Uncertainty quantification of modified Cahn-Hilliard equation for image inpainting
Yin Xian
TL;DR
This paper investigates the impact of initial condition uncertainty on the modified Cahn-Hilliard equation used for image inpainting, employing statistical analysis and chaos expansion methods.
Contribution
It introduces a framework for quantifying uncertainty in the modified Cahn-Hilliard equation for image inpainting, combining polynomial chaos and perturbation techniques.
Findings
Uncertainty affects the solution behavior significantly.
Statistical properties of solutions are characterized.
Experimental results validate the analysis.
Abstract
In this paper, we review modified Cahn-Hilliard equation for image inpainting and explore the effect when the initial condition is uncertain. We study the statistical properties of the solution when the noise is present. The generalized polynomial chaos and the perturbation expansion are used to analyze the equation. Experimental results are attached for comparison of solution behavior.
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Taxonomy
TopicsSolidification and crystal growth phenomena · Advanced Mathematical Modeling in Engineering · Generative Adversarial Networks and Image Synthesis