- Temporally Constant Unbalanced Optimum Transport for Unsupervised Motion Segmentation(arXiv)
Writer : Ming Xu, Stephen Gould
Summary : We suggest a novel strategy to the motion segmentation job for lengthy, untrimmed movies, based mostly on fixing an optimum transport downside. By encoding a temporal consistency prior right into a Gromov-Wasserstein downside, we’re capable of decode a temporally constant segmentation from a loud affinity/matching value matrix between video frames and motion courses. Not like earlier approaches, our technique doesn’t require understanding the motion order for a video to achieve temporal consistency. Moreover, our ensuing (fused) Gromov-Wasserstein downside will be effectively solved on GPUs utilizing just a few iterations of projected mirror descent. We reveal the effectiveness of our technique in an unsupervised studying setting, the place our technique is used to generate pseudo-labels for self-training. We consider our segmentation strategy and unsupervised studying pipeline on the Breakfast, 50-Salads, YouTube Directions and Desktop Meeting datasets, yielding state-of-the-art outcomes for the unsupervised video motion segmentation job
2.Unbalanced L1 optimum transport for vector valued measures and software to Full Waveform Inversion (arXiv)
Writer : Gabriele Todeschi, Ludovic Métivier, Jean-Marie Mirebeau
Summary : Optimum transport has just lately began to be efficiently employed to outline misfit or loss features in inverse issues. Nonetheless, it’s a downside intrinsically outlined for optimistic (chance) measures and due to this fact methods are wanted for its purposes in additional common settings of curiosity. On this paper we introduce an unbalanced optimum transport downside for vector valued measures ranging from the L1 optimum transport. By lifting knowledge in a self-dual cone of a better dimensional vector house, we present that one can get better a significant transport downside. We present that the favorable computational complexity of the L1 downside, a bonus in comparison with different formulations of optimum transport, is inherited by our vector extension. We contemplate each a one-homogeneous and a two-homogeneous penalization for the imbalance of mass, the latter being doubtlessly related for purposes to physics based mostly issues. Particularly, we reveal the potential of our technique for full waveform inversion, an inverse downside for prime decision seismic imaging.
