Low-Rank Tensor Completion with Spatio-Temporal Consistency

Video completion is a computer vision technique to recover the missing values in video sequences by filling the unknown regions with the known information. In recent research, tensor completion, a generalization of matrix completion for higher order data, emerges as a new solution to estimate the missing information in video with the assumption that the video frames are homogenous and correlated. However, each video clip often stores the heterogeneous episodes and the correlations among all video frames are not high. Thus, the regular tenor completion methods are not suitable to recover the video missing values in practical applications. To solve this problem, we propose a novel spatiallytemporally consistent tensor completion method for recovering the video missing data. Instead of minimizing the average of the trace norms of all matrices unfolded along each mode of a tensor data, we introduce a new smoothness regularization along video time direction to utilize the temporal information between consecutive video frames. Meanwhile, we also minimize the trace norm of each individual video frame to employ the spatial correlations among pixels. Different to previous tensor completion approaches, our new method can keep the spatio-temporal consistency in video and do not assume the global correlation in video frames. Thus, the proposed method can be applied to the general and practical video completion applications. Our method shows promising results in all evaluations on both 3D biomedical image sequence and video benchmark data sets. Video completion is the process of filling in missing pixels or replacing undesirable pixels in a video. The missing values in a video can be caused by many situations, e.g., the natural noise in video capture equipment, the occlusion from the obstacles in environment, segmenting or removing interested objects from videos. Video completion is of great importance to many applications such as video repairing and editing, movie post-production (e.g., remove unwanted objects), etc. Missing information recovery in images is called inpaint∗To whom all correspondence should be addressed. This work was partially supported by US NSF IIS-1117965, IIS-1302675, IIS-1344152.  In computer vision, an important application area of artificial intelligence, there are many video completion algorithms. The most representative approaches include video inpainting, analogous to image inpainting (Bertalmio, Bertozzi, and Sapiro 2001), motion layer video completion, which splits the video sequence into different motion layers and completes each motion layer separately (Shiratori et al. 2006), space-time video completion, which is based on texture synthesis and is good but slow (Wexler, Shechtman, and Irani 2004), and video repairing, which repairs static background with motion layers and repairs moving foreground using model alignment (Jia et al. 2004). Many video completion methods are less effective because the video is often treated as a set of independent 2D images. Although the temporal independence assumption simplifies the problem, losing temporal consistency in recovered pixels leads to the unsatisfactory performance. On the other hand, temporal information can improve the video completion results (Wexler, Shechtman, and Irani 2004; Matsushita et al. 2005), but to exploit it the computational speeds of most methods are significantly reduced. Thus, how to efficiently and effectively utilize both spatial and temporal information is a challenging problem in video completion. In most recent work, Liu et. al. (Liu et al. 2013) estimated the missing data in video via tensor completion which was generalized from matrix completion methods. In these methods, the rank or rank approximation (trace norm) is used, as a powerful tool, to capture the global information. The tensor completion method (Liu et al. 2013) minimizes the trace norm of a tensor, i.e. the average of the trace norms of all matrices unfolded along each mode. Thus, it assumes the video frames are highly correlated in the temporal direction. If the video records homogenous episodes and all frames describe the similar information, this assumption has no problem. However, one video clip usually includes multiple different episodes and the frames from different episodes Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence