Light Density and Pixel Density

Started Jan 26, 2011 | Discussions thread
Joofa Senior Member • Posts: 2,759
Re: On Pixel size

RoysLaw wrote:

Very interesting argument! Granted that I am not as knowledgeable as you guys on the sensor internals and the chain of its process but I would assume that this process varies per technology and application. Isn't it possible that both is true depending on which technology and or application is used?

Anyone care to provide some links regarding this argument?

...

Hi,

Actually, no sensors internals need to be brought in this discussion. This is a simple argument based upon the image samples obtained from a camera. The idea behind this thought is that any measure of noise would mean that you have a number of noisy samples and from them you generate some numbers that describe the noise, say average value of noise, standard deviation etc. An important thing, which is usually ignored, is that these noisy samples should ideally have been drawn from the same underlying distribution that generates the noisy samples. But the problem is that for the type of noise being discussed, i.e., shot noise, its distribution varies from pixel to pixel in an image. Hence, in theory each pixel needs to be treated differently, and one would acquire a large number of pictures of the same static scene in the same lighting conditions and then fix a pixel location and analyze all the pixels at that location in all images.

But in real photography you typically have only one image. So for each pixel location you have just one sample. Hence, one can't figure out measures such as average, standard deviation, etc. from just one sample. To get past this impasse what many do is to take an image that is all flat, or a portion of an image that is flat and figure out the spatial average and standard deviation and assume that is equal to the temporal (i.e., if they had more than one images) mean and average at each pixel location.

Many, including Emil Martinec, on his noise analysis have taken this simplistic viewpoint, and generated graphs showing the obvious and well-known relationship of noise with frequency, etc. However, a real image is not uniform patch. One can try to find out uniform patches in an image and do the said spatial analysis. But, firstly, each of those patches have a different standard deviation, etc. And, secondly, they don't say much about the whole image.

In real life one wants simple answers such as "is there a way to quantify the amount of noise in an image using as few numbers as possible?". The answer is yes, it is possible to do so with certain assumptions.

The issue is confounded by the usual mantra you would see flouted around these threads that "noise has both amplitude and frequency", "noise is a vector", and so on. While, such are valid issues, but does one want to have, say 16 million numbers, associated (if you want to go in frequency analysis) with a simple question regarding "what is the measure of noise in this 16 MP image?"

As I just mentioned it is possible to develop simple models that answer such questions with just a couple of numbers describing image noise that are applicable for real, natural images, and also include those flat/uniform fields as special cases, so everything is fully incorporated.

Sincerely,

Joofa

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Dj Joofa

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