U. Glaeser

If it were separable (that is, H(ξ x, ξ y) could be determined by finding H(ξ x) and H(ξ y) independently),
with H(ξ x) = H(ξ y), or isotropic, the spatial response could be characterized via a single 1-D function.
Although the assumption of separability is often useful, the spatial CSF of the human visual system is not,
in fact, separable. It has been shown that visual sensitivity is reduced at orientations other than vertical
and horizontal. This may be due to the predominance of vertical and horizontal structures in the visual
environment, leading to the development or evolution of the visual system to be particularly sensitive at
(or conversely, less sensitive away from) these orientations. This is referred to as the “oblique effect.”
Temporal Frequency Response
The most straightforward approach to extending the above spatial vision model to include motion is to
modify the CSF to include temporal frequency sensitivity, so that H(ξx, ξy) becomes H(ξx, ξy, ξt). One way to estimate the temporal frequency response of the visual system is to measure the flicker
response. Although the flicker response varies with intensity and with the spatial frequency of the
stimulus, it is again generally lowpass, with a peak in response in the vicinity of 10 Hz. The attenuation
of the response above 10 Hz increases rapidly, so that at 60 Hz (the field rate of NTSC television) the
flicker response is very low.
It is natural, as in the 2-D case, to ask whether the spatiotemporal frequency response H(ξx, ξy, ξt) is
separable with respect to the temporal frequency. There is evidence to believe that this is not the case.
The flicker response curves for high and low spatial frequency patterns do not appear consistent with a
separable spatiotemporal response.
Reconstruction Error
To a first approximation, the data discussed above indicate that the HVS behaves as a 3-D lowpass filter,
with bandlimits (for bright displays) at 60 cycles/degree along the spatial frequency axes, and 70 Hz
temporally. This approximation is useful in understanding errors, which may occur in reconstructing a
continuous spatiotemporal signal from a sampled one. Consider the case of an image undergoing simple
translational motion. This spatiotemporal signal occupies an oblique plane in the frequency domain.
With sampling, the spectrum is replicated (with periods determined by the sampling frequencies along
the respective dimensions) to fill the infinite 3-D volume. The spectrum of a sufficiently sampled (aliasingfree)
image sequence produced in this way is shown in Fig. 28.15.
The 3-D lowpass reconstruction filter (the spatiotemporal CSF) can be approximated as an ideal
lowpass filter, as shown in Fig. 28.16. As long as the cube in Fig. 28.16 completely encloses the spectrum
xy FIGURE 28.15 The spectrum of a sampled image undergoing uniform translational motion.
© 2002 by CRC Press LLC
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