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This paper presents a fast, high-performance method for super resolution with external learning. The first contribution leading to the excellent performance is a bimodal tree for clustering, which successfully exploits the antipodal invariance of the coarse-to-high-res mapping of natural image patches and provides scalability to finer partitions of the underlying coarse patch space. During training an ensemble of such bimodal trees is computed, providing different linearizations of the mapping. The second and main contribution is a fast inference algorithm, which selects the most suitable mapping function within the tree ensemble for each patch by adopting a Local Naive Bayes formulation. The experimental validation shows promising scalability properties that reflect the suitability of the proposed model, which may also be generalized to other tasks. The resulting method is beyond one order of magnitude faster and performs objectively and subjectively better than the current state of the art.

Abstract-Real camera systems have a limited depth of field (DOF) which may cause an image to be degraded due to visible misfocus or too shallow DOF. In this paper, we present a blind deblurring pipeline able to restore such images by slightly extending their DOF and recovering sharpness in regions slightly out-of-focus. To address this severely ill-posed problem, our algorithm relies first on the estimation of the spatiallyvarying defocus blur. Drawing on local frequency image features, a machine learning approach based on the recently introduced Regression Tree Fields is used to train a model able to regress a coherent defocus blur map of the image, labeling each pixel by the scale of a defocus point-spread-function. A non-blind spatiallyvarying deblurring algorithm is then used to properly extend the DOF of the image. The good performance of our algorithm is assessed both quantitatively, using realistic ground truth data obtained with a novel approach based on a plenoptic camera, and qualitatively with real images.Index Terms-Out-of-focus deblurring, extension of depth of field, Regression tree fields, defocus blur map.

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Abstract. Regression-based Super-Resolution (SR) addresses the upscaling problem by learning a mapping function (i.e. regressor) from the low-resolution to the high-resolution manifold. Under the locally linear assumption, this complex non-linear mapping can be properly modeled by a set of linear regressors distributed across the manifold. In such methods, most of the testing time is spent searching for the right regressor within this trained set. In this paper we propose a novel inverse-search approach for regression-based SR. Instead of performing a search from the image to the dictionary of regressors, the search is done inversely from the regressors' dictionary to the image patches. We approximate this framework by applying spherical hashing to both image and regressors, which reduces the inverse search into computing a trained function. Additionally, we propose an improved training scheme for SR linear regressors which improves perceived and objective quality. By merging both contributions we improve speed and quality compared to the stateof-the-art.