Histogram equalisation by Gaussian particle diffusion

Greyscale histogram equalisation is formulated by particle diffusion, which is extendable to any dimension. A histogram is approximated by a Gaussian mixture and its potential energy function is defined by its disparity from the uniform distribution. As a mechanical analogy, the equivalent dynamic system, corresponding to this potential, can be derived as a second-order ordinary differential equation. Adding viscosity terms to the dynamic system, we can acquire the stability which is validated by experimental results.