  In this paper, we introduce a new framework for unsupervised deep homography
estimation. Our contributions are 3 folds. First, unlike previous methods that
regress 4 offsets for a homography, we propose a homography flow
representation, which can be estimated by a weighted sum of 8 pre-defined
homography flow bases. Second, considering a homography contains 8
Degree-of-Freedoms (DOFs) that is much less than the rank of the network
features, we propose a Low Rank Representation (LRR) block that reduces the
feature rank, so that features corresponding to the dominant motions are
retained while others are rejected. Last, we propose a Feature Identity Loss
(FIL) to enforce the learned image feature warp-equivariant, meaning that the
result should be identical if the order of warp operation and feature
extraction is swapped. With this constraint, the unsupervised optimization is
achieved more effectively and more stable features are learned. Extensive
experiments are conducted to demonstrate the effectiveness of all the newly
proposed components, and results show that our approach outperforms the
state-of-the-art on the homography benchmark datasets both qualitatively and
quantitatively. Code is available at
https://github.com/megvii-research/BasesHomo.
