Cahn‐Hilliard inpainting and the Willmore functional

Abstract

The Cahn-Hilliard equation has its origin in material sciences and serves as a model for phase separation and phase coarsening in binary alloys. A new approach in the class of fourth order inpainting algorithms is inpainting of binary images using the Cahn-Hilliard equation. Like solutions of the Cahn-Hilliard equation converging to two main values during the phase separation process, the grayvalues inside the missing part of the image are oriented towards the binary states black and white. We present stability/instability results for solutions of the Cahn-Hilliard equation and their connection to the Willmore functional. In particular we will consider the Willmore functional as a quantity to find the optimal scale of the inpainting