In this paper, we propose the differentiable mask-matching network (DMM-Net) for solving the video object segmentation problem where the initial object masks are provided. Relying on the Mask R-CNN backbone, we extract mask proposals per frame and formulate the matching between object templates and proposals at one time step as a linear assignment problem where the cost matrix is predicted by a CNN. We propose a differentiable matching layer by unrolling a projected gradient descent algorithm in which the projection exploits the Dykstras algorithm. We prove that under mild conditions, the matching is guaranteed to converge to the optimum. In practice, it performs similarly to the Hungarian algorithm during inference. Meanwhile, we can back-propagate through it to learn the cost matrix. After matching, a refinement head is leveraged to improve the quality of the matched mask. Our DMM-Net achieves competitive results on the largest video object segmentation dataset YouTube-VOS. On DAVIS 2017, DMM-Net achieves the best performance without online learning on the first frames. Without any fine-tuning, DMM-Net performs comparably to state-of-the-art methods on SegTrack v2 dataset. At last, our matching layer is very simple to implement; we attach the PyTorch code ($<50$ lines) in the supplementary material. Our code is released at https://github.com/ZENGXH/DMM_Net.
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