Mixed Curvature-Based Diffusion Models for Local Image Inpainting

Abstract

The image inpainting problem consists of restoring an image from a (possibly noisy) observation, in which data from one or more regions is missing. Several inpainting models to perform this task have been developed, and although some of them perform reasonably well in certain types of images, quite a few issues are yet to be sorted out. For instance, if the image is expected to be smooth, the inpainting can be made with very good results by modeling the solution as the result of a diffusion process using the heat equation. For non-smooth images, however, such an approach is far from being satisfactory. On the other hand, Total Variation (TV) inpainting models based on high order PDE diffusion equations can be used whenever edge restoration is a priority. More recently, the introduction of spatially variant conductivity coefficients on these models, such as in the case of Curvature-Driven Diffusions (CDD), has allowed inpainted images with well defined edges and enhanced object connectivity. The CDD approach, nonetheless, is not quite suitable wherever the image is smooth, as it tends to produce piecewise constant solutions. Based upon this, we propose using CDD to introduce a-priori information into an anisotropic diffusion model that allows for both edge preservation and object connectivity while precluding the staircasing effect that TV-based methods entail. Comparisons between the results of the implemented models will be illustrated by several computed examples, along with performance measures.