  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.
