MIXED CURVATURE-BASED DIFFUSION MODELS FOR LOCAL IMAGE INPAINTING

FRANCISCO IBARROLA; RUBEN SPIES

Congreso; 8th INTERNATIONAL CONFERENCE ON INVERSE PROBLEMS. MODELING AND SIMULATION; 2016

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 means of a Bayesian approach and a maximum a posteriori computation [1]. For non-smooth images, however, such an approach is far from being satisfactory. Even though the introduction of anisotropy by prior smooth gradient inpainting to the latter methodology is known to produce satisfactory results for slim missing regions [1], the quality of the restoration decays as the occluded regions widen. 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) [2], has allowed inpainted images with well defined edges and enhanced object conectivity. The CDD approach, nonetheless, is not quite suitable wherever the image is smooth, as it tends to produce piecewise constant solutions.We explore inpainting methods built upon curvature-based diffusion PDEs which result in restored images complying with both edge preservation and object connectivity while precluding the staircasing effect that TV methods always entail. Furthermore, the introduction of Sobolev gradient based diffusion [3] is shown to mitigate some stability issues encountered in CDD-based difussion processes. Comparisons between the resutls of the implemented models are illustrated with several computed examples, along with performance measures as a formal comparison tool.