Which is exactly the same thing. Because our vision is basically ratiometric (i.e. non-linear), we are more sensitive to changes in the shadows than the highlights. An encoding that spreads gradation errors evenly is one that is also close to perceptually uniform.

I am not getting my point across. Relative error is an essential parameter in any measurement system, whether the quantity being measured follows a linear, power, or log function. That is why we use CV (coefficient of variation, standard deviation/mean) rather than the standard deviation when discussing relative error. Weight is a linear function. When weighing a 100 kg football player a scale accurate to the nearest 0.5 kg is adequate, but this scale would not be appropriate for weighing a 2 kg premature infant. The relative errors would be 0.5% and 25% respectively. We need finer gradation at the low end even with a linear function.

Gamma, a power function, was originally introduced in electronic imaging to account for the nonlinearity of cathode ray tubes and not to account for the non-llinearity of the perception of luminance, which is approximately logarithmic (not a power function), but a side effect was that gamma improved gradation in the shadows. However, gamma fails at low luminances where the slope approaches infinity as luminance approaches zero. For this reason, gamma encodings use a linear ramp at very low luminances.

Gamma encoding also fails when one is dealing with HDR imaging, where a log encoding yields constant relative error (see

encoding by Greg Ward). One can also improve relative error at the low end by brute force (using more significant digits), but this can be wasteful since the greater precision is not needed at the high end, or by using floating point notation.

Perceptual uniformity is useful in image editing so that a given increment in the control will produce the same proportional change at the low end as at the high end. Many critical users calibrate their monitors to L*a*b rather than gamma, since L*a*b is designed to be perceptually uniform. However, a linear ramp is still needed at low luminances.

When dealing with a wide range of luminances (e.g. HDR), gamma is abandoned and one goes over to log or linear floating point encoding as discussed by Ward in the quoted article.

Regards,

Bill