- Temporally Fixed Unbalanced Optimum Transport for Unsupervised Movement Segmentation(arXiv)
Author : Ming Xu, Stephen Gould
Abstract : We propose a novel technique to the movement segmentation job for prolonged, untrimmed motion pictures, primarily based totally on fixing an optimum transport draw back. By encoding a temporal consistency prior proper right into a Gromov-Wasserstein draw back, we’re able to decode a temporally fixed segmentation from a loud affinity/matching worth matrix between video frames and movement programs. Not like earlier approaches, our method would not require understanding the movement order for a video to realize temporal consistency. Furthermore, our ensuing (fused) Gromov-Wasserstein draw back will probably be successfully solved on GPUs using only a few iterations of projected mirror descent. We reveal the effectiveness of our method in an unsupervised learning setting, the place our method is used to generate pseudo-labels for self-training. We think about our segmentation technique and unsupervised learning pipeline on the Breakfast, 50-Salads, YouTube Instructions and Desktop Assembly datasets, yielding state-of-the-art outcomes for the unsupervised video movement segmentation job
2.Unbalanced L1 optimum transport for vector valued measures and software program to Full Waveform Inversion (arXiv)
Author : Gabriele Todeschi, Ludovic Métivier, Jean-Marie Mirebeau
Abstract : Optimum transport has simply currently started to be effectively employed to stipulate misfit or loss options in inverse points. Nonetheless, it is a draw back intrinsically outlined for optimistic (likelihood) measures and because of this truth strategies are needed for its functions in further widespread settings of curiosity. On this paper we introduce an unbalanced optimum transport draw back for vector valued measures starting from the L1 optimum transport. By lifting data in a self-dual cone of a greater dimensional vector home, we current that one can get higher a major transport draw back. We current that the favorable computational complexity of the L1 draw back, a bonus as compared with totally different formulations of optimum transport, is inherited by our vector extension. We ponder every a one-homogeneous and a two-homogeneous penalization for the imbalance of mass, the latter being doubtlessly associated for functions to physics based points. Notably, we reveal the potential of our method for full waveform inversion, an inverse draw back for prime resolution seismic imaging.
