Stevens, Stanley S. (1975), Psychophysics (New York: Wiley).

Van Nes, Floris L., and Bouman,

Maarten A. (1967), “Spatial modulation transfer in the human eye,” in J. Opt. Soc. Am. 57 (3): 401–406.

Barten, Peter G.J. (1999),

Contrast Sensitivity of the Human Eye and Its Effect on Image Quality

(Knegsel, Netherlands: HV Press). Also published by SPIE Press.

difference (JND), defined where the difference between two stimuli is detected as often as it is undetected.

Logarithmic coding rests on the assumption that the threshold function can be extended to large luminance ratios. Experiments have shown that this assumption does not hold very well. At a given state of adaptation, the discrimination capability of vision degrades at low luminances, below several percent of diffuse white. Over a wider range of luminance, strict adherence to logarithmic coding is not justified for perceptual reasons. Coding based upon a power law is found to be a better approximation to lightness response than

a logarithmic function. In video, and in computing, power functions are used instead of logarithmic functions. Incidentally, other senses behave according to power functions, as shown in Table 23.1.

Contrast sensitivity function (CSF)

The contrast sensitivity of vision is about 1% – that is, vision cannot distinguish two luminance levels if the ratio between them is less than about 1.01. That threshold applies to visual features of a certain angular extent, about 1⁄8°, for which vision has maximum ability to detect luminance differences. However, the contrast sensitivity of vision degrades for elements having angular subtense smaller or larger than about 1⁄8°.

In vision science, rather than characterizing vision by its response to an individual small feature, we place many small elements side by side. The spacing of these elements is measured in terms of spatial frequency, in units of cycles per degree (CPD, or ~/°); each cycle comprises a dark element and a white element. At the limit, a cycle comprises two samples or two pixels in adjacent columns; in the vertical dimension, the smallest cycle corresponds to two adjacent image rows.

Table 23.1 Power functions in perception

Figure 23.5 The contrast sensitivity function (CSF) of human vision varies with retinal illuminance, here shown in units of troland (Td). The curve at 9 Td, which typifies television viewing, peaks at about 4 cycles per degree (CPD, or ~/°). Below that spatial frequency, the eye acts as a differentiator; above it, the eye acts as an integrator.

0.001

1

0.1

λ = 525 nm

ω = 2 mm

9 Td 90 Td 900 Td

0.9 Td

0.09 Td

0.009 Td

0.0009 Td

Spatial frequency [cycles/°]

Troland [Td] is a unit of retinal illuminance equal to object luminance (in cd·m-2) times pupillary aperture area (in mm2).

Contrast sensitivity can also be plotted as a function of temporal modulation.

Figure 23.5 above shows a graph of the dependence of contrast sensitivity (on the y-axis) upon spatial frequency (on the x-axis, expressed in cycles per degree). Contrast sensitivity of 100 corresponds to

a ratio of 1.01 (1%) being perceptible. The graph shows a family of curves, representing different adaptation levels, from very dark (0.0009 Td) to very bright

(900 Td). The curve at 9 Td is typical of electronic displays.

For video engineering, three features of Figure 23.5 are important:

•First, the 90 Td curve has fallen to a contrast sensitivity of unity at about 60 cycles per degree. Vision isn’t capable of perceiving spatial frequencies greater than this; a display need not reproduce detail higher than this frequency. This limit of vision sets an upper bound on the resolution (or bandwidth) that must be provided.

•Second, the peak of the 90 Td curve has a contrast sensitivity of about 1%; luminance ratios less than this need not be preserved. This limits the number of bits per pixel that must be provided.

•Third, the curve falls off at spatial frequencies below about one cycle per degree. Luminance can diminish (within limits) toward the edges of the image without the viewer’s noticing; such was the case in traditional CRT consumer displays, though fall-off doesn’t occur in LCD and PDP displays. Fall-off does occur in projection.

Campbell, Fergus W. and Robson, John G. (1968), “Application of Fourier analysis to the visibility of gratings,” in J. Physiol. (London) 197: 551–566.

In traditional video engineering, the spatial frequency and contrast sensitivity aspects of this graph are used independently. Most video compression systems, including JPEG and MPEG, exploit the interdependence of these two aspects, as will be explained in

JPEG and motion-JPEG (M-JPEG) compression, on page 491.