Perceptual Template Model (PTM) 22
1.4 Overview 24

Chapter II. Characterizing the Temporal Dynamics of
Perceptual Decision
2.1 Experiment I 25
2.1.1 Observers 25
2.1.2 Display and Visual Stimuli 25
2.1.3 Design 27
2.1.4 Cued-Response Procedure 29
2.1.5 Procedure 31
2.2 Results 32
2.2.1 Reaction Time Distributions 32
2.2.2 Speed-Accuracy Functions 34
2.2.2.1 Exponential Fits 34
2.2.2.2 Dynamic Decision PTM 35
2.3 General Discussion 45

Chapter III. Effects of Perceptual Learning on the Temporal
Dynamics of Perceptual Decision

3.1 Overview 49
3.1.1 Perceptual Learning 50
3.1.2 Plasticity in the Nervous System 50
v
3.1.3 Mechanisms of Perceptual Learning 51
3.1.4 Summary 52
3.2 Experiment II 53
3.2.1 Observers 53
3.2.2 Display and Visual Stimuli 53
3.2.3 Design 56
3.2.4 Procedure 56
3.3 Results 57
3.3.1 Data Analysis 57
3.4 Discussion 63
Chapter IV. General Discussion & Conclusion 65
Bibliography 69

vi
LIST OF TABLES

Table 1 Parameters (full model and reduced model) for
exponential fits.

38
Table 2 Parameters from model fits with dynamic-
decision PTM. Full and reduced models shown.

44
Table 3 Maximum-likelihood model estimation results.

60

vii

LIST OF FIGURES

Figure 1 A schematic diagram of the perceptual template
model.

23
Figure 2

Typical trial sequence 28
Figure 3

Four sets of hypothetical speed-accuracy trade-
off functions

30
Figure 4

Zero noise condition. A histogram of the
standard reaction time experiment.

33
Figure 5

High noise condition. A histogram of the
standard reaction time experiment.

34
Figure 6

Zero noise Condition. Discrimination
performance (d’) as a function of total
processing time.

39
Figure 7

High noise Condition. Discrimination
performance (d’) as a function of total
processing time.

40
Figure 8

SAT Functions. Zero Noise Condition. 41
Figure 9

SAT Functions. High Noise Condition. 42
Figure 10

Illustration of a typical trial sequence. 54
Figure 11

Results of fits from the maximum-likelihood
estimation. Zero Noise Condition.

58
Figure 12

Results of fits from the maximum-likelihood
estimation. High Noise Condition.

59
Figure 13

Estimated contrast threshold derived from
maximum-likelihood estimation with d’ set to
1.349. Zero Noise Condition.

61
Figure 14

Estimated contrast threshold derived from
maximum-likelihood estimation with d’ set to
1.349. High Noise Condition.

62

viii
ABSTRACT

We combined the external noise method (1) with the cue-to-
respond speed accuracy trade-off (SAT) paradigm (2) to
characterize the temporal dynamics of perceptual decision-making.
Observers were required to identify the orientation of one of
eight briefly presented peripheral Gabor targets (+/- 12 deg) in
both zero and high noise. An arrow, occurring in the center of
the display cued the observer to the target location 234 ms
before the onset of a brief target display; an auditory beep,
occurring at one of eight delays (SOA=25 to 800 ms) after the
target onset, cued the observers to respond. Five Gabor
contrasts, spanning a wide range of performance levels, were
tested in each external noise condition. Increasing accuracy of
discrimination (d’) was measured over processing times from 210
to 940 ms (as a function of SOA to the cue) in each external
noise and Gabor contrast condition. All ten SAT functions were
well fit by exponential functions with identical time constant
and intercept but different asymptotic levels. This suggests
that, despite enormous variation in the external noise and
contrast energy in the stimulus, and in the ultimate accuracy of
performance, information accumulated with the same rate and
starting time across all the external noise and contrast
conditions. In addition, we conducted a standard response time
version of the experiment both before and halfway through the SAT
procedure. Data from the response time version of the experiment
were all consistent with the speed-accuracy trade-off data, but
ix
primarily differed in response accuracy. A simple elaboration of
the perceptual template model (3) with a dynamic decision process
in which information accumulates with the same rate but with step
sizes proportional to the signal to noise ratio in the perceptual
representation of the visual input fully accounts for the
results.
The cued-to respond Speed-Accuracy Tradeoff (SAT) paradigm
(1) combined with external noise manipulations was used to
evaluate the effects of perceptual learning on the temporal
dynamics of perceptual decision. Observers were trained in a 2AFC
Gabor (+/- 12˚) orientation-discrimination task in eight
sessions. An auditory beep occurred at one of 8 delays (SOA =
25ms to 800ms) that cued the subjects to respond. Subject’s
performance was constrained to 79.1% and 70.7% correct at the
longest SOA by a 3-to-1 and a 2-to-1 staircase respectively that
adjusted the contrast of the signal stimuli. All subjects showed
learning, demonstrated by an average reduction of contrast
threshold levels of 23% in high noise and 22% in low noise. An
elaborated perceptual template model with a dynamic decision
process (2) provided very good fits to the data. The best-fitting
model included identical time constant and intercept (t
0
) across
all the training sessions. The result suggests that perceptual
learning enhances stimulus (in the zero external noise condition)
and excludes external noise (in the high external noise
condition) without altering the temporal dynamics of perceptual
decision.
1

I. DYNAMIC DECISION PERCEPTUAL TEMPLATE MODEL

2
1. INTRODUCTION
Perceptual decision has recently become an active area of
research in cognitive psychology and in neuroscience. Perceptual
decision provides for an interesting area of research because of
its unique role of offering a glimpse of how the brain connects
sensory information to behavior. Thus, understanding the basis
of perceptual decision affords us an opportunity to model the
principles that govern decision. An important step in making
progress towards this goal is to develop a comprehensive
framework that maps sensory information to the decision process.
Up until recently, perceptual decision has been studied either
from a signal detection perspective or a dynamic temporal
analysis approach, but never jointly.
Signal detection theory (SDT) has provided researchers with
a powerful methodology for understanding how decisions are made.
The SDT framework suggests that decision for a discriminative
task can be characterized by two general components: sensory
information and criterion. Sensory information comprises of
stimulus features such as spatial frequency, signal contrast,
stimulus orientation and external noise, which affects the
sensitivity of detecting or discriminating a signal stimulus.
Criterion is a subjective value that the observer chooses in
order to optimize their performance. By shifting the criterion
along the decision axis, either through choosing a low or high
criterion, an observe may bias their response. However, SDT has
3
historically characterized decision in terms of accuracy while
largely ignoring the temporal properties.
On the other hand, researchers in cognitive psychology
offer an equivalent modeling based on alternative behavioral
techniques involving response time and magnitude estimation.
Typically, researchers in this domain look at the incoming
moment-by-moment fluctuation of sensory information. This
approach suggest that these fluctuations impinge on the
parameters governing decision such as the rate of information
accumulation and the time it takes to reach a criterion level and
are dependent on both sensory and decision parameters.
Until recently, the approach to study perceptual decision
took two relatively independent routes. The aim of this
dissertation is to provide a comprehensive and coherent observer
model to characterize the temporal dynamics of perceptual
decision. Specifically, a systematic measure of both reaction
time and performance accuracy will be evaluated across several
performance criteria. To map the sensory information to the
decision process, the Perceptual Template Model (Lu & Dosher,
1998) will be extended to incorporate a dynamic process.
In addition, we will extend the dynamic decision Perceptual
Template model to a study in perceptual learning. Historically,
perceptual learning has been characterized by improvements under
several domains such as contrast threshold reduction and
performance accuracy improvement. However, the temporal
properties of perceptual learning have not fully understood. The
4
results from this study seems to suggest that despite the
enormous improvement observed in performance, the temporal
dynamics remained relatively unchanged.
The results from these experiments offer important new
theoretical constraints on models of the sensory system.

1.1 PREVIOUS ATTEMPTS TO INTEGRATE PERCEPTION AND REACTION
TIME
Historically, perceptual decision has been studied in the
context of reaction time (RT); from stimulus features (Hovland,
1937; Gregg & Brogden, 1950; Birren & Botwinick, 1955; Woodrow,
1915; Vickers, 1972; Palmer et al, 2004), choice (Vickers, 1979;
Nickerson & Burnham 1969; Donders, 1868), across stimulus
modalities (Kiesow, 1903; Baxter & Travis, 1938; Woodworth &
Schlosbert, 1954, Wright, 1951) and stimulus complexity (Welford,
1981, Luce, 1968). Reaction-time tasks are critical because it
provides us with a window into how perceptual decisions are
formed. Many of these studies provide an account on either RT or
accuracy, and some have attempted to describe their relationship.
Several studies developed theories that have attempted to
provide the foundation for understanding the relationship between
response time and response probability. An example of such theory
includes the Neural Timing Theory (Luce & Green, 1972). They
suggest that the overall response time is the sum of the decision
latency, which depends both on the signal intensity and a
decision rule. The Neural Timing Theory suggest that the sense
5
organ (for example, the human eye) is assumed to be a transducer
that converts the intensity of the incoming signal into several
trains of pluses. The output of a sensory system is treated as a
set of sequences of discrete, brief events or “neural pulses”.
The intensity is represented by the temporal pattern of the
pluses and decisions are based on the interarrival times (IATs)
of the neural pulses.
The Fast Guess Theory (FGT) (Yellot, 1971; Ollman, 1996)
assumes that the number of guesses a subjects make in response to
a task increases as the amount of time given to make this
judgment decreases. The Fast Guess Theory emphasizes on
controlling response accuracy through the proportion of guesses.
Thus changes in mean RT are a byproduct of changes in response
accuracy.
The Fixed Sample Size Signal Detection Theory (Green &
Luce, 1967) assumes that for a given RT deadline, a certain
number of sensory samples have accrued. By summing these
samples, a subject may improve accuracy in the same way as
experimenter who increases the sample size. If each sample
requires a fixed average sampling time, then the average time to
gather a fixed number of samples is constant, regardless of the
stimulus presented or the response made. However, accuracy
depends on the number of samples accrued, thus as sample size
increases, so do accuracy.
On the other hand, Relative Judgment Theory (RJT) (Link &
Heath, 1975; Link, 1975) suggest that the parameters driving the
6
relationship between reaction time and response probability are
under subjective control. RJT assumes that the accumulation rate
towards two criteria (in a two judgment task) is the same for
both response alternatives.
Furthermore, several studies have attempted to directly map
stimulus features (such as contrast and spatial frequency) to RT
(Breitmeyer, 1975, Burkhardt, Gottesman, & Keeman, 1987; Hartwell
& Cowan, 1993; Mihaylova, Stomonyakov, & Vassilev, 1999, Parker,
1980; Tolhurst, 1975) in an effort to systematically infer what
role stimulus information has on the decision processes. It has
also been suggested that as the stimuli become more
discriminable, response latencies decrease and response accuracy
increases (Johnson, 1939; Link & Tindall, 1971; Pickett, 1967;
Pike, 1968; Vickers, 1970) which is congruous with the intuition
that the subject is accumulating stimulus information in time.
However, many of these studies do not explain the relationship
between stimulus features and RT in terms of our understanding of
the early processing of signal stimulus in the primary visual
pathway.
For example, using a 2AFC paradigm for contrast
discrimination, Tippana and colleagues (2001) measured choice
reaction times to contrast differences and compared it to
increment thresholds obtained psychophysically at pedestal
contrast near detection thresholds. They discovered that choice
reaction times were shorter at low pedestal contrast and longer
at higher pedestal contrast when compared to detection. However,
7
in their analysis, they argue against a purely sensory process
explanation. In order support the argument that the decision
process can be explained in terms of sensory processes only, they
argued that temporal integration time should become shorter as
contrast levels increases (Georgeson, 1987; Snowden, 1996), which
is contradictory to their findings. They proposed that the
addition of a decision-making process offers a more plausible
account for the behavior of CRTs. They propose that the
dependence of CRTs on pedestal contrast could be explained by
changes in the response criterion that can occur from trial-to-
trial or within a block (Green and Swets, 1966; Grice et al.,
1977; Chung & Wolfe, 1996; Lages & Treisman, 1998). They suggest
that the variability of the information accumulation process
influences the response criterion because when the variability of
a signal is low, it is considered to be more reliable, therefore
a decision can be made with less evidence.
In addition Tippana and colleagues stated the need for a
model that is capable of accounting for both contrast perception
and reaction times. They agree that most models of reaction
times deal primarily with the decision-making processes without
any consideration for the preceding sensory processing (Link &
Heath, 1975; Vickers, 1979; Ashby, 1983; Nosofsky & Palmer, 1997;
Ratcliff & Rounder, 2000). Although they strongly support the
need, they have not devised a way to integrate a nonlinear
transducer model (a common model for contrast discrimination)
with a decision-making process to account for CRTs.
8
In another study, Ratcliff (1999) suggest that the
accumulation of information is not constant over time and this
variability is assumed to be normally distributed. As a result of
this variability inherent in the accumulation of information,
there is a possibility of the accumulation process terminating at
the wrong boundary (Ratcliff, 1999). The rate at which a process
approaches a boundary (amount of information accumulated per unit
of time) is termed the drift rate. According to Ratcliff, on
average, a stimulus with a large and positive drift rate will
approach the positive boundary quickly resulting in a low
probability that the inherent variability of the process will
drive it towards the negative boundary. According to Ratcliff
(1999) the differences in drift rates can be attributed to “easy”
or “difficult” stimuli. Under this rational, “easy” stimuli
would result in a drift rate with an extreme value which response
fast and accurate on average. On the other hand,” difficult”
tasks would have the opposite effect. The drift rate for
“difficult” task would be in an intermediate value and responses
are slower and less accurate on average.
In Ratcliff & Rounder’s study (2000) they address the
question of how mask affects the stimulus information that enters
the decision process. One of their hypotheses assumes that
information output from early perceptual processes oscillates
according to the early onset and subsequent masking of the
stimulus. This is termed the non-stationary drift hypothesis. A
second hypothesis that they proposed, the stationary drift, is
9
that information entering the decision process from early
perceptual processes remains constant over time, which represents
the total amount of information encoded between stimulus onset
and subsequent masking. They quantify these hypotheses using the
diffusion model framework (Ratcliff, 1978). Their model contains
three general components: a race between two processes, a change
detector for luminance transient and luminance energy integrator.
The model assumes that the information output from a stimulus
begins to accumulate from a starting point and continues towards
one of two criteria. Each criterion represents one of two
possible responses. The Drift Rate is the rate at which
information is accumulated. A decision is made only when the
amount of information reaches one of the two criteria. The scope
of their study was to distinguish between the stationary and non-
stationary drift hypothesis. However, their conclusion does not
deal directly with the perceptual processes front end. The scope
of their study focused on the decision process and the
information output from the perceptual processing stage is
assumed. Furthermore, their model is rather constrained,
leading one to question its generalisability.
A recent study by Palmer, Huk & Shadlen (2005) propose a
theory of perceptual decision based on a diffusion model. Palmer
et. al suggest that although psychometric functions provide a
tool for analyzing the relationship between accuracy and
stimulus strength, the underling time course describing the
relationship between response time and stimulus strength has not
10
been studied. They assume that d’ is linear with stimulus
strength and the shape of the psychometric function follows from
the distribution of the noisy representation. They propose that
proportional scaling can be generalized by allowing d’ to be a
power function. Their model is capable of accounting for the
effect of stimulus strength on both response time and accuracy
with a single sensitivity parameter. However, as we will see, a
linear integration is not sufficient enough to describe the
interaction between the stimulus and the perceptual system.
From these studies, one can concluded several points.
These studies all seem to suggest that most research on
perceptual processing deals with processing at the input and
encoding stages. None of the earlier research has produced a
model that can fully account for data that associates a
particular response with a response time. Many of these studies
argue the need for a model that accounts for the time course in
the formation of decision and linking them to perceptual
processing models.
Over the years, various statistical models have been
developed to explain a variety of reaction-time decision tasks.
Two general classes of model have emerged. One class of model has
been developed to explain complex decisions among differently
weighted alternatives (Criterion Models) (Luce & Raiffa, 1957;
Rapoport, 1959). A second class of models that has been widely
accepted is the sequential-sampling models. (Stone, 1960; Pike,
1966; Laming, 1968; Link & Heath, 1975; Vickers, 1970; Ratcliff,
11
1978; Heath, 1992; Ratcliff, 1980; Smith, 1995). In the next
two sections, I will review several dominant RT models.

1.2 REACTION TIME MODELS
1.2.1 CRITERION MODELS
1.2.1.1 COMPLETE CRITERION MODELS
In one of the earliest models of decision, Hick (1952a)
suggested that the subject makes a chain of sub-decisions, each
of equal duration. Each sub-decision locates the stimulus as
being in half of the remaining possibilities, and rejects the
other. This process continues until only one alternative is left
where the corresponding response is selected and made.

1.2.1.2 RELATIVE CRITERION MODELS
Relative criterion models embody the idea of processing on
each trial as the sampling over time of evidence for the stimuli.
In the process, the model forms tentative identities for each
sample and evaluates the accumulated evidence until one response
alternative gains sufficient support relative to the other.

1.2.2 SEQUENTIAL SAMPLING FRAMEWORK
Many models have been proposed to account for simple two-
choice decisions, among them are a class known as sequential
sampling models. Under the sequential sampling framework,
performance in a task depends on two main factors: (1) the
quality of the information gained from processing the stimulus
12
and (2) the quantity of the information required before a
decision can be made. By adjusting the decision criteria, the
quantity of information required to make a response can be
controlled by the subject. According to the sequential sampling
framework, the relationship between the quality of the
information and decision criteria can explain the interaction
between RT and accuracy in a two-choice task. RTs are longer and
performance accuracy is degraded when a difficult stimuli is
presented when compared to a response to a less difficult
stimulus (Pachella, 1974; Luce, 1986).
Under the category of sequential sampling framework, there
exist many models that differ on one or multiple dimensions. A
brief review of these models will be provided in the following
section.

1.2.2.1 RANDOM-WALK MODELS
Random-Walk models (RMW), in general, assume evidence is
accrued as a single total. A response is made when either an
upper or lower criterion is reached (Link & Heath, 1975;
Ratcliff, 1978). There are two distinct subclasses to the RWM;
Discrete Time and Continuous Time. Although both sub models
assumes that evidence is accrued as a single total.

1.2.2.2 WEINER DIFFUSION
The Weiner diffusion model assumes that a decision is the
result of continuously accumulating noisy stimulus information
13
until one of two response criteria is reached. The Weiner
diffusion model assumes the noise arise from the moment-by-moment
fluctuations in the decision process and/or trial-by-trial
variability in the quality of information about the stimulus.
This ‘noise’ may often result in the information accumulation
processes terminating at the wrong criterion.

1.2.2.3 ORNSTEIN-UHLENBECK DIFFUSION
The Ornstein-Uhlenbeck Diffusion model is a variation of
other diffusion models. The drift rate of information accrual is
offset by a unit of decay that perturbs the accumulation of
information back to the initial starting point. The Ornsetin-
Uhlenbeck models have been used across various domains from
describing behaviors of single neurons as a function of simple
reaction time task (Smith, 1995) to decision-making and choice
behaviors under uncertainty (Busemeyer and Townsend, 1993).

1.2.2.4 ACCUMULATOR MODELS AND COUNTER MODELS
This class of models assumes that evidence for competing
response alternatives accrues in parallel, and a response is made
when the evidence for one of these two competing response
alternatives reaches a criterion. One of the earlier parallel-
counter models was proposed by LaBerge (1962). In LaBerge’s
model, sampling of the information occurred in discrete time and
state space. In essence, for a given point in time, a unit of
information would be added to one of a pair of evidence counters.
14
The problem with this model is that at low levels of stimulus
discriminability, the amount of evidence in each of the two
counters remained relatively equal. As a result, LaBerge’s model
would predict RT distributions to be negatively skewed.

1.2.2.5 LEAKY COMPETING ACCUMULATOR MODEL
Usher and McClelland (2001) Leaky Competing accumulator
model is similar to the Weiner diffusion model in many respects.
It predicts the same range of behavioral data, as does the Wiener
diffusion model because the addition of mutual inhibition between
the accumulators means that evidence for one response becomes
evidence against the other.
In all these classes of models, the time component required to
for rate of information accrual to reach a response, or the rate
of accrual to be the first to reach a criterion is defined with
the decision time component of RT.
Random-walk models (relative stopping rule) argue that
information accrual occurs as a single total; where under a two-
response task, information favoring one response is automatically
favors against the other. On the other hand, accumulator models
(absolute stopping rule) assume information accrues for both
responses independently. Only when one of these totals reaches a
certain criterion, a response is made. (La Berge, 1979; Townsend
& Ashby, 1983; Smith & Vickers, 1988).
The sequential sampling framework (which encompasses all
the models mentioned above) allows for an account of the speed-
15
accuracy trade-off (SAT) phenomena that occurs in many cognitive
tasks (Dosher, 1976; Wickelgren, 1977; Luce, 1986). Sequential
sampling models attribute SAT effects to changes in the amount of
evidence accumulated to make a response that is represented in
the models by changes in the values of the decision criteria.
Sequential-sampling models make two assumptions about the
information entering the decision stage. First, they assume the
representation of the stimuli in the visual system is noisy and
the noise maybe attributed to the stimulus itself or to the
processing inefficiencies of the observer. Secondly, they assume
that the time to reach a decision is dependent on the information
content of the noisy samples of the stimulus signal. Based on
these assumptions, sequential-sampling models make two
predictions. First, it predicts mean RT and accuracy to be
negatively correlated (Pachella, 1974). The models argue that
the rate of information accumulation depends on the
discriminability of stimuli. When signal strength decreases
(lower discriminability), the rate of information accumulation
decreases accordingly, resulting in a lower accuracy and longer
RT. Conversely, higher signal strength (greater
discriminability) would lead to a faster rate of information
accumulation, concluding in an increase in accuracy and a
decrease in RT.
Sequential-sampling models provide us with a way to
characterize the dynamics of perceptual decision in the context
of stimulus strength, accuracy and RT. They attribute
16
inefficiency exhibited by the decision process to the ‘noisy’
output from a visual filter or to decision noise. It assumes
multiple sampling of the ‘noisy’ stimulus information will help
reduce internal noise and improve reliability. However,
sequential-sampling models do not provide a way to quantify the
overall efficiency of the perceptual system nor does it provide a
way to distinguish the various sources of inefficiencies leading
into the decision stage and what roles these inefficiencies play
on decision making. Although sequential-sampling models provide a
robust framework to interpret perceptual decisions, sequential-
sampling models’ in it self, does not offer the ability to map
processing inefficiencies from the stimulus signal input of the
human observer to the decision stage.

1.3 SENSORY ANALYSIS – A SIGNAL DETECTION APPROACH
1.3.1 SIGNAL DETECTION THEORY
Signal detection theory (SDT) has provided an approach for
researchers to understand how humans make decisions about brief
occurrences of events. This approach assumes the sensory
processes to have a continuous output based on random Gaussian
noise and when a signal is present, the signal combines with that
noise. Measures of the sensitivity of the sensory process are
based on the differences between the mean output under no signal
condition and that under signal condition. The output of the
sensory process on an experimental trial is compared to the
decision criteria to determine which response to give. According
17
to the signal detection framework, there are two main components
to decision making: the acquisition of the information and
criterion. When detecting or discriminating a stimulus,
acquiring more information increase the likelihood of getting a
hit or a correct rejection, while reducing the likelihood of
making an error. The second component to the decision process is
criterion. According to SDT, the observer takes an observation
of the sensory events occurring within a fixed time interval.
Based on these observations, the observer would make a decision
as to whether, in a given trial, contained “noise” or a signal as
well. Under the SDT framework, an observer decides whether the
signal arose from noise alone or from noise-plus-signal by
adopting a critical cutoff, or criterion. If the internal
criterion is set high, subjects may have a tendency to respond
“yes” to the presence of a signal. On the other hand, if a
subject sets the internal criterion to be low, there is a higher
probability of missing the presence of a signal and leading to a
greater tendency of saying “no”.
Signal detection theory assumes that nearly all decision
takes place in the presence of uncertainty. There are two general
factors that contribute to uncertainty: internal noise and
external noise. External noise may arise from the environment or
may be implicitly added to the stimulus such as masks and
distracters.
It has been generally assumed (Jastrow, 1888) that the
sensory representation of a stimulus does not maintain a fixed
18
value, but rather is representative of a distribution over time.
The reason being is that discrimination/detection is not error-
free, but rather, affected by internal noise. Sources of
internal noise may arise from spontaneous neural activity
(Barlow, 1956; Kuffler et al., 1957; Barlow & Levick, 1969a,b;
Burgess, Wagner, Jennings, & Barlow, 1981, Tolhurst, Movshon, &
Thompson, 1981), coarse coding of stimulus properties, receptor
noise, the stimulus itself and loss during information
transmission. (Hecht et al, 1942; de Vries, 1956; Nagaraj, 1965;
Pelli, 1981).
An advantage to SDT framework is that it provides an
estimate of sensitivity (d’) that is independent of the
observer’s response criterion. Furthermore, it can be used to
quantify optimal decision processes, which then can then be used
to estimate sub-optimal human observers in a given task.
However, a shortfall of the SDT framework lies in it’s inability
to account for the trading relationship between time and accuracy
of performance; a relationship that has been largely ignored,
even though it is central to sensory and cognitive performances
(Swets & Birdsall, 1967).

1.3.2 EXTERNAL NOISE METHOD
In order to estimate the amount noise internal to the
observer that may contribute to uncertainty during the decision
process, many have adapted the external noise method. A
technique that is common in the field of electrical engineering
19
used to estimate intrinsic noise in devices is to refer the
intrinsic noise to an externally added source. (Mumford &
Schelbe, 1968). Pelli (1981) was among the first to apply this
technique to human sensory processing. This technique was
developed to allow us to discriminate between changes in internal
noise and efficiency of a system by examining the input-output
relationship. Input into the visual system can take various
forms such as signal energy, stimulus features and/or noise.
Processing of the input signals by the visual system results in
some form of output, usually characterized as percent correct,
d’, or thresholds. By systematically varying the signal input
through external noise and stimulus contrast manipulations and
measuring the output, performance of the human visual system can
be understood both qualitatively and quantitatively.
When an observer makes a psychophysical judgment about a
weak, briefly presented stimulus, the observer first matches the
spatial and temporal characteristics of the stimulus to an
internal representation before a response can be made. In order
to gauge the impact of internal noise on this representation, it
is common to model the performance of human observers to that of
an ideal observer. In doing so, it allows us to quantify the
overall efficiency of the perceptual system. (Green, 1960,
Burgess, Wagner, Jennings, & Barlow, 1981). There are several
competing observer based models developed specifically to
estimate the processing efficiency within a system; (1) noisy
linear amplifier model (Pelli, 1981), (2) a multiplicative noise
20
model (Burgess & Colborne, 1988), (3) a multiplicative noise plus
uncertainty model (Eckstein, Ahumada & Watson, 1997) and (4) the
perceptual template model (Lu & Dosher, 1999).
Historically, many have adapted a noisy linear amplifier
model (LAM) which adds systematically increasing amounts of
external noise to the signal stimulus in order to quantify
performance thresholds change relative to the amount of external
noise (Pelli, 1981). Given a particular threshold d’, we can
solve for threshold contrast c as a function of external noise:

2 2 2
'
eq ext
N N
d
C + =
βη
τ
(1)

This simple noisy linear amplifier model can be
characterized in three stages: (1) perceptual templates, (2) an
independent, additive internal noise source, and (3) decision
process (Figure 2). LAM models human behavior with two
parameters: equivalent internal noise (Neq) and sampling
efficiency (η). Rearranging eq (2) to solve for d’,
discriminablity of the signal stimulus at the decision stage is
determined by the signal-to-noise ratio expressed in equation
(3).

2 2
'
eq ext
N N
c
d
+
=
β
(3)

21
Equivalent internal noise, as estimated by LAM, is assumed
to be independent of the stimulus and is additive. Sampling
efficiency is characterized by the ability of the observer to
extract information from the stimulus while taking into account
limits imposed by internal and external noises. The model is
blind to any internal noise that scales with stimulus strength
thus any changes in stimulus-dependent noise will reflect changes
in sampling efficiency. With only these two parameters, the
linear amplifier model is quantatively true at the performance
criterion being measured. However, to characterize observer
performance at multiple performance levels, additional parameters
are necessary (Lu & Dosher, 2004, Tjan, 2002). In order to
characterize observer performance at multiple levels, the linear
amplifier model needs to be elaborated to include multiplicative
noise (Burgess & Colborne, 1988) and either a non-linear
transducer function (Lu & Dosher, 1999) or channel uncertainty
(Pelli, 1985; Eckstein et. al., 1997).
Although the LAM has been widely implemented to various
perceptual tasks, the model is inherently too simple. In
addition, predictions by LAM were in conflicts to other
experimental data. To address this issue, Pelli (1985)
introduced a modified version of LAM to included uncertainty,
arguing that observers need to monitor many irrelevant channels
when detecting or discriminating a signal embedded in noise.
On the other hand, Burgess and Colborne (1988) proposed
that the discrepancy found in LAM can be explained by an addition
22
of a noise component (multiplicative noise) whose strength is
proportional to the external stimulus energy. They found that
the ratio of internal/external noise to be around 0.75. This
ratio is independent of the external noise when external noise
was high. However, the same cannot be said for low external
noise levels, where this ratio tended to increase. They conclude
that internal noise of an observer is comprised of two
components. One component is assumed to have a constant spectral
density for a given luminance. The other component is assumed to
be directly proportional to the external noise strength.
Another model that is an extension to the LAM is the
Perceptual Template Model (PTM) (Lu & Dosher, 1998; Dosher & Lu,
1998). The PTM is a considerable improvement to the LAM and will
be discussed in the following section.

1.3.3 PERCEPTUAL TEMPLATE MODEL (PTM)
The perceptual template model (Figure 1) provides the best
qualitative and quantitative account of a range of data set. The
perceptual template model (PTM) extends the linear amplifier
model (LAM) to include (1) a non-linear transducer function and
(2) a stimulus-dependent noise component. PTM in its basic form
consist of four parameters: (1) gain to the signal stimulus (β),
(2) exponent of the non-linear transducer function (γ), internal
additive noise (N
a
), and coefficient of the multiplicative
internal noise (N
m
).

23
Figure 1: A schematic diagram of the perceptual template model.

Noise and signal in the stimulus are processed through a task-
relevant perceptual template, followed by a nonlinear transducer
function, multiplicative and additive internal noises and a
decision process. The temporal dynamics of the decision stage is
modeled by an exponential function

PTM attributes our perceptual inefficiencies to 3 factors:
internal additive noise, internal multiplicative noise and
24
template retuning. Internal additive noise can be described as
the limiting factor in a perceptual task performed at threshold.
Internal additive noise has a mean of 0, a fixed standard
deviation, and is assumed to be Gaussian. Internal
multiplicative noise can be understood as the constant resulting
from the ratio of the difference of threshold to background
intensity. It follows a Gaussian distribution and also has a mean
of 0 with a standard deviation proportional to the total energy
of the input stimuli. Another component to the PTM is the non-
linear transducer function, which represents the proportion of
the observer’s perceptual performance to the signal contrast.
Finally, template returning can be seen as a way that the
perceptual system reshapes it’s templates to concentrate on a
range of stimulus features. This reshaping of the template can
introduce unnecessary influences from external noise and other
distracters that may impact performance.

)
) 1 (
) , ( '
2 2 2 2 2 2
a m ext m
ext
N C N N N
C
N C d
+ + −
=
γ γ γ
γ γ
β
β
(4)

1.4 OVERVIEW
Perceptual decision provides a window into how various
processes come together to form a decision. In studies
pertaining to simple perceptual tasks, the dynamics of decision
are often not emphasized. Perceptual decision has been studied
in the context of signal detection theory; however, the
25
underlying time course has not been investigated. In cognitive
psychology, the dynamic process of perceptual decision has been
well studied. Although some studies have attempted to unify the
domains of sensory information and dynamic temporal properties,
there is not a quantitative model that is capable of doing so.
The purpose of these studies here was to apply a signal
detection plus external noise model and template matching (PTM)
with a dynamic decision process to illustrate the dynamics of
perceptual decision. Experiment 1 involves using the perceptual
template model (PTM) with a modified dynamic decision process to
partial out the contributions of varying signal contrast and
processing time in the presence or absence of external noise to
perceptual decision in a two alternative forced choice
orientation discrimination task.

2.0 CHARACTERIZING THE TEMPORAL DYNAMICS OF PERCEPTUAL
DECISION
2.1.1 OBSERVERS
Four observers (three male, one female) recruited from the
general graduate student population participated in the study.
The observers reported normal or corrected-to-normal vision.

2.1.2 DISPLAY AND VISUAL STIMULI
All visual stimuli were generated using a Macintosh G4
computer running Mac OS9 and Matlab programs based on the
26
Psychtoolbox extensions (Brainard 1997; Pelli 1997). They were
displayed on a Nanao Technology Flexscan 6600 high-resolution
monitor with P4 phosphor running at a refresh rate of 120 Hz.
Fine control of luminance levels was achieved through a
specialized circuit (Pelli & Zhang 1991), which combined two
eight-bit output of a video card to produce a 12.6 bit, 6144
distinct gray levels. A linear lookup table was generated to
divide the range of the monitor into 256 levels. Observers,
sitting in a dimly lit room, viewed the displays binocularly.
The visual stimuli consist of a 1
st
order sinusoidal Gabor
or a Gabor + Gaussian “white noise”
€
±12 deg (or
€
±
π
15
) from the
vertical. The luminance profile of the Gabor is derived from the
following equation:
€
l(x,y) = l
0
{1.0 + csin[2πf (xcos(π /15) ± ysin(π /15))]exp(−
x
2
+ y
2
2σ
2
)}
(5)

With a viewing distance of approximately 68 cm, the stimulus on
screen subtended 1.8 by 1.8 deg on the retina with a center
frequency of f= 3.0 cycles/deg. The mean luminance, L
o
, was 46
cd/m2. Maximum contrast of each Gabor stimulus was randomly
chosen from a set estimated contrast. External noise pixel
contrast was drawn independently from a Gaussian distribution
with a mean of 0 and a standard deviation of 0.33. To ensure
that the external noise conformed to a Gaussian distribution, the
maximum standard deviation of the noise was kept at 33% of
maximum achievable contrast.
27

2.1.3 DESIGN
This experiment comprise of four segments: a practice
session, contrast estimation, simple choice RT controls, and 2AFC
orientation discrimination task were run in separate sessions.
The practice session consisted of a character
identification task (‘5’ or ‘S’) in an RSVP stream of numbers.
Observers performed this task in the presence of a cued-to-
respond paradigm. At the onset of each trial, a central fixation
appeared followed by the RSVP stream. The numbers comprising the
RSVP stream were sampled in the range of 0 through 9 (excluding
5) without replacement. Embedded halfway through the stream was
either the number ‘5’ or the letter ‘s’. Observers were asked to
identify the target as quickly and as accurately after the onset
of a cue to respond. The purpose of this practice session was to
accustom the observers to initiate a response immediately after
the onset of the cue.
We then conducted a reaction-time (RT) control at the
beginning and after every two sessions of the main experiment to
investigate the potential impact of a cued-to-respond paradigm on
RT. The design of the control experiment was identical to that
of the main experiment in ever respect, except, instead of
manipulating response time, we allowed the observers to make a
response freely.
Two staircases were used to estimate contrast threshold at
a performance criteria of 79.3% and 71.7% for each observer. A
28
session comprised of an orientation discrimination task of a
Gabor subtended +/- 12 deg from vertical in both the presence and
absence of external noise. The stimuli were presented at the
same eccentricity as the main experiment. These estimated
thresholds were used to calculate contrast across a wider
performance range.
Figure 2: Schematic representation of a typical trial sequence

Each trial sequence began with a centrally located fixation cross. An
arrow pre-cued the target location 234 msec prior to the onset of the
target. A secondary arrow appeared adjacent and simultaneously with
the target and remained 'on' until the observer made a response. In
the SAT version, an auditory beep occurred between 25 and 800 ms after
the onset of the target display. The observer was required to make a
response as quickly as possible after the beep. At the termination of
each trial, feedback was given to the observer's in terms of his/her
accuracy and response time.
29
The lowest performance range was calculated from ½ the estimated
performance from the 71.1% staircase. The contrast for the upper
two performance range was calculated by taking the difference
between two estimated contrast and adding the difference to the
contrast estimated at 79.7% performance criteria ((Contrast
79.7%
-
Contrast
71.1%
) + Contrast
79.7%
) and by doubling the difference and
adding it to the same contrast estimated at 79.7% performance
criteria (2x(Contrast
79.7%
- Contrast
71.1%
) + Contrast
79.7%
).
In the main experiment, a centrally placed arrow would cue
observers to one of eight spatial locations. They would perform
an orientation discrimination task. Their processing time would
be manipulated by an auditory cue set at one of eight SOA delays.
Auditory SOA delays, external noise, and contrast were randomly
interleaved. Each session consisted of 1440 trials; a total of 8
sessions were run.

2.1.4 CUED-RESPONSE PROCEDURE
In order to observe a speed-accuracy trade-off in a
classical, choice RT tasks, blocked designs are required, where
deadlines, speed instructions and payoffs vary between blocks of
trials. A particular useful experimental method for
investigating theoretical predictions relating response
probability and response time utilizes experimenter-defined RT
deadlines (Fitts, 1966) Using this method in a typical two
alternative two response paradigm, the experimenter would inform
the subject of an RT deadline prior to the presentation of a
30
stimulus. The subject then must attempt to produce an RT less
than the deadline. On some trials RT may exceed the RT deadline,
but most were able to respond within the fixed period.
Figure 3: Hypothetical speed-accuracy trade-off functions.

Each function is an exponential approach to a limit characterized by 3
parameters: intercept, rate, and asymptote. By varying the parameters,
we would expect to see changes to one of four possible outcomes. In
figure (A), both functions share the same rate and intercept and only
vary in their asymptotic performance. In figure (B), the intercept and
asymptote remains the same and only the rate differs. Figure (C) shows
a condition where the functions have both the same rate and asymptote
and different intercept. Figure (D) demonstrates a condition where all
three parameters (intercept, rate and asymptote) are different.

A decrease in RT deadlines has two effects. Not only does
mean RT decline, but the probability of responding correctly also
31
declines. This relationship between RT and response probability
is often referred to as a speed-for-accuracy tradeoff. This
paradigm assumes that the subject may either control RT, thereby
changing response accuracy, or control response accuracy, to
produce a change in RT.
We adapted a similar cued-response procedure first used by
Reed and Dosher (Dosher, 1976, 1981; Reed, 1973). Where in the
Fitts’ design instructed subjects to respond within a fixed
interval, the random-interrupt-respond-now used by Reed & Dosher
would cue the subjects to respond following the onset of the
stimulus. One of several respond-cues at varying SOAs would be
presented to the subject. By adapting this paradigm, not only
can one can sample a complete speed-accuracy trade-off function,
but also minimize the speed accuracy tradeoffs. Furthermore, by
varying performance, accumulation rate, or the start of
information accumulation, one could obtain one or a mixture of
speed-accuracy trade-off functions as illustrated in Figure 3.

2.1.5 PROCEDURE
In the practice sessions, observers maintained fixation
while viewing a centrally placed fixation cross. At the onset of
each trial, the fixation is replaced with an RSVP stream.
Observers would perform a character identification task. Auditory
feedbacks were provided for each correct response. Reaction time
(measured from stimulus onset to response from subject) feedback
was provided at the conclusion of each trial.
32
In the contrast estimation sessions, observers performed a
discrimination task of a Gabor oriented +/- 12 deg from vertical.
Auditory feedback was provided for each correct response.
In the main and control experiments, each trial began with
a centrally placed fixation. Following the onset of a trial, an
arrow would replace the fixation and pre-cue the target location
234 millisecond prior to the onset of the target stimulus. A
secondary arrow would then appear adjacent to and simultaneously
with the target stimulus and would remain until a response is
made.
However, in the cued-to-respond paradigm (main experiment),
an auditory tone would occur at one of eight SOA delays (0.025
0.05 0.075 0.1 0.2 0.3 0.5 0.8 seconds) following the target
stimulus onset. As with the practice sessions, observers were
instructed to make a response immediately upon hearing the
auditory tone. At the conclusion of each trial, feedback was
provided for both response time and correctly discriminating the
stimulus. Figure 2 illustrates a typical trial sequence

2.2 RESULTS
2.2.1 REACTION TIME DISTRIBUTIONS
The results of the standard RT experiments for all subjects
were plotted as Vincentized-Distributions and are shown in Figure
4 (Low Noise Condition) and Figure 5 (High Noise Condition). To
determine how many histogram bins should be used for estimating
33
distributions that provides the most efficient, unbiased
estimation of the probability density function is achieved when:

€
Sb = 3.49σN
−1/3
(6)

where Sb is the width of the histogram bin, σ is the standard
deviation of the distribution and N is the number of samples
(Scott, 1979). Each panel represents each observer’s RT data for

Figure 4: Reaction Time Distribution. Zero Noise Condition.

A histogram of the standard reaction time experiment in zero noise
condition overlaid with the percentage correct for each contrast
performance level and subject. Mean reaction time highlighted in blue.

a single contrast condition. An accuracy plot is overlay for
each RT distribution and contrast level. Although the RT
distributions remained relatively similar across both high and
low noise conditions and contrast levels, subject’s accuracy
34
increased as a function of increased contrast levels. This is
true for all four subjects.

Figure 5: Reaction Time Distribution. High Noise Condition.

A histogram of the standard reaction time experiment in high noise
condition overlaid with the percentage correct for each contrast
performance level and subject. Mean reaction time highlighted in blue.

2.2.2 SPEED-ACCURACY FUNCTIONS
2.2.2.1 EXPONENTIAL FITS
The percentage of yes (target-present) response and mean
RTs were calculated for each performance level, cue delay, and
noise condition. Time-accuracy functions graph d’ as a function
of total processing time, or cue delay plus RT to the cue,
corresponding to the total average time between display onset and
response
35
The asymptotic accuracy and dynamics are estimated from a
description of the data as an exponential approach to an
asymptotic level:

€
d'=α(1−exp(−β(t−δ)), t > δ; 0 otherwise. (6)

Exponential models parameterize each time-accuracy function with
an asymptote (α), a rate (β), and an intercept (δ). Here, α is
the asymptotic (maximal) accuracy, the intercept δ describes the
point at which accuracy first rises above chance, and the rate β
describes the dynamics from chance to asymptote. This equation
provides an excellent empirical summary of time-accuracy
functions and allows comparison to other published data (Dosher,
1976, 1979, 1981,1982; McElree & Dosher, 1989, 1993; Reed, 1973;
Sutter & Graham, 1995; Sutter & Hwang, 1999). The results from
these fits are shown in Figure 6 and Figure 7.

2.2.2.2 DYNAMIC DECISION PTM
In addition, we take the original PTM (eq 4), which
predicts asymptotic performance for a given contrast C and a
particular external noise N
ext
. and combined an exponential
function (eq 6) in order to characterize the temporal properties
of the decision process:
€
d'(C,N
ext
PT) =
β
γ
C
γ
(1−N
m
2
)N
ext
2γ
+N
m
2
β
2γ
C
2γ
+N
a
2
(1−e
−(PT−t
0
)/τ
) (7)

36
Both the exponential and the dynamic decision PTM models were fit
to time-accuracy d’ data by minimizing the squared deviations
between the model and the data:

€
(d
i
−d
i
*
)
2
i=1
n
∑
(8)

where d
i
is the observed d’ value and d
i
*
is the d’ value predicted
by the model. Minimization of the squared differences between
parameters observed in the experiment and those derived from both
the exponential function as well as the dynamic decision PTM was
accomplished using the Nelder-Mead simplex search algorithm
implemented in MATLAB (Mathworks, 1999). The goodness-of-fit is
summarized by

€
R
2
=1.0−
(d
i
−d
i
*
)
2
i=1
n
∑
(d
i
−d
i
m
)
2
i=1
n
∑
(9)

where d
i
and d
i
*
are as described in the previous equation, d
i
m
is
the mean of the observed d’ values, n is the total number of
predicted data values, and k is the number of model parameters.
The index r
2
is the proportion variance accounted for by the
model; R
2
is the percent variance accounted for by the model,
adjusted by the number of free parameters (Wannacott & Wannacot,
1981). Nested models were compared using an F test:
37

€
F
df1,df 2
=
(SSE
restricted
−SSE
full
)
(k
full
−k
restricted
)
(SSE
full
)
(n−k
full
)
(10)
The SSEs are the sum of squared errors for a more restricted and
fuller model, and the ks are the number of model parameters. The
degree of freedom are df1 = (k
full
– k
restricted
) and df2 = (n – k
full
).
A full model supposes 24 parameters in total: (1) multiplicative
noise (Nm), (1) additive internal noise (Na), (1), γ, (1) β, (10)
τ, and (10) t
0
. In addition, we fit two models in which either τ
or t
0
was free to varied. The most reduced model, assumes equal
t
0
and τ across all performance levels. The F-statistic indicates
whether the additional variance explained by additional
parameters in a full model provide a significant improvement in
the variance explained by a sub (restricted) model.
Stimulus noise and contrast had essentially no effect on
the average RT’s. However, slight variations in the shortest cue
delays were observed, which is typical in the SAT paradigm
(Dosher, 1976; Reed, 1973). The total processing time is
considered to be the average time from the display onset to
subject response.
The corresponding average time-accuracy functions (d’ vs.
total processing time) are shown in Figure 6 & 7 for the
exponential fits and in Figures 8 & 9 for the dynamic decision
PTM. The data for zero noise and high noise are displayed

38
Table 1: Parameters (full model and reduced model) for exponential fits.
CC RK SJ WC AVG
Full Reduced Full Reduced Full Reduced Full Reduced Full Reduced
a
L1
0.315 0.2206 0.0542 0.0734 0.2575 0.0692 0.4417 0.4322 0.1638 0.1427
a
L2
0.8769 1.0575 0.3937 0.6563 1.0089 0.4498 1.3391
1.5843
0.6726 0.7875
a
L3
1.6185 1.7864 0.5181 1.6329 1.4625 1.3892 2.3108 2.3952 1.3871 1.4262
a
L4
3.0196 2.9434 1.0767 3.5961 1.9287 2.151 1.8651 2.356 3.0118 2.0294
a
L5
4.517 3.481 1.7394 5.0189 3.8136 3.7055 2.8321 2.9526 2.6003 2.6964
b
L1
1.9981 6.2358 11.5182 0.7188 1.5651 8.5909 21.7892 5.3206 47.1106 7.9875
b
L2
13.497 0.1043 3.1756 9.4551 17.9676
b
L3
7.9464 8.9138 8.723 7.8703 11.0759
b
L4
6.6416 16.1786 17.1702 8.9115 1.3317
b
L5
3.3453 13.4355 7.5661 5.8074 8.7832
d
L1
0.6994 0.3084 0.4374 0.1427 0.5756 0.2366 0.2118 0.2179 0.2814 0.2859
d
L2
0.3155 0.2033 0.591 0.2139 0.2918
d
L3
0.303 0.2754 0.2628 0.2399 0.298
d
L4
0.3225 0.3224 0.2487 0.1995 0.0782
d
L5
0.301 0.3708 0.2329 0.2171 0.2846
a
H1
0.3411 0.174 0.0317 0.1291 0.1861 0.3309 0.0167 0.2284 0.3032 0.1383
a
H2
1.313 1.3654 0.9271 2.1167 0.6652 0.7864 0.8555 1.3382 0.9782 1.0351
a
H3
1.6414 2.0401 1.6081 4.2723 1.765 1.97 1.5439 2.155 1.6845 1.885
a
H4
2.4771 2.5074 2.2541 5.5361 2.6776 2.8725 9.4703 2.3682 2.4025 2.3634
a
H5
2.7593 2.8053 2.3969 6.3229 4.9441 4.8661 3.4031 2.8944 3.1215 2.9026
b
H1
0.4835 6.2358 0.6023 0.7188 25.7022 8.5909 24.1061 5.3206 0.6739 7.9875
b
H2
4.7782 6.4556 10.8561 25.6785 9.8209
b
H3
15.715 7.4425 10.4956 21.0459 13.499
b
H4
4.9253 18.9284 12.0381 4.4249 8.3126
b
H5
6.7777 11.7284 8.0783 3.729 6.3882
d
H1
0.1262 0.3084 0.3782 0.1427 0.135 0.2366 0.3448 0.2179 0.0776 0.2859
d
H2
0.2525 0.411 0.147 0.1992 0.2788
d
H3
0.323 0.4063 0.2156 0.21 0.2938
d
H4
0.27 0.4099 0.2405 0.1204 0.2924
d
H5
0.313 0.3782 0.2392 0.2217 0.2852
R
2
0.9335 0.9147 0.928 0.9128 0.9214 0.9152 0.8864 0.8796 0.9445 0.9547
39

separately. The individual data are plotted separately. The
smooth functions represent the best-fitting exponential models.
The data for both the zero noise and high noise conditions
are quite similar. For both conditions, the asymptotic
performance varied according to the amount of stimulus contrast
presented, while the rate remained relatively stable.

Figure 6: Zero noise condition.

Discrimination performance (d’) as a function of total processing
time (test onset to response) for varying contrast range for all
four subjects and the average of all four subjects.

40
Figure 7: High Noise Condition

Discrimination performance (d’) as a function of total processing time
(test onset to response) for varying contrast range for all four
subjects and the average of all four subjects

Empirical estimates of the asymptotic (maximal) d’ accuracy
were calculated by averaging performance across contrast levels
and cue delays. The accuracy data for both zero noise and high
noise conditions seem to asymptote as a function of the amount of
signal contrast. For zero noise conditions, average d’ the
average RTs across the contrast range and external noises were
essentially unaffected. Total processing time is the average
time from display onset to response. Figure 8 & 9 shows the d’
averaged over observers, as a function of total processing time
for zero and high noise conditions. The data for zero noise and
high noise are plotted separately. The average data are
representative of the individual observer data. The smooth
41
functions are best fitting PTM + exponential models. The data
for both zero and high noise are quite similar.

Figure 8: SAT Functions. Zero Noise Condition.

Data from the experiment are show as dots. Predictions from the best
fitting model are shown as smooth curves.

42
Figure 9: SAT Functions. High Noise Condition.

Data from the experiment are show as dots. Predictions from the best
fitting model are shown as smooth curves.

The results of exponential model fits and the exponential-
PTM are summarize in Table 1 and Table 2. The exponential fits
provide a standard description of time-accuracy functions for
individual observer data and average data. (The next section will
consider fits with the exponential-PTM.) Exponential models
parameterize each time-accuracy function with an asymptote (α), a
rate (β), and an intercept (δ). Asymptotic accuracy differed
significantly between each of the five-contrast range. The
simplest model which at identical temporal dynamics (identical
43
rates of increase and identical starting points) provided the
most parsimonious best fit for all 4 observers as well as their
average. A 10 λ 2 β and 2 δ fit the data quite well, yielding R
2
for the average data of 0.9547. Individual R
2
are CC = 0.9147, RK
=0.9128, SJ =0.9152 and WC = 0.8796. Across all four subjects,
the most reduced model was statically equivalent to the most
saturated model (Averaged, F(18,56) = 0.57264; p > 0.90; CC,
F(18,56) = 0.63906; p > 0.85; RK, F(18,56) = 0.23063; p > 0.90;
SJ, F(18,56) = 0.13797; p > 0.9; WC, F(18,56) = 0.10811; p
>0.90).

44
Table 2: Parameters from model fits with dynamic-decision PTM.
CC RK SJ WC AVG
Full Reduced Full Reduced Full Reduced Full Reduced Full Reduced
N
m
0.1948 0.2655 0.3746 0.3914 0.0258 0.0877 0.2716 0.2987 0.2599 0.2698
N
a
2.46E-03 2.18E-
03
0.0052 0.0043 9.84E-03 7.00E-
03
4.59E-
03
4.60E-
03
0.0058 3.70E-
03
γ
1.2503 1.3307 0.8628 0.9322 2.1613 2.12 1.6281 1.6572 1.2768 1.3085
β
2.5902 2.6473 2.7142 2.6481 2.1635 2.343 2.4567 2.4371 2.3087 2.5639
τ
1
0.0611 0.1559 0.0001 0.1543 0.0017 0.1115 0.0153 0.1806 0.0018 0.1284
τ
2
0.074 0.1361 0.4028 0.1785 0.1319
τ
3
0.1676 0.1603 0.1278 0.1302 0.1037
τ
4
0.1305 0.1201 0.1216 0.273 0.1325
τ
5
0.1836 0.0402 0.1086 0.1844 0.1193
τ
6
1.2388 0.196 0.0085 0.1252 0.1313
τ
7
0.0956 0.2254 0.1005 0.1999 0.1094
τ
8
0.0987 0.1449 0.063 0.1641 0.0942
τ
9
0.2098 0.1452 0.1127 0.1967 0.1402
τ
10
0.2378 0.0786 0.1214 0.2107 0.1437
t
0
0.1949 0.3079 0.3587 0.2938 0.2515 0.2384 0.2032 0.2163 0.2798 0.2849
t
0
0.3161 0.2757 0.2896 0.2129 0.2908
t
0
0.2976 0.3002 0.2612 0.2254 0.295
t
0
0.3211 0.1782 0.2426 0.1874 0.2762
t
0
0.3104 0.3906 0.2326 0.2145 0.2836
t
0
0.001 0.3296 0.2414 0.2925 0.2922
t
0
0.2916 0.3506 0.1324 0.2024 0.2715
t
0
0.3133 0.3836 0.2274 0.2202 0.2895
t
0
0.2726 0.3827 0.2388 0.2257 0.2879
t
0
0.302 0.4051 0.2394 0.2183 0.2884
r
2
0.9234 0.913 0.90645 0.8964 0.9084 0.8929 0.8886 0.9694 0.9644 0.9557

45
2.3 GENERAL DISCUSSION
We obtained the contrast-dependent effects with
discrimination judgments as were found in previous studies
(citations). A simple elaboration of the perceptual template
model (Lu & Dosher, 1999; Dosher & Lu, 1999) with the addition of
a dynamic decision process was able to fully account for the
results in this study. Despite the enormous variation in
contrast energy and consequent variation in the asymptotic
performance, the dynamic-PTM model accounted for the results as
having the same rate of information accumulation across all
contrast and external noise ranges. These results provide
evidence for stimulus information being processed through the
visual channels prior to entering the decision stage. In other
words, these results suggest that noise within the system (either
external or internal) has little impact in the decision stage
since any impact it may have, will only affect the gain in the
system and not the temporal dynamics represented in the decision
stage.
These results run contrary to many studies in the cognitive
domains on perceptual decisions. For example, Smith et. al.
(Smith, Ratcliff & Wolfgang, 2004) addressed the relationship
between the physical stimulus trace and the observer’s decision
and how this relationship is affected by spatial attention. They
suggest that sequential sampling models provides for the most
natural account of accuracy and RT in simple decision. As in
signal detection theory (Green & Swets, 1966), the sequential

46
sampling models assumes the representation of the stimuli in the
visual system is noisy. In order to make a decision, successive
samples of the noisy stimulus are accumulated until the amount
necessary to reach a certain criterion. The time taken to reach
this state is represented in the decision component as RT.
Like others (Carrasco et al., 2000; Lee et al., 1997) ,
Smith et al. suggest a connection between attention and masking
mechanisms. To a certain extent pattern masks can be viewed as
sources of external noise, and the attentional mask dependency
found by Smith et al, (2004) and Carrasco et al. (2000) can be
interpreted as a manifestation of external noise exclusion.
However, Smith et al. (2004) argues against this because they
believe that backward pattern masks reduce stimulus
identifiability by interrupting processing rather than by adding
noise to visual channels. Their model assumes that the rate of
information gain from masked-attended locations is greater than
that from masked-unattended locations. The reason, they argue,
for masked stimuli, cuing provides an advantage because the rapid
rate of accumulation from the cued location means more
information can be obtained from such location before the mask
suppresses the stimulus. Their results showed that d’ and MRT
both varied systematically with stimulus contrast. They
accounted for the data using a sequential sampling framework,
because, they argued, that decisions from near-threshold stimuli
or contrast dependent stimuli cannot be accounted by signal
detection or similar methods. The reason being, signal detection

47
theory or gain models have no mechanism to account for RT or for
the joint dependence of accuracy and RT on stimulus contrast.
It is true, that up to this point many SDT based models are
incapable of directly addressing the joint dependency of accuracy
and RT. For example Lu & Dosher (1998) and Dosher & Lu (1998)
proposed a model that contains multiple attentional mechanisms,
which is capable of predicting mask dependencies through
processes such as noise exclusion or reduction. External noise
in this case is added to the visual channels and cuing to the
target stimulus will improve sensitivity to the stimulus by way
of excluding the noise resulting in an increased cuing effect in
high external noise displays (Dosher & Lu, 2000; Lu, Lesmes, and
Dosher 2002). The perceptual template, in this form, is not
capable of accounting for the dynamic processes expressed in by
Smith and colleagues.
However, in the studies presented above, we adopted a
dynamic-PTM that included an exponential function used to account
for the temporal dynamics of decision. The absences of any rate
change across contrast noise levels seems to suggest that noises
affect the visual processing system prior to the decision stage.

48

II. TEMPORAL DYNAMICS OF PERCEPTUAL LEARNING

49
3.0 EFFECTS OF PERCEPTUAL LEARNING ON THE TEMPORAL DYNAMICS
OF PERCEPTUAL DECISION
3.1 OVERVIEW
3.1.1 PERCEPTUAL LEARNING
It has long been established that perceptual learning
involves improvements and or changes to perceptual processes,
however the precise nature of these improvements are still being
debated (Ghoose, GM, 2004; Seitz, A., Watanabe, T., 2005;
Smirnakis, SM, Schmid, MC., Brewer, AA., Tolias, AS., Schuz, A.,
Augath, M., Werner, I., Wandell, BA., Logothetis, NK., 2005;
Claford, MB., Chino, YM., Das, A., Eysel, UT., Gilbert, CD.,
Heine, SJ, Kass, JH., Ullman, S., 2005).
The classical approach to perceptual learning took the
route of Eleanor and James Gibson’s ecological view to
perception. The Gibsons viewed perceptual learning as a way of
accessing previously unused information gained from the
surrounding environment. Perceptual learning within this context
aims to identify the external properties used by observers to
improve their performance. Although this ecological approach to
perceptual learning is still being studied (Pick, 1992; Bingham,
1995; Reed, 1996), the focus of the current study will be limited
to a system’s approach to the time-course underlying visual
perceptual learning.
Perceptual learning can be described as a relatively
permanent and consistent change in the perception of a stimulus
following practice and is independent of conscious experience.

50
Perceptual learning has been demonstrated across a variety of
stimuli: spatial frequency (Fiorentini & Berardi, 1980; Fine and
Jacobs, 2000), orientation (Fiorentini & Berardi, 1980; Dorais &
Sagi, 1997), motion direction discrimination, (Zanker, 1999), and
vernier task discrimination (McKee & Westheimer, 1978; Beard,
Levi, & Reich, 1995; Kumar & Glaser 1993; Saarinen & Levi, 1995),
object identification (Furmanski and Engle, 2000), and face
(Gold, Bennett & Sekuler, 1999). Perceptual learning generally
characterized as improvements across sessions/days (as a function
of percent correct, d’, or contrast threshold reduction).
However, it is still unclear what drives the improvements
observed in perceptual learning. Some have suggested that
improvements are mediated by changes to the sensitivity of
relevant neurons (Fine & Jacob, 2002) or simply a reweighing
process that reward neurons best tuned for optimal responses
(Saarinen & Levi, 1995 ); Petrov, Dosher, and Lu, 2005).

3.1.2 PLASTICITY IN THE NERVOUS SYSTEM
It is widely believed that perceptual learning, in general,
reflects underlying neuronal changes, however, the precise
mechanisms as well as the neuronal population involved is still
being debated. Plasticity exhibited within the nervous system
and take may forms. A prime example of is the notion of
specificity, which as served as the basis for claims of
plasticity in the early visual cortex (Ahissar & Hochstein, 1993,
1996; Ball & Sekuler, 1987; Fahle, 1997; Shiu & Pashler, 1992).

51
Another example of plasticity in the nervous system is
monocular deprivation. Imbalanced binocular input after the
closure of one eye causes a shift in ocular dominance in visual
cortex, such that neurons reduce their responsiveness to stimuli
delivered to the deprived eye while the open eye increases its
influence on cortical cells. When the deprived eye is later
allowed to regain vision, binocular responses in the visual
cortex have the capacity to recover. However, the underlying
mechanisms governing plasticity is still widely debated.

3.1.3 MECHANISMS OF PERCEPTUAL LEARNING
One way in which perceptual learning may occur is though
increasing the attention paid to particular perceptual dimensions
or features that are important, and/or by decreasing attention to
irrelevant information. For example learning has been reported
to be restricted to the relevant or attended feature of a
perceptual stimulus (Ahissar and Hochstein, 1998). On the other
hand, some studies have claimed that perceptual learning may
occur even when the relevant information from the stimuli are
subliminal (Seitz and Watanabe, 2003).
Observer models offer us another way to understand the
underlying mechanisms of perceptual learning through
characterizing the limitations in performance of the observers
and it allows us to identify what has improved through training
or practice. The Perceptual Template Model (PTM) developed by Lu
& Dosher, 1998, Dosher & Lu, 1998, offers us an insight to how

52
perceptual learning impact performance. PTM is made up of 5
distinct components: (1) a perceptual template, (2) a non-linear
transducer function, (3), a multiplicative internal noise that is
proportional to the energy in the stimulus, (4), additive
internal noise, and (5) a decision process that operates on the
noisy internal representation of the stimulus.
PTM offers three distinct mechanisms to characterize
perceptual learning: stimulus enhancement, external noise
exclusion, and changes to contrast gain control. Each of the
mechanisms has a key signature in perceptual task performance.
If learning is observed through the mechanism of excluding
external noise, by filtering out external noise added to the
stimulus, thresholds in high external noise region will be
reduced. On the other hand, if learning reflects stimulus
enhancement through amplification of the stimulus, the result
would be threshold reductions in the zero or low noise region.
If learning occurs via changes in gain control, threshold
reductions would be send across all external noise conditions.

3.1.4 SUMMARY
Perceptual learning is often characterized as performance
improvements in perceptual tasks as a result of training or
practice. The interest in perceptual learning stems from how
changes occur in low-level sensory representations up to higher
order changes to these representations and how they are expressed
in a task. Some believe that perceptual learning may reflect

53
plasticity in the earliest possible area in the visual cortex
(Karni & Sagi, 1991) while others believe that perceptual
learning reflects the changes to the connections from the sensory
representations to decision, where a weighted average of the
noisy visual channel outputs is forwarded to a decision process
(Lu & Dosher, 1998; Dosher & Lu, 1999; Petrov, Dosher & Lu,
2005).

3.2 EXPERIMENT II
3.2.1 OBSERVERS
Ten observers (four male, six female) recruited from the
general undergraduate and graduate student population
participated in the study. The observers reported normal or
corrected-to-normal vision and naïve to the purpose of the study.
The observers were randomly assigned into two groups, each of
which received a different type of training – identifying the
motion direction of a moving sine-wave grating either embedded in
external noise or not. Group I was trained in high external
noise; Group II was trained in zero external noise.

3.2.2 DISPLAY AND VISUAL STIMULI
All visual stimuli were generated using a Macintosh G4
computer running Mac OS9 and Matlab programs based on the
Psychtoolbox extensions (Brainard 1997; Pelli 1997). The
computer was equipped with Nanao Technology Flexscan 6600 high-
resolution monitor with P4 phosphor running at a refresh rate of

54
120 Hz and a 640 x 480 spatial resolution. Fine control of
luminance levels was handled through a specialized circuit (Pelli
& Zhang 1991), which combined two eight-bit output of a video
card to produce a 12.6 bit, 6144 distinct gray levels. A linear
lookup table was generated to divide the range of the monitor
into 256 levels.
Figure 10: Illustration of a typical trial sequence.

Sinusoidal motion presented in fovea.

Observers, sitting in a dimly lit room, viewed the displays
binocularly. Observers were instructed to maintain fixation
throughout the experiment and a chinrest was provided to ensure
observers maintained head positions.

55
The visual stimuli consist of five frames of moving
sinusoidal luminance modulations with 90’ phase-shifts between
successive frames:

5 ,...., 1 ]}, ) 1 (
2
2 sin[ 0 . 1 { ) , (
0
= + − + + = k k fx c l y x l θ η
π
π (10)

where the luminance lo of the sine-wave gratings was the same as
that of the uniform background. With a viewing distance of
approximately 68 cm, the stimulus on screen subtended 1.8 by 1.8
deg on the retina with a center frequency of f= 3.0 cycles/deg.
The mean luminance, Lo, was 46 cd/m2. Contrast c was determined
by adaptive staircase procedures. The first phase (theta
[0,2pi]) and the direction of motion (eta = +/- 1) were chosen
randomly across trials.
In the high external noise condition (Group I), within each
frame of the sine-wave gratings, an independent external noise
image frame of the exact size was constructed. Each frame was
approximately 1 by 4 pixel in size (0.03 x 0.12 deg). The
luminance of each noise image was drawn independently from a
Gaussian distribution with a mean of lo and a standard deviation
of 0 or 0.33.
In Group I, signal and external noise images were
interleaved in alternating 0.03 deg rows and combined spatially
and temporally. The duration of each frame lasted 33 ms.

56
3.2.3 DESIGN
The practice and main experiments were run in separate
sessions. A practice session consisted of a character
identification task (‘5’ or ‘S’) in an RSVP stream of numbers.
Observers performed this task in the presence of a cued-to-
respond paradigm. The purpose of this practice session was to
accustom the observers to initiate a response immediately after
the onset of the cue.
In the main experiment, observers for both Groups I and II
were instructed to identify the motion direction of a moving
sine-wave grating in each trial. The grating was embedded in
high external noise (Group I) or displayed in the absence of any
external noise (Group II). Two adaptive staircase procedures
(Levitt, 1971) were used to estimate contrast thresholds for
motion direction discrimination at two criterion performance
levels in each condition. The 3/1-staircase procedure racked
thresholds at 79.3% correct (d’ = 1.634). For every three
consecutive correct responses, signal contrast decreased by 10%
and would increase by 10% for every incorrect response made. In
the 2/1-staircases, thresholds were tracked at 70.7% correct (d’
= 1.089). Signal contrast would decrease by a factor of 10% for
every two consecutive correct response and increase by a factor
of 10% for every incorrect response.
3.2.4 PROCEDURE
At the initiation of each trial, a center fixation appeared
that lasted for 83 ms followed by five frames (signal/noise

57
images), each of which lasted 33 ms, concluding with a fixation
that remained till the observer made a response. Observers were
instructed to make a response as soon as they heard the cue-to-
respond.

3.3 RESULTS
3.3.1 DATA ANALYSIS
Eight SAT functions were measured for each observer in each
of the two external noise conditions. An exponential function

] 1 [ ) ( ) , ( '
) (
0
t PT
e c session session PT d
− −
− × =
β γ
α (11)

was fit to each SAT function using a maximum likelihood procedure
(Hays, 1981). For each SAT function, the likelihood is defined
as a function of the total numbers of trials N
i
, the number of
correct trials K
i
, and the percent correct predicted by equation
(12) in each signal contrast condition, i:

likelihood =
#
1
!
( ) (1 )
!( !)
i i i
trial
k n k i
i i
i i i i
n
Pc Pc
k n k
−
=
−
−
∏
(12)

In all, eight different SAT functions models were fit to
the data for each observer in each external noise condition.
Specifically, for each session, we fit one model (8β 8t
0
) in which
both parameters are free to vary, two models in which (1β 8t
0
) or

58
(8β 1t
0
) one of the two parameters are free to vary, and one model
(β t
0
) in which both parameters are constrained (Figures 9 & 10).
The optimal fits were selected by nested-model test based on χ
2

statistics

( ) 2 log
alternative
null alternative
null
likelihood
df df
likelihood
χ
2
− = × (13)

Figure 11: Results of fits from the maximum-likelihood estimation. Zero
noise condition.

To determine whether the full model differ significantly
from the reduced (alternative) model, we asked whether the rate

59
of information accumulation for each session differed
significantly from a more reduced model. A χ
2
test revealed that

Figure 12: Results of fits from the maximum-likelihood estimation. High
noise condition.

the rate of information as well as the slope intercepts from both
the full model and the reduced model collected showed that both
were equivalent. In fact, it turns out that the best fitting
model had the rate of information accumulation as well as the
intercept constant, with only asymptotic performance varying
across all subjects in both zero noise conditions ( AB: χ
2
= 42.2,
df = 14, p>0.9 AN: χ
2
= 35, df = 14, p > 0.9 & JJ: χ
2
= 26, df =
14, p > 0.9) as well as high noise conditions (JM: χ
2
= 102, df =
14, p>0.9 JL: χ
2
= 22 & XM: χ
2
= 130, df = 14, p > 0.9.

60
Table 3: Maximum-likelihood model estimation results.
ab an jj jm xl jl
g 0.7808 1.5969 0.2484 1.124 0.8038 1.4696 0.1166 1.0679 0.1543 0.9715 0.1906 0.8088
a1 4.2482 12.891 3.0815 19.668 3.7819 2.8677 2.4642 67.3116 2.8886 67.0526 3.0835 30.9278
a2 4.1386 15.582 1.8555 34.755 2.37 3.2648 2.1469 62.8139 2.3507 95.5849 3.4531 64.6565
a3 4.2017 16.496 3.4324 32.56 3.0752 5.013 1.821 64.3798 2.5242 117.7101 2.9833 38.3961
a4 4.4852 16.49 2.2494 36.418 3.3578 5.96 2.2987 83.7706 2.6513 98.7506 2.7757 61.135
a5 4.516 21.997 2.4229 36.403 3.32 7.1787 1.8768 85.9333 2.2738 87.5611 2.9671 44.9851
a6 5.8272 26.506 2.6625 38.36 4.2359 9.5456 1.7564 78.9488 2.9558 95.998 3.8956 58.7107
a7 5.6792 20.342 3.2104 43.476 3.6364 9.8762 2.1466 97.733 2.7353 109.7909 2.9062 44.2014
a8 8.0575 23.805 2.5508 41.104 4.2821 9.6981 1.7383 104.0933 1.6805 99.315 2.7847 57.7312
b1 4.7981 3.9927 8.9343 5.24 1.6723 9.8598 11.909 5.9519 12.434 8.5753 9.7808 13.3935
b2 11.68 9.0735 4.7829 6.1824 7.9151 11.234
b3 19.876 1.8416 4.1869 5.691 5.1141 2.5539
b4 7.4732 18.503 8.6318 5.2755 7.0354 22.571
b5 7.6668 3.0845 15.171 6.7146 15.895 9.0836
b6 3.6226 12.601 6.9367 6.5419 5.077 4.7307
b7 5.2819 4.8197 12.129 8.7305 15.403 4.3935
b8 2.4955 7.6031 5.392 15.705 4.5818 24.287
t01 0.0312 0.002 0.3669 0.284 0.1344 0.2393 0.3737 0.299 0.2889 0.3285 0.1428 0.3105
t02 0.175 0.0541 0.1531 0.3112 0.3149 0.0821
t03 0.2529 0.1655 0.1031 0.2664 0.1795 0.1629
t04 0.1543 0.3221 0.2462 0.297 0.3054 0.3159
t05 0.1358 0.1779 0.2419 0.3037 0.3714 0.3104
t06 0.0032 0.3336 0.2176 0.2945 0.3097 0.2167
t07 0.0792 0.2121 0.2521 0.2927 0.3474 0.2981
t08 0.0045 0.2771 0.2323 0.2939 0.1064 0.3272
L
6730 6687 7207 7172 7020 6994 7305 7203 7118 6993 6971 6841

61
Figure 13: Estimated contrast threshold derived from maximum-likelihood
estimation with d’ set to 1.349. Zero Noise Condition.

In order to better understand the nature of these identical
rates of information accumulation and intercept, we estimated
contrast thresholds for all subjects. Contrast threshold were
calculated from the best-fitting models:

γ
β
α
/ 1
) (
0
exp 1 (
'
t PT t
d
C
− −
− ×
= (14)

The learning curves, expressed as log contrast versus log
day, are shown in Figure 11. For subjects JM, average threshold
contrast reduction was 34%, XL at 49% and JL at 55%, with an

62
average reduction across all three subjects to be about 45%.
Subjects in the high external noise conditions showed similar
amount of learning: AN 48% reduction, EM 32% reduction and AB
with a 32% threshold contrast reduction. On average, all three
subjects showed a 34% improvement across 8 sessions of training.
(Figure 11). Since all the estimated contrast threshold showed
significant improvements across sessions, this provides a clear
indication that perceptual learning has been occurring.
Figure 14: Estimated contrast threshold derived from maximum-likelihood
estimation with d’ set to 1.349. High Noise Condition.

Contrast Threshold
Sessions
High Noise
1 2 3 4 5 6 7 8
0.0442
0.0884
0.1768
0.3536
0.7071
AB
1 2 3 4 5 6 7 8
0.0441
0.0882
0.1765
0.3533
0.7069
JJ
1 2 3 4 5 6 7 8
0.0441
0.0882
0.1765
0.3533
0.7069
AN
1 2 3 4 5 6 7 8
0.0441
0.0882
0.1765
0.3533
0.7069
AVG

63
3.4 DISCUSSION
Perceptual learning can be seen as a process that extracts
relevant information from a stimulus over time in order maximize
efficiency and improve performance. Widely accepted assumptions
in behavioral researches suggest plasticity in the visual system
and perceptual learning alters this plasticity. Using ideal
observer models as a tool, to understand an observer’s behavior.
Based on limitations derived from these ideal observer models,
one can gain a better understanding on what limitations may be
imposed on the observer itself.
For example, in this study on perceptual learning, as
subjects perform a task, one would expect performance to improve
in both accuracy and processing time. One would expect to see a
decrease in contrast threshold (which we do), as well as a
reduction in processing time since common intuition would assume
an overall improvement. The reduction in contrast threshold
uphold many previous studies in this area, however, no changes
observed in the temporal dynamics of decision gives us a greater
understanding of how the nervous system functions.
As stated earlier, may studies have offer varying
explanations as to the underlying mechanisms of perceptual
learning. Karni & Sagi (1991) suggest that perceptual learning
primary takes place in the primary visual cortex, however others
believe that it takes place just out side the sensory system and
before the decision mechanisms (Dosher, Petrov, & Lu, 2005) . Yet
others feel that perceptual learning reflects a re-tuning of

64
perceptual templates (Dosher & Lu, 1999). This notion of
template re-tuning suggests that a mechanism of improvement stems
from focusing the perceptual template tightly on only relevant
information while ignoring the irrelevant ones. Yet a study by
Li, Levi & Klein (2004) suggest that perceptual learning improves
efficiency of the overall system not by re-tuning the perceptual
templates, but rather, re-tuning the decision templates. Here,
they suggest that the observer’s decision template (which
reflects the weightings of inputs from basic visual mechanisms)
provide an interpretation of how perceptual learning is
occurring.
However, the results stemming from our study offers yet
another interpretation as well as added constraints to the notion
of perceptual learning. We found that despite enormous
improvements seen in the observers while performing the task,
these improvements had little impact, if any, on the temporal
characteristics between sessions. These results offer us an
insight into to the underlying mechanism of perceptual learning,
in that output from the basic visual mechanisms remains
relatively stable over time, that as the system process incoming
signals, the stimulus representation that is outputted into the
decision stage remains relatively constant.

65
CHAPTER 4
4.1 GENERAL DISCUSSION & CONCLUSION
In Study I, we set out to create a unifying model capable
of accounting for the interactions between accuracy and RT. We
began by integrating an observer-based model with a dynamic
decision process. Observer model allow us to quantify the
overall efficiency of the perceptual system. For example, the
perceptual template model (Lu & Dosher, 1999), posit our
inefficiencies to 3 factors: internal additive noise (limiting
factor in a perceptual task performed at threshold), internal
multiplicative noise (ratio of the difference between backgrounds
to threshold) and template retuning (perceptual system retuning
the templates to operate optimally. However, the question becomes
whether these inefficiencies of the perceptual system are
transferred to the decision stage. Current studies, (Ratcliff
et. al and Smith et. al., Ratcliff, 1978; Ratcliff & Smith, 2004;
Smith & Ratcliff, 2004) suggest that these inefficiencies do
impact the perceptual process. However, they do provide a way to
quantify these inefficiencies. With an integrated dynamic
decision process, the perceptual template model seems to provide
an adequate account.
Concurrent to studies by Ratcliff & Smith, Palmer, Huk and
Shadlen (2004) propose a model that aims to define the rules of
perceptual decision by characterizing accuracy and RT through the
proportional-rate and power-rate diffusion. To understand the

66
relationship between response time and accuracy in terms of
stimulus strength, Palmer et. al. first measured separately
reaction time as a function of stimulus strength and accuracy as
a function of stimulus strength. The measures were then combined
as a threshold ratio of the two measurements, with thresholds
defined as halfway-time-threshold/halfway-accuracy-threshold.
They claim that this allows for specific testing between
chronometric and psychometric functions. From these ratio
estimates, they predict that a common underlying mechanism
couples the two dependent measures. However, they assume a
linear transformation of the stimulus input.
In Study I, we sampled performance accuracy across 10
contrast levels within two noise conditions. When we modeled our
data with the PTM + dynamic decision, we found that the most
parsimonious model accounted for and describe the temporal
dynamics of perceptual decision. The parsimonious model
characterized the interactions between accuracy and RT with a
constant rate of information accumulation and intercept. Perhaps
more important is despite the huge variation in contrast energy,
the rate of information accumulation and starting time were not
perturbed. One possible explanation for the performance is that
the relationship between signal and noise is fully characterized
by the observer model prior to the decision stage. The signal
entering the decision stage is devoid of any processing
inefficiencies that may impact information accumulating rate or
starting time.

67
In Study II, we applied the theoretical framework we
developed previously and applied it to a perceptual learning
study. We jointly measured performance accuracy and procession
across 2 noise conditions over several sessions. The results
showed, as expected, overall improvement in task performances
exhibited by a significant reduction in contrast threshold. When
we modeled our data with the dynamic-PTM, we found that the most
parsimonious model accounted for and described the impacts of
perceptual learning on the temporal dynamics of perceptual
decision. One intriguing caveat from this study is that despite
the enormous amounts of learning exhibited, the only thing that
seems to be changing is their processing of the representation of
the stimulus and NOT their decision structure.
In order to understand how various sensory processes govern
higher brain function we first must understand how these
processes govern simple decisions. A step in making this progress
is to develop a framework for understanding simple decisions.
In our studies, we began by providing a framework that maps the
characteristic of signal inputs, such as contrast, noise, and
features, on to the decision stage. By integrating a human
observer model with a dynamic decision process we are able to
understand how signal strength, reaction time and performance
accuracy interact. In applying this methodology to studies of
perceptual learning, we discovered that despite the enormous
amount of learning that has occurred, the decision process is
left relatively unchanged across sessions.

68
The results from these studies offer us a better
understanding of how our system process sensory information.
With the development of the dynamic-PTM, we are able to gain a
better understanding of how our system handles sensory
information and how these signals are interpreted by the decision
stage.

69
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Asset Metadata

Creator Chu, Wilson (author)

Core Title Temporal dynamics of perceptual decision

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Psychology

Publication Date 04/11/2010

Defense Date 03/08/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,perceptual decision,perceptual learning,psychophysics

Language English

Advisor Lu, Zhong-Lin (committee chair), Hellige, Joseph (committee member), Hirsch, Judith A. (committee member), Manis, Franklin R. (committee member), Tjan, Bosco S. (committee member)

Creator Email wilsonchu333@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1094

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Legacy Identifier etd-Chu-20080411.pdf

Dmrecord 52002

Document Type Dissertation

Rights Chu, Wilson

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email uscdl@usc.edu

Abstract (if available)

Abstract We combined the external noise method (1) with the cue-to-respond speed accuracy trade-off (SAT) paradigm (2) to characterize the temporal dynamics of perceptual decision making. Observers were required to identify the orientation of one of eight briefly presented peripheral Gabor targets (+/- 12 deg) in both zero and high noise. An arrow, occurring in the center of the display cued the observer to the target location 234 ms before the onset of a brief target display