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Advanced search Home  Applications » Imaging Capture and display in widedynamicrange imaging PDF version  Permalink It is commonly accepted^{1} that the dynamic range (DR) of an image, i.e. the image color definition, is equal to the image maximum signaltonoise ratio (max SNR). We also know that the maximum amount of image information is given by the product of resolution (crossimage definition) and color definition. Therefore, increasing the DR of images is by no mean less important than increasing their resolution. It is worth remembering however that DR and resolution cannot possibly be tradedoff against each other, since they live in orthogonal subspaces of the image. Below, we analyze the two most commonlyused methods to increase dynamic range. Purely logarithmic photoresponse Working with a purely logresponse practically eliminates saturation altogether, thereby making the maximum signal unlimited. It can be shown however^{2} that to first order, the DR at the output of any 11 analytic mapping equals the DR at its input. To realize this in the log case we recall that the smallsignal gain of the log function is inversely proportional to the average input signal. This implies that, at this sensor's output, a local contrast whose magnitude is usually small relative to the average luminance, maintains a prettymuch constant SNR for all levels of average luminance. At the same time, however, such a local contrast becomes progressively ‘washedout’ as the average luminance increases: a familiar and most undesirable property of the log transmission. The multipleexposure method Multiexposure (ME) means to apply shorter exposure times to originally saturated pixels, such that saturation is altogether avoided. This is generically illustrated in Figure 1, where the exposure periods are determined according to the simplest normalized series of where k is a natural number. Note that the overall sensor's gain to light is proportional to the exposure period. Therefore, to avoid contrast reversals, the gain of segment 2 must be elevated by a factor of 2, and so on.The RMS of the camera shot noise, however, is proportional to the square root of the exposure time. Therefore the RMS of the camera output noise in the continuous transmission arrangement above is elevated by a factor of in segment 2, a factor in segment 3, and so on. The DR of this arrangement is therefore given by and the added DR in bits isOne can see that there is not much point in having the shortest exposure period less than a 1/3 of the default, since e.g., in 1/4default the output noise is twice that of the default, thereby amplifying the minimum detectable local contrast by a factor of 2 and causing an alreadysignificant 'noisewashout’ effect. This limits the added DR of the ME arrangement, in practice, to just a single bit. The role of display DR As it turns out,^{3} in normal indoor lighting we cannot see more than 5 to 6 bits per color (bpc) with most cathoderaytube, liquidcrystal, and plasma displays. The effect of this bottleneck is demonstrated by the upper half of Figure 2, an 8bpc RGB picture Room (courtesy of Vincent Laforet, Photographer in Residence at the NewYork Times) where the maximum amount of lost visual content due to the display is about nine bits per pixel (24 minus 15). Figure 1. Figure 2. To get around the display bottleneck, we consider a similar situation that takes place inside our retina.^{4} The neural channels that carry all sensory information to the cortex cannot possibly support more than 7 bits of DR. Nevertheless, the DR we actually perceive can easily exceed 30bpc. The mechanism that makes this possible has been analytically modeled^{5} and is called retinal dynamicrange compression (DRC). Reconstruction of retinal DRC The basis of retinal DRC is the spatial feedback automaticgaincontrol (fbAGC), described in Figure 3. Here, the acquired image E_{i} is multiplied by the scalar forward gain K and fed into the first input of an image pixelwise multiplier. The output is then fed back into the multiplier's second input after having passed through a linear spatial low pass filter (LPF, to average) and being subtracted from unity. The average transmission (DC) of this model^{5} is which is known as Michaelis’ equation. Its graph (see Figure 4) is known as Weber's law.Figure 3. The DR compression ratio (CR) is defined as the output/input ratio for E_{i} = 1/K (the kneepoint). We then have: CR = K/2. The compression ratio is thus readily controlled through the parameter K. The fbAGC gain for variations of low spatial frequencies (the ‘DCgain’) is given by Figure 4. The fbAGC gain for local contrast variations (the ‘ACgain’) is obtained by assuming that, for such variations, the LPF output output remains constant. Denoting this constant by Ē E_{o} we have from which we getTaking the quotient (G_{AC} /G_{DC}) as a measure of the detail enhancement of the retinal DRC, we see that the amount of this detail enhancement, or the ‘effective visual acuity’ increases linearly with the average luminance of the viewed scene: a well known property of human and animal vision. The lower half of Figure 2 is Room after retinal DRC to 5bpc. Conclusions On the capture side of widedynamicrange imaging, we have demonstrated that dealing with saturation alone cannot significantly increase the DR of image sensors. We therefore conclude that this can only be achieved via significant noise reduction. On the display side of the problem, Figure 2 above demonstrates how retinal DRC can increase the potential number of perceived distinguished colors—by a factor of 512 in the current example—and shows how this affects our watching experience.^{–} References
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