Capturing long-range correlations with patch models

The use of image patches to capture local correlations between pixels has been growing in popularity for use in various low-level vision tasks. There is a trade-off between using larger patches to obtain additional high-order statistics and smaller patches to capture only the elemental features of the image. Previous work has leveraged short-range correlations between patches that share pixel values for use in patch matching. In this paper, long-range correlations between patches are introduced, where relations between patches that do not necessarily share pixels are learnt. Such correlations arise as an inherent property of the data itself. These long-range, patch correlations are shown to be particularly important for video sequences where the patches have an additional time dimension, with correlation links in both space and time. We illustrate the power of our model on tasks such as multiple object registration and detection and missing data interpolation, including a difficult task of photograph relighting, where a single photograph is assumed to be the only observed part of a 3D volume whose two coordinates are the image x and y coordinates and the third coordinate is the illumination angle θ. We show that in some cases, the long-range correlations observed among the mappings of different volume patches in a small training set are sufficient to infer the possible complex intensity changes in a new photograph due to illumination angle variation.