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We present a novel patch-based probabilistic graphical model for semi-supervised video segmentation. At the heart of our model is a temporal tree structure that links patches in adjacent frames through the video sequence. This permits exact inference of pixel labels without resorting to traditional short time window-based video processing or instantaneous decision making. The input to our algorithm is labeled key frame(s) of a video sequence and the output is pixel-wise labels along with their confidences. We propose an efficient inference scheme that performs exact inference over the temporal tree, and optionally a per frame label smoothing step using loopy BP, to estimate pixel-wise labels and their posteriors. These posteriors are used to learn pixel unaries by training a Random Decision Forest in a semi-supervised manner. These unaries are used in a second iteration of label inference to improve the segmentation quality. We demonstrate the efficacy of our proposed algorithm using several qualitative and quantitative tests on both foreground/background and multiclass video segmentation problems using publicly available and our own datasets.