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I have two sets of data, and I want to know if the second set is sufficiently different from the first to be considered different.

More specifically, I have a sample set A from a number of pixels in the vicinity of point X in an image, and another sample B of pixels in the vicinity of point Y in the same image.

I want to know if point X and point Y could be part of the same object in the image (based on color values). For example, if A and B are both mostly blue then the answer is yes, but if A is red and pink and B is blue then the answer is no.

My only idea so far (based on vague memories of a statistics class I took years ago) is to calculate the standard deviation in A and B, and from that calculate a threshold that gives you 95% certainty, and see if they are within a certain distance of each other. Is this correct?

Otherwise, what's the best way to do this?

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What sort of data you have? It seems like the Kolmogorov-Smirnov test could be appropriate here. It is used to check wether two samples come from the same distribution. It can be easily calculated in R with the command ks.test. – user10525 May 9 '12 at 23:33
They are pixels from an image. More specifically, I have a border detection algorithm, but I want to verify borders by checking that pixels on opposite sides of the border are "different". – CaptainCodeman May 9 '12 at 23:52
I'm used to seeing color defined by values on 3 different variables. Are you talking about color as something that can be defined by a value on a single variable? – rolando2 May 10 '12 at 3:01
No, I'm using all 3 RGB values. So basically, a color is a point in 3D space. – CaptainCodeman May 10 '12 at 10:44
Well, more accurately, in some parts (e.g. border detection) I'm effectively using one variable: I find the mean, and then use the distance from the mean as a one-dimensional variable. – CaptainCodeman May 10 '12 at 11:03

1 Answer

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You want to compare the distributions of the samples. If the border is distinct, using a single hue dimension with a Kolmogorov-Smirnov test might suffice. If hue alone does not provide enough separation you'll have to add another dimension. If you want to stick to chromaticity (color without the brightness dimension), I would suggest the a* and b* color-opponent dimensions in the CIELAB color model. With two dimensions you can apply this KS test. If you want to go whole hog and use all three dimensions, look here.

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Interesting, but I'm curious: why should the algorithm be different when you have more dimensions? I've just been assuming that a color is a point in 3D space (by RGB), and measure distances accordingly. Is there an advantage to taking it down to 1 or 2 dimensions? – CaptainCodeman May 10 '12 at 10:43
When you have a small sample, they will be sparse in high dimensions so obtaining a meaningful, accurate histogram will be more difficult. – Emre May 10 '12 at 17:49
Thanks a lot Emre, I've looked into these, good stuff indeed. – CaptainCodeman May 11 '12 at 11:24

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