A two-step mixed inpainting method with curvature-based anisotropy and spatial adaptivity

FRANCISCO IBARROLA; RUBEN SPIES

Workshop; International workshop in Industrial Mathematics; 2016

A Two-Step MixedInpainting Method with Curvature-Based Anisotropy and Spatial Adaptivity Ruben D. Spies IMAL, CONICET-UNL, Santa Fe,Argentina    The image inpainting problem consists ofrestoring an image from a (possibly noisy) observation, in which data from oneor more regions is missing. Several inpainting models to perform this task havebeen developed, and although some of them perform reasonably well in certaintypes of images, quite a few issues are yet to be sorted out. For instance, ifthe image is expected to be smooth, the inpainting can be made with very goodresults by means of a Bayesian approach and a maximum a posteriori computation.For non-smooth images, however, such an approach is far from beingsatisfactory. Even though the introduction of anisotropy by prior smoothgradient inpainting to the latter methodology is known to produce satisfactoryresults for slim missing regions, the quality of the restoration decays as theoccluded regions widen. On the other hand, Total Variation (TV) inpaintingmodels based on high order PDE diffusion equations can be used whenever edgerestoration is a priority. More recently, the introduction of spatially variantconductivity coefficients on these models, such as in the case of Curvature- DrivenDiffusion (CDD), has allowed inpainted images with well-defined edges andenhanced object connectivity. The CDD approach, nonetheless, is not quitesuitable wherever the image is smooth, as it tends to produce piecewiseconstant restorations. In this work we present a two-step inpainting process.The first step consists of using a CDD inpainting to build a pilot image fromwhich to infer a-priori structural information on the image gradient. Thesecond step is inpainting the image by minimizing a mixed spatially variantanisotropic functional, whose weight and penalization directions are based uponthe aforementioned pilot image. Results will be presented along with comparisonmeasures in order to illustrate the performance of this inpainting method.(This is a joint work withFrancisco J. Ibarrola)