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Image analysis and enhancement tasks such as tone mapping, colorization, stereo depth, and photomontage, often require computing a solution (e.g., for exposure, chromaticity, disparity, labels) over the pixel grid. Computational and memory costs often require that a smaller solution be run over a downsampled image. Although general purpose upsampling methods can be used to interpolate the low resolution solution to the full resolution, these methods generally assume a smoothness prior for the interpolation.
Kopf et al. (Sun,) studied this question.