Uniform distribution from a fractal Perlin noise f

Question

My Perlin noise function (which adds up 6 octaves of 3D simplex at 0.75 persistence) generates a 2D array array of doubles.

These numbers each come out normalized to [-1, 1], with mean at 0. I clamp them to avoid exceptions, which I think are due to floating-point accuracy issues, but I am fairly sure my scaling factor is good enough for restricting the noise output to exactly this neighborhood in the ideal case.

Anyway, that's all details. The point is, here is a 256-by-256 array of noise:

The histogram with a normal fit looks like this:

Matlab's lillietest is a function which applies the Lilliefors test to determine if a set of numbers comes from a normal distribution. My result was, repeatedly, 1, which means that these numbers are not normally distributed.

I would like a function f(x) such that, when applied to the list of values from my noise function, the results appear uniformly distributed.

I would like this function to be implementable in C# and not take minutes to run.

Once again, it shouldn't matter where the numbers come from (the question is about transforming one distribution into another, specifically a normal-like one to uniform). Nevertheless, my noise function implementation is based on this and this. You can find the above array of values here.

Answer 1

Oddly enough I just wrote an article on your very question:

http://ericlippert.com/2012/02/21/generating-random-non-uniform-data/

There I discuss how to turn a uniform distribution into some other distribution, but of course you can use similar techniques to transform other distributions.

Answer 2

You will probably be interested in one of the following (related) techniques:

• Probability integral transform

• Histogram equalization