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Within the existing reconstruction process of distributed video coding (DVC), there are two major approaches: the maximum probability reconstruction and the minimum mean square error (MMSE) reconstruction. Both of them assume that each node, a pixel in pixel domain DVC or a coefficient in transform domain DVC, is i.i.d., and reconstruct the value of each node independently by only exploiting statistical correlation between source and side-information. These kinds of models produce considerable amount of artifacts in decoded Wyner-Ziv (WZ) frames and degrade the objective performance. In this paper, we propose a context-adaptive Markov random field (MRF) reconstruction algorithm which exploits both the statistical correlation and the spatio-temporal consistency by modeling the corresponding MRF of a generic DVC architecture, and solve the inference by finding its MRF-based maximum a posteriori (MAP) estimate. The energy function of the MRF model consists of two terms: a data term measuring the statistical correlation, and a geometric regularity term enforcing local spatio-temporal structure consistency which is modeled by optical flow estimation with regard to the critical parameters under a wide variety of DVC scenarios. In case the unreliability of the derived local structure, a confidence parameter is introduced to prevent inappropriate penalizing. To find the reconstructed patch assignment with the largest expected probability in the context-adaptive MRF, the energy minimization for the MRF-based MAP estimate of the WZ frames is solved by global optimization and greedy strategies. Compared to the existing maximum probability and MMSE reconstruction with i.i.d. model, a better subjective and objective performance is validated by extensive experiments.