Doug Kerr said:

Hi, Sean,

Certainly true, if we are talking about the function. The issue here is the dynamic range of the camera.

My only specific interest in functions here is that a bug free piece of code to read an image file is a well defined function and to differentiate the

**domain **(set of valid input image files) and the

**range** (set of outputs) from the

**dynamic range** which is a function of the

*system *as a whole. By

*system* I mean the lens, sensor (celluloid or silicon based), and the software end.

Doug Kerr said:

And there is an outlook that imputes that from a property of the code space: the ratio of the luminance corresponding to the largest value to that represented by the lowest non-zero value. (Or to some people, the ratio of the largest code value to the lowest non-zero code value, nonsensical if the code space is non-linear with luminance, as it is in many of the cases that are discussed.)

Which is what I was attempting to differentiate by introducing the concepts of domain and range. The range need not be a uniform space. I hesitate to say the

*metric is not uniform* as the definition of the metric/distance between any two points in the range may not satisfy the three requirements. But, on the same note the underlying intuitive concepts map to that concept. To satisfy my curiosity here I need to find time to read the working space definitions and work forward to see if the things are ideally behaved (i.e., they satisfy the analytical requirements to allow mathematical intuition to be safe).

Doug Kerr said:

We often hear the dynamic range of the camera simplistically described as the ratio of the largest and smallest luminance which, in the same shot, can be "captured" by the camera. That is of course not explicit.

A meaningful elaboration of that outlook (and note that this ignores the role of noise, which I am not advocating) is this:

**The ratio of the greatest to the least luminance about which detail (manifest as differences in luminance) can be captured in the delivered camera output.**

Now, if, for example, the output being considered has possible values of 0-255, then the lowest luminance that could meet the definition of the "least" luminance in the above would be that with code value 1 (since variations in luminance about that level would be with code excursions from 0 through 2). Similarly, the greatest luminance that met the corresponding criterion would be that which had code value 254 (since variations in luminance about that level would be with code excursions from 253 through 255).

If the coding system has the gamma precompensation function prescribed by the "sRGB" color space, that ratio of luminance is about 3300.

I cannot imagine dynamic range without noise and non-uniform scaling of the range to make technical sense. Nonetheless, there are times and places where appealing to common sense (which is often technically andn physically wrong) can be of pedagological value. If one can give the layperson a feeling to work with, then you have brought them forward although you lied to them. I that Terry Pratchett's term for this

**Lies To Children** is a great term (like claiming atoms are the smallest item in the universe or that time is constant).

Being lazy/busy at times I ask the following: Assuming that a properly exposed 12 bit RAW file has a standard deviation of 2 in 8-bit sRGB, what is its dynamic range? Assuming JPEG exposure has a standard deviation of 3 in 8-bit sRGB, what is its dynamic range?

Doug Kerr said:

Now, this is not at all to say that I subscribe to an "ignores noise" definition of the dynamic range of a camera. You will in fact find in an earlier post from me in this thread a link to my paper in which I discuss at length the ISO definition of the dynamic range of a digital camera.

Doug Kerr said:

I have not had time to read it, but I did scan it and the one thing I found wanting was having definitions clearly isolated from the text. Albeit, I admit this is the mathematician in me wanting a certain format of writing where the emotional/intuitional appeal follows the answer.

That approach is wholly compatible with the definiton you cite above. (Thanks for the cite to the Yang paper - I had not read it, and will try to tonight.)

You are welcome. I have yet to have time to read it either. In all honesty I was looking for a dissertation in the subject realm as they tend to define everything tersely and technically in chapter one when I found it.

You might take a look at

An Introduction To Statistical Signal Processing which is an online text from the same group if you enjoy the subject area. I have wanted to read this for a while, but time is a killer and I would rather shoot photos when the sun shines ;o).

I would also suggest taking a serious but critical (too many pre-prints lacking peer review) look at

CiteSeer which at times makes access to a serious research library system seem inconvenient. It has some very nice measures of interrelationships of articles that blows google out of the water.

all the best,

Sean