I have 2 distributions. One is a population distribution for a type of image. Another is a sample of an undetermined distribution. I want to compare the distributions to see if they are the same (or reject that they are different).
The two distributions I have are 3 dimensional and discrete, but fit within a 28x28x3 array.
To be more specific, my data are greyscale images. 2 of the dimensions are actually spacial dimensions of the image, and 1 is the intensity of the image.
I want to take the first 2 dimensions as coordinates, and then perform a $\chi^2$ test for goodness of fit, taking the intensity of the sample distribution at a given pixel as the observed, and the intensity of the the population distribution at the same pixel as the expected. Then I can conclude on whether the data I have observed are consistent with the distribution I have.
I would use a Kolmogorov–Smirnov Test, but that requires a continuous distribution, and my distributions are not continuous, only my variables are.
So is this a proper usage of the $\chi^2$ test for Goodness of Fit, or do I need to use a different method to compare these distributions?