The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hyper-complex numbers, quaternions specifically, and provide the architecture components needed to build deep quaternion networks. We develop the theoretical basis by reviewing quaternion convolutions, developing a novel quaternion weight initialization scheme, and developing novel algorithms for quaternion batch-normalization. These pieces are tested in a classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set. These quaternion networks show improved convergence compared to real-valued and complex-valued networks, especially on the segmentation task, while having fewer parameters
One common use of quaternions is for representing rotation into a more compact form. PoseNet @cite_7 used a quaternion as the target output in their model where the goal was to recover the @math DOF camera pose from a single RGB image. The ability to encode rotations may make a quaternion network more robust to rotational variance.
@cite_7
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We present a robust and real-time monocular six degree of freedom relocalization system. Our system trains a convolutional neural network to regress the 6-DOF camera pose from a single RGB image in an end-to-end manner with no need of additional engineering or graph optimisation. The algorithm can operate indoors and outdoors in real time, taking 5ms per frame to compute. It obtains approximately 2m and 6 degree accuracy for large scale outdoor scenes and 0.5m and 10 degree accuracy indoors. This is achieved using an efficient 23 layer deep convnet, demonstrating that convnets can be used to solve complicated out of image plane regression problems. This was made possible by leveraging transfer learning from large scale classification data. We show the convnet localizes from high level features and is robust to difficult lighting, motion blur and different camera intrinsics where point based SIFT registration fails. Furthermore we show how the pose feature that is produced generalizes to other scenes allowing us to regress pose with only a few dozen training examples. PoseNet code, dataset and an online demonstration is available on our project webpage, at this http URL