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Long-term modeling of background motion in videos is an important and challenging problem used in numerous applications such as segmentation and event recognition. A major challenge in modeling the background from point trajectories lies in dealing with the variable length duration of trajectories, which can be due to such factors as trajectories entering and leaving the frame or occlusion from different depth layers. This work proposes an online method for background modeling of dynamic point trajectories via tracking of a linear subspace describing the background motion. To cope with variability in trajectory durations, we cast subspace tracking as an instance of subspace estimation under missing data, using a least-absolute deviations formulation to robustly estimate the background in the presence of arbitrary foreground motion. Relative to previous works, our approach is very fast and scales to arbitrarily long videos as our method processes new frames sequentially as they arrive.

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