Inpainting using Airy Diffusion

摘要

One inpainting procedure based on Airy diffusion is proposed, implemented via Maple and applied to some digital images. Airy diffusion is a partial differential equation with spatial derivatives of third order in contrast with the usual diffusion with spatial derivatives of second order. Airy diffusion generates the Airy semigroup in terms of the Airy functions which can be rewritten in terms of Bessel functions. The Airy diffusion can be used to smooth an image with the corresponding noise elimination via convolution. Also the Airy diffusion can be used to erase objects from an image. We build an algorithm using the Maple package ImageTools and such algorithm is tested using some images. Our results using Airy diffusion are compared with the similar results using standard diffusion. We observe that Airy diffusion generates powerful filters for image processing which could be incorporated in the usual packages for image processing such as ImageJ and Photoshop. Also is interesting to consider the possibility to incorporate the Airy filters as applications for smartphones and smart-glasses.