Warped Convolutional Networks: Bridge Homography to sl(3) algebra by Group Convolution
This work addresses the challenge of integrating geometric transformations like homography into deep learning models for computer vision applications, though it appears incremental as it builds on existing group convolution and Lie algebra concepts.
The paper tackles the problem of learning homography representations in neural networks by connecting homography to SL(3) group and sl(3) algebra using group convolution, resulting in a method that achieves effective performance on tasks like planar object tracking, homography estimation, and classification as shown in experiments on POT, S-COCO-Proj, and MNIST-Proj datasets.
Homography has an essential relationship with the special linear group and the embedding Lie algebra structure. Although the Lie algebra representation is elegant, few researchers have established the connection between homography and algebra expression in neural networks. In this paper, we propose Warped Convolution Networks (WCN) to effectively learn and represent the homography by SL(3) group and sl(3) algebra with group convolution. To this end, six commutative subgroups within the SL(3) group are composed to form a homography. For each subgroup, a warping function is proposed to bridge the Lie algebra structure to its corresponding parameters in homography. By taking advantage of the warped convolution, homography learning is formulated into several simple pseudo-translation regressions. By walking along the Lie topology, our proposed WCN is able to learn the features that are invariant to homography. Moreover, it can be easily plugged into other popular CNN-based methods. Extensive experiments on the POT benchmark, S-COCO-Proj, and MNIST-Proj dataset show that our proposed method is effective for planar object tracking, homography estimation, and classification.