High‐order Markov random field for single depth image super‐resolution

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Abstract
Although there is an increasing interest in employing the depth data in computer vision applications, the spatial resolution of depth maps is still limited compared with typical visible‐light images. A novel method is proposed to synthetically improve the spatial resolution of a single depth image. It integrates the higher‐order terms into the Markov random field (MRF) formulation of example‐based methods in order to improve the representational power of those methods. The inference is performed by approximately minimising the higher‐order multi‐label MRF energies. In addition, to improve the efficiency of the inference algorithm, a hierarchical scheme on the number of MRF states is proposed. First, a large number of states are used to obtain an initial labelling by solving the minimisation problem of inference for only the first‐order energies. Then, the problem is solved for the higher‐order energies in a smaller number of states. Performance comparisons show that proposed method improves the results of first‐order approaches that are based on simple four‐connected MRF graph structure, both qualitatively and quantitatively.

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