|
Human visual CSF
A simple and widely used psychophysical
test is the measurement of the contrast threshold of sine-wave gratings that is just detectable
against a uniform background.
A grating can be described
by the formula
L(x) = L0[1 + m cos(2p
sf x) cos(2p
tf t)],
where L0 is the mean luminance, m the contrast, sf the spatial frequency,
and tf the temporal frequency of the grating.
When the reciprocal of the contrast threshold value is expressed as a function of
spatial frequency, the resulting function is referred to as the CSF. Under normal
viewing conditions (i.e., photopic illumination level and slow temporal variations),
the CSF has a band-pass shape, displaying attenuation at both low and high spatial
frequencies. To some extent, the CSF is similar to the MTF in optics, characterizing
a system's response to different spatial frequencies. The behavior of the CSF is,
however, much more complicated; it varies with the mean luminance, the temporal
frequency, and the field size of the grating pattern.
Why does CSF behaves differently in different conditions?
One popular
explanation of the CSF shape relies on retinal lateral inhibition. In
this theory, the visual responses are determined by retinal ganglion cells,
which take light inputs from limited retinal areas. These areas are called receptive fields. They are circular in shape and each
of them contains two distinct function zones: the center and surround. The inputs
to the two zones tend to cancel each other, the so-called center-surround antagonism.
Such spatial antagonism attenuates uniform signals, as well as low frequency signals.
This might explain why the system as a whole is insensitive to low frequencies, but it is difficult to offer a coherent
description of all CSF behaviors based on this theory.
Explanation based on Implicit Masking:
In the effort to model the CSF, Yang and Makous suggested that the DC component,
that is, a component at 0 cycle per degree (cpd) and 0 Hz, in any visual stimulus
has all the masking properties of any other Fourier component. The associated effect
of the DC component in visual detection was called
implicit masking. The basic assumption here is that the energy of the
DC component can spread to its neighboring frequencies, because of spatial inhomogeneities
of the visual system. When a target is superimposed on a background field of similar
features, the required stimulus strength for detection, i.e., threshold strength,
is generally increased. This is a nonlinear interaction. It follows that the DC
component can reduce the visibility of the targets at low spatial frequencies as
a consequence of the energy overlap, given such nonlinear interactions. This concept simplifies the explanation of CSF behavior considerably, as
discussed in the following.
First, let us explore the roll-off of the
CSF at the low spatial frequencies. Each of the frequency components spreads to
a limited extent. The interaction between the target and the DC components should
disappear when the spatial frequency of the stimulus is high enough. In this case, there is no effect of implicit masking. Therefore, the drop of contrast sensitivity because of implicit masking is
restricted to low spatial frequencies.
Second, this assumption offers an explanation
of the effect of luminance on the contrast sensitivity at low spatial frequencies:
as mean luminance decreases, the component at zero frequency decreases too. When this happens, other factors such
as noise can dominate, and thus the relative attenuation at low frequencies decreases.
Third, this assumption also offers an explanation
of the dependence of the attenuation on temporal frequency. The DC component of
a grating is at zero temporal frequency and zero spatial frequency in a 2-D spatiotemporal
frequency domain, so the effects of implicit masking apply only to very low temporal
and spatial frequencies. Test gratings that are modulated at high temporal frequencies
would be exempt from the effect of implicit masking, no matter what the spatial
frequency of the grating is.
Finally, the effect of field size on contrast sensitivity can be explained by the
breadth of implicit masking. The extent of implicit masking is determined by the
spread of the DC energy in the frequency domain. The larger the viewing field, the
less the spread. This explains why the peak sensitivity shifts to lower spatial
frequency as field size increases, owing to the decreasing breadth of implicit masking.
The exact amount of spread depends also on retinal inhomogeneities.
Calculating CSF values
The descriptive model based on implicit
masking has several model parameters, the value of which can be optimized based on particular experimental data sets. One problem here is that the published
data in one experiment can deviate significantly
from those in other experiments
due to some not well-know causes, which can be experimental settings, test procedures,
and individual differences etc.
In the calculation, you have the
options to choose which
data set to use as the baseline. The data sets include:
- Kelly (1972) data,
- Van Nes and Bouman (1967) data, and
- a combination of multiple data sets.
Go to the calculation page
|