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Homography has an essential relationship with the special linear group andthe embedding Lie algebra structure. Although the Lie algebra representation iselegant, few researchers have established the connection between homography andalgebra expression in neural networks. In this paper, we propose WarpedConvolution Networks (WCN) to effectively learn and represent the homography bySL(3) group and sl(3) algebra with group convolution. To this end, sixcommutative subgroups within the SL(3) group are composed to form a homography.For each subgroup, a warping function is proposed to bridge the Lie algebrastructure to its corresponding parameters in homography. By taking advantage ofthe warped convolution, homography learning is formulated into several simplepseudo-translation regressions. By walking along the Lie topology, our proposedWCN is able to learn the features that are invariant to homography. Moreover,it can be easily plugged into other popular CNN-based methods. Extensiveexperiments on the POT benchmark, S-COCO-Proj, and MNIST-Proj dataset show thatour proposed method is effective for planar object tracking, homographyestimation, and classification.

Warped Convolutional Networks: Bridge Homography to sl(3) algebra by Group Convolution