Petition for a Canon 20D MkII (8MP no noise)

Started May 18, 2009 | Discussions thread
ejmartin Veteran Member • Posts: 6,274
A little visualization for the math challenged

To make the relation of the coin toss analogy to photography a bit more vivid, we can take the coin tosses and arrange them into a pixel array:

White pixels are heads, black are tails; I had the computer generate the values randomly (well, as random as computers can get). We can now bin the results in groups of 2x2,4x4,8x8,16x16, and 32x32 pixels; in the following sequence, the grayscale level is the percentage of heads (white) in that NxN block:

As the blocks get bigger and bigger, the fluctuations between blocks go down and down; this is the effect of bigger samples having smaller fluctuation. If you take the animated gif into photoshop, you should see the width of the histogram go down as you step through the frames; that is the decrease in fluctuations that comes with larger sample sizes. Note that nothing has been done to the original set of "coin tosses"; all I have done is to group them together. In other words, nothing has been done to the original "image"; only the coarseness at which that image is sample is changing.

Note that I have purposely kept the image size fixed during the coarse-graining of the image, so that one can see the tradeoff of noise vs resolution. Those who are inclined to pixel peep would make the following comparison:

This is the same binning as before, but now the binned regions are rescaled to the size of a single pixel. The pixel-peeper says, "look how much less noise there is with bigger pixels!", when in fact what they are observing is the smaller fluctuations inherent on larger scales in the image, made by larger samples of photons. I hope it is clear for those who think that the pixel-level view is somehow "absolute" that the pixel level is representing different scales in the image depending on the level of resolution that the pixel achieves (hint: the image size changes with each binning).

BTW, the original image is close to what would be observed in a hypothetical super-duper high pixel count sensor which resolves individual photons, when the sensor is halfway to saturation; either a photon is detected at a given pixel or it isn't, and half saturation means that on average half the pixels detect a photon. Suitable coarse-graining achieves grayscale values according to the percentage of pixels that record a photon. If I had skewed the coin toss so that the probability of heads was P instead of 1/2, then a fraction P of the pixels would be white and the grayscale level would be P after coarse-graining. The photon component of noise at larger scales is no more nor less than it would be with a conventional large pixel sensor of today.

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