Contrast Enhancement via Image Evolution Flows

A framework for contrast enhancement via image evolution flows and variational formulations is introduced in this paper. First, an algorithm for histogram modification via image evolution equations is presented. We show that the image histogram can be modified to achieve any given distribution as the steady state solution of this differential equation. We then prove that the proposed evolution equation solves an energy minimization problem. This gives a new interpretation to histogram modification and contrast enhancement in general. This interpretation is completely formulated in the image domain, in contrast with classical techniques for histogram modification which are formulated in a probabilistic domain. From this, new algorithms for contrast enhancement, including, for example, image and perception models, can be derived. Based on the energy formulation and its corresponding differential form, we show that the proposed histogram modification algorithm can be combined with image regularization schemes. This allows us to perform simulations contrast enhancement and denoising, avoiding common noise sharpening effects in classical schemes. Theoretical results regarding the existence of solutions to the proposed equations are presented.