Histogram Modification via Differential Equations

The explicit use of partial differential equations (PDEs) in image processing became a major research topic in the past years. In this work we present a framework for histogram (pixel-value distribution) modification via ordinary and partial differential equations. In this way, the image contrast is improved. We show that the histogram can be modified to achieve any given distribution as the steady state solution of an image flow. The contrast modification can be performed while simultaneously reducing noise in a unique PDE, avoiding noise sharpening effects of classical algorithms. The approach is extended to local contrast enhancement as well. A variational interpretation of the flow is presented and theoretical results on the existence of solutions are given.