I am new in the image processing and I am working on a problem which demand that if we can map each pixel value of an image to the univariate normal distribution. I have done the below approach but I want to know if it is mathematically valid or not or what are the condition we need to assume to say this is mathematically correct.
Suppose we have an images $I$ of the size $mtimes n$
so I computed the common variance for the whole image and for each pixel I am assume the pixel value itself as a mean and common variance as a variance and mapping it to the univariate gaussian the same process I am doing for all the pixel.