The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance, hindering the effective long-range interactions. To relax the geometric constraint, we give the analysis by reformulating it as a Markov Random Field and introduce a learnable unary term. Besides, we propose a learnable spanning tree algorithm to replace the original non-differentiable one, which further improves the flexibility and robustness. With the above improvements, our method can better capture long-range dependencies and preserve structural details with linear complexity, which is extended to several vision tasks for more generic feature transform. Extensive experiments on object detection/instance segmentation demonstrate the consistent improvements over the original version. For semantic segmentation, we achieve leading performance (82.1% mIoU) on the Cityscapes benchmark without bells-and-whistles. Code is available at https://github.com/StevenGrove/LearnableTreeFilterV2.
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