论文标题
扭曲的卷积网络：按小组卷积到SL（3）代数的桥梁均应
Warped Convolutional Networks: Bridge Homography to sl(3) algebra by Group Convolution
论文作者
论文摘要
同型与特殊线性组和嵌入谎言代数结构具有重要关系。尽管谎言代数表示优雅，但很少有研究人员在神经网络中建立了同构和代数表达之间的联系。在本文中，我们提出了扭曲的卷积网络（WCN），以有效地学习和代表SL（3）组和SL（3）代数的同谱。为此，SL（3）组中的六个换向子组组成以形成同构象。对于每个子组，提出了一个翘曲函数，以将Lie代数结构桥接到其同型中的相应参数。通过利用扭曲的卷积，同构学学习被提出为几个简单的伪翻译回归。通过沿着谎言拓扑散步，我们提出的WCN能够学习同型不变的功能。此外，它可以很容易地插入其他基于CNN的其他基于CNN的方法中。在Pot Benchmark，S-Coco-Proj和Mnist-Proj数据集上进行了广泛的实验表明，我们提出的方法对平面对象跟踪，同型估计和分类有效。
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.
