Contrast Sensitivity Function

he contrast sensitivity function described here will be used to develop the color image metric described in chapter 8. Contrast sensitivity is sometimes called visual accuity [], []. We will use the term contrast sensitivity here, since we have used this terminology throughout chapter 8. Mannos and Sakrison [] proposed a model of the human contrast sensitivity function. The contrast sensitivity function tells us how sensitive we are to the various frequencies of visual stimuli. If the frequency of visual stimuli is too high we will not be able to recognize the stimuli pattern any more. Imagine an image consisting of vertical black and white stripes. If the stripes are very thin (i.e. a few thousand per millimeter) we will be unable to see individual stripes. All that we will see is a gray image. If the stripes then become wider and wider, there is a threshold width, from which on we are able to distinguish the stripes. The contrast sensitivity function proposed by Manos and Sakrison is

f in equation is the spatial frequency of the visual stimuli given in cycles/degree. The function has a peak of value 1 aproximately at f=8.0 cycles/degree, and is meaningless for frequencies above 60 cycles/degree. Figure shows the contrast sensitivity function A(f).

Figure 2.5: Contrast sensitivity function

The reason why we can not distinguish patterns with high frequncies is the limited number of photoreceptors in our eye. There are several other functions proposed by other authors, but we choose the above function [] because it can be simply analitically described. The same function is also used by Rushmeier et al. [] and Gaddipati et al. [], which was another motivating factor in using this function.

According to Weber's law, from the beginning of the century, the ratio of the just noticeable difference and the luminance L is constant, and equals 0.02 for a wide range of luminances. Nowadays there are better descriptions of just noticeable difference, and it is clear that it is not constant but depends on the adaptation level, and can be approximated using Weber's law just at certain adaptation levels.

The mapping function proposed by Greg Ward in [] relies on the work of Blackwell conducted in the early 1970s. Using a briefly flashing dot on a uniform background Blackwell established the relationship between adaptation luminance, , and just noticeable difference in luminance as:

That means that if there is a patch of luminance on the background of luminance it will be discernible, but the patch of luminance , where will not.

A more complex function for the whole range of human vision is used by Ferwerda et al. [], and later by Larson et al. in []. It accounts for both rod and cone, response, and is given in equation .

Ferwerda et al. [] and Larson et al. [] also exploit the changes in visual acuity. Visual acuity is the measure of the visual system's ability to resolve spatial details. It drops off significantly for low illumination levels. Actually it is about at and drops off to about at .

Ferwerda et al. also used the time aspect of adaptation. We are all familiar with the fact that we can not see immediately after entering the cinema if the film has already begun. After some period of time we can see the details again. Using Ferwerda's model it is possible to simulate such time changes of adaptation in computer graphics.