Image inpainting by correspondence maps: A deterministic approach

The success of some recent texture synthesis methods, see [8, 17], suggests that there exists an underlying formulation explaining their performance and paving the way to more involved modeling. Based on their ideas, we formalize a low-level global deterministic solution for image inpainting. A correspondence map is defined as linking each blank or missing pixel to the pixel where its value is taken from, in the seed image. The above-mentioned algorithms are seen as descent procedures to minimize a functional of this correspondence map, the inpainting energy. We discuss why they should not be seen as procedures to sample a probability distribution on the correspondence maps. We therefore question the claims that probability is anywhere involved at this explanatory level. The algorithm we use is mostly taken from [17]. The latter however suffers from a strong directional bias, the direction in which texture is grown. We restore rotationinvariance at the level of both the target function and the algorithm. Our encouraging numerical results could not have been obtained by a directional texture-growing algorithm.

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