Abstract : Inpainting consists in computing a plausible completion of missing parts of an image given the available content. In the restricted framework of texture images, the image can be seen as a realization of a random field model, which gives a stochastic formulation of image inpainting: on the masked exemplar one estimates a random texture model which can then be conditionally sampled in order to fill the hole.
In this paper is proposed an instance of such stochastic inpainting methods, dealing with the case of Gaussian textures. First a simple procedure is proposed for estimating a Gaussian texture model based on a masked exemplar, which, although quite naive, gives sufficient results for our inpainting purpose. Next, the conditional sampling step is solved with the traditional algorithm for Gaussian conditional simulation. The main difficulty of this step is to solve a very large linear system, which, in the case of stationary Gaussian textures, can be done efficiently with a conjugate gradient descent (using a Fourier representation of the covariance operator). Several experiments show that the corresponding inpainting algorithm is able to inpaint large holes (of any shape) in a texture, with a reasonable computational time. Moreover, several comparisons illustrate that the proposed approach performs better on texture images than state-of-the-art inpainting methods.