Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing

摘要

In this work, we analyse a series of approaches to evolve images. It is motivated by combining Gaussian blurring, the Mean Curvature Motion, used for denoising and edge-preserving, and maximal blurring, used for inpainting. We investigate the generalised method using the combination of second-order derivatives in terms of gauge coordinates.For the qualitative behaviour, we derive a solution of the series and mention its properties briefly. Relations with anisotropy and general diffusion equations are discussed. Quantitative results are obtained by a novel implementation whose stability is analysed. The practical results are visualised on a real-life image, showing the expected qualitative behaviour. When a constraint is added that penalises the distance of the results to the input image, one can vary the desired amount of blurring and denoising.