Reaction Time to Spatial Frequency Measured with the Point Process Method
Robert F. Dougherty
Based on a poster presented at ARVO in May 1998.
In real world situations where response time to sudden events is
important, unexpected events (by definition!) do not happen in discrete
trials preceded by warning tones. For example, while driving a car down
a residential street, something may suddenly cross your path. The object
must be identified and appropriate action taken. If it is a tumbleweed,
the appropriate action may be to proceed, allowing your vehicle to run
it over. However, if the obstacle appears to be a child, you will want
to slam on the brakes as quickly as possible. Occasionally, such as
during a windstorm, you may encounter many obstacles, most of which may
be run over. However, you must remain vigilant, for one of those
obstacles may turn out to be a child.
To push this example, assume that the tumbleweeds are randomly
dispersed. Then, the time between one tumbleweed crossing your path and
the next will be an exponentially distributed random deviate having some
mean (proportional to the density of tumbleweeds). Such exponentially
distributed random periodic events are known as Poisson point processes.
The nature of Poisson processes are such that the occurrence of one
event (a tumbleweed blows across your path) is completely unpredictive
about when the next event (or tumbleweed) will occur.
The unpredictable nature of the time of the next event in a Poisson
processes is in stark contrast to many reaction time studies. Such
studies are generally divided into discrete trials which typically
feature a warning event, a random delay drawn from a rectangular
distribution, followed by the target event. The discrete trial with its
warning event is something that is rarely encountered in the real world.
Also, non-exponentially distributed random delays are not entirely
A more ecologically valid method for assessing reaction time to
sudden, brief events has been proposed by
(refs 1 & 2). This method
involves runs of several minutes during which the observer must respond
as rapidly as possible to the target events. These events come without
warning and with exponentially distributed random delays between them.
The present study validates this "point process method" by
exploring a well known relation between spatial frequency and reaction
- To further develop an RT paradigm based on point-processes (refs 1 & 2)
- To measure reaction time to stimuli of various spatial frequencies
- Point Process Method Advantages:
- A more realistic RT task- real world events don't come in discrete trials
with warning tones!
- More efficient
- Provides more information (e.g., can extract non-linearities when stimuli
closely follow one another)
System Identification: Noise
- The white noise response is one method used to characterize a linear system
- A white noise stimulus is presented to a system and its response is measured
- The stimulus may be cross-correlated with the response to produce an estimate
of the system's impulse response
Point Process RT Method
- Present stimuli as a Poisson process (a point-process version of noise)
- Continuously flash stimuli with exponentially distributed random delays between flashes
- Subject responds whenever a stimulus is seen (responses form a second point process)
- Point process data are made into a time series of 0s and 1s for analysis
- Cross correlate stimulus & response to determine system transfer function (ref 3)
- Stimuli were foveal, 1.5 deg extent Gabors on a 32 deg x 23 deg, 10 cd/m^2 gray field
- Brief duration- one 75Hz screen refresh (i.e., 13 ms)
- Spatial frequencies: 0.5, 1, 2, 4, 8 & 16 cycles/deg
- Apple 17" Multiscan display, Power Mac 8500 (contrast resolution
enhanced with bit-stealing (ref 4), Gravis gamepad response device
- Gabors were presented during 1-3 minute runs with exponential-random delays
between presentations (3 second mean delay)
- Detection thresholds measured with 2IFC staircase
- Contrast set to 2.5 times threshold
Contrast Sensitivity functions for the 3 observers.
Error bars = 95% CI; from bootstrap (ref 5) variance of psychometric function fit
- Stimulus and response point processes converted into a discrete time series
of 0's (no event) and 1's (event)
- The temporal bin size used for the conversion to a time series determines the
- smaller bins provide better resolution, but require more data to produce
- The cross correlation of these time series estimates the impulse response of
One Observer's Cross Correlations
A Second Observer's Cross Correlations
A Third Observer's Cross Correlations
- RT estimate = peak of cross intensity function
- Data for 3 observers (BD, DR & TH) compared to traditional RT method (ref
6: MWG & BB, at 5.5 times detect threshold; from their fig. 1)
- RT to high spatial frequencies is slower than RT to low SFs
- ~20 ms increase per SF octave
- The RT-to-SF slope replicates previous findings
- Overall, our RT estimates may be slower- perhaps due to predictiveness of
non-exponential random delay used in most RT studies (see ref 2)
- Point process RT method works!
Other Uses for Noise
- Point process method for auditory & somatosensory RT
- Simultaneous visual, auditory and somatosensory RT (can reveal cross modal
facilitation and inhibition)
- Multifocal ERG & VEP (e.g., ref 7)
- Visual field mapping with fMRI (can provide cortical retinotopy and an
estimate of the hemodynamic response)
- Point process visual search task- no discrete trials makes for a more
ecologically valid task
- Simpson, W.A. (1997). personal communication.
- Simpson, W.A., Braun, W.J., Bargen, C. & Newman, A.J. (1998). A new
approach to simple visual reaction time using point processes. Investigative
Ophthalmology & Visual Science, 39: S405.
- Brillinger, D.R. (1994). Time series, point processes, and hybrids. Canadian
Journal of Statistics, 22: 177-206.
- Tyler, C.W., Chan, H., Liu, L., McBride, B., Kontsevich, L.L. (1992). Bit
stealing: how to get 1786 or more gray levels from an 8-bit color monitor. SPIE
proceedings, 1666: 351-364.
- Foster, D.H. & Bischof, W.F. (1991). Thresholds from psychometric
functions: Superiority of bootstrap to incremental and probit variance
estimators. Psychological Bulletin, 109: 152-159.
- Greenlee, M.W. & Breitmeyer, B.G. (1989). A choice reaction time analysis
of spatial frequency discrimination. Vision Research, 29: 1575-86.
- Baseler, H.A. & Sutter, E.E. (1997). M and P components of the VEP and
their visual field distribution. Vision Research, 37: 675-690.