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In this paper, a space-time hole filling approach is presented to deal with a disocclusion when a view is synthesized for the 3D video. The problem becomes even more complicated when the view is extrapolated from a single view, since the hole is large and has no stereo depth cues. Although many techniques have been developed to address this problem, most of them focus only on view interpolation. We propose a space-time joint filling method for color and depth videos in view extrapolation. For proper texture and depth to be sampled in the following hole filling process, the background of a scene is automatically segmented by the random walker segmentation in conjunction with the hole formation process. Then, the patch candidate selection process is formulated as a labeling problem, which can be solved with random walks. The patch candidates that best describe the hole region are dynamically selected in the space-time domain, and the hole is filled with the optimal patch for ensuring both spatial and temporal coherence. The experimental results show that the proposed method is superior to state-of-the-art methods and provides both spatially and temporally consistent results with significantly reduced flicker artifacts.