Abstract
The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.
Highlights
Image completion aims to synthesize missing regions in an incomplete image or a video sequence with the content-aware information captured from accessible or unperturbed regions
Motivated by several works [48,49,50,51] on the use of various interpolation methods for solving image completion problems, other recent works [52,53,54,55,56] on image processing aspects, and the concept of tensor product spline surfaces [57], we show the relationship of the Tucker decomposition with factorizable radial basis function (RBF) interpolation and use it to compute the factor matrices
A: 90% uniformly distributed random missing tensor fibers in its third mode, which corresponds to 90% missing pixels (“dead pixels”), B: 95% uniformly distributed random missing tensor entries (“disturbed pixels”), C: 200 uniformly distributed random missing circles—created in the same way as in the first case, but the disturbances are circles with a random radius not exceeding 10 pixels, D: resolution up-scaling—an original image was down-sampled twice by removing the pixels according to a regular grid mask with edges equal to 1 pixel
Summary
Image completion aims to synthesize missing regions in an incomplete image or a video sequence with the content-aware information captured from accessible or unperturbed regions. Image completion is one of the fundamental research topics in the area of computer vision and graphics technology, motivated by widespread applications in various applied sciences [1]. It is used for the restoration of old photographs, paintings, and films by removing scratches, dust spots, occlusions, or other user-marked objects, such as annotations, subtitles, stamps, logos, etc. Image completion techniques may fix error concealment problems or recover missing data-blocks lost during transmission or video compression [2,3]. The recent works emphasize their usefulness in remote sensing imaging to remove occlusions, such as clouds and “dead”
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