Real-world 3D structured data like point clouds and skeletons often can be represented as data in a 3D rotation group (denoted as [Formula: see text]). However, most existing neural networks are tailored for the data in the euclidean space, which makes the 3D rotation data not closed under their algebraic operations and leads to sub-optimal performance in 3D-related learning tasks. To resolve the issues caused by the above mismatching between data and model, we propose a novel non-real neuron model called quaternion product unit (QPU) to represent data on 3D rotation groups. The proposed QPU leverages quaternion algebra and the law of the 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted chain of Hamilton products. We demonstrate that the QPU mathematically maintains the [Formula: see text] structure of the 3D rotation data during the inference process and disentangles the 3D representations into "rotation-invariant" features and "rotation-equivariant" features, respectively. Moreover, we design a fast QPU to accelerate the computation of QPU. The fast QPU applies a tree-structured data indexing process, and accordingly, leverages the power of parallel computing, which reduces the computational complexity of QPU in a single thread from O(N) to O(logN). Taking the fast QPU as a basic module, we develop a series of quaternion neural networks (QNNs), including quaternion multi-layer perceptron (QMLP), quaternion message passing (QMP), and so on. In addition, we make the QNNs compatible with conventional real-valued neural networks and applicable for both skeletons and point clouds. Experiments on synthetic and real-world 3D tasks show that the QNNs based on our fast QPUs are superior to state-of-the-art real-valued models, especially in the scenarios requiring the robustness to random rotations. The code of this work is available at https://github.com/SuferQin/Fast-QPU.

This paper presents BatchQR, a mobile APP that can batch read densely arranged QR codes attached to caps of the tubes and vials in clinical and biological labs. BatchQR could work in two modes: photo mode and preview mode, which are respectively suitable for scenarios that favor one-time batch processing capacity and real-time tracking performance. For the photo mode, we first propose an IFFT based lightweight code detection mechanism, which can adaptively adjust operating parameters to identify densely arranged QR codes in practice. We propose an image refocus mechanism to deal with blurs/distorts that may appear in the photo, and a lightweight learning based classifier to filter out falsely detected QR codes. We further optimize BatchQR by enabling batch reading in the preview mode of the camera, which is more in line with common usage habits. To this end, we develop a QR code tracking algorithm based on Kalman filtering, which keeps track of each code image dynamically. We also design a parallel acceleration mechanism based on multi-core CPU and GPU, which significantly mitigates the end-to-end delay. Comprehensive experimental results show that BatchQR can read up to 160 Version 1-H QR codes in one shot, with 95 percent accuracy and 100-400ms delay, which is only 0.1 percent of the time consumed by the regular QR code reader in the same situation.

We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted chain of Hamilton products. We prove that the representations derived by the proposed QPU can be disentangled into "rotation-invariant" features and "rotation-equivariant" features, respectively, which supports the rationality and the efficiency of the QPU in theory. We design quaternion neural networks based on our QPUs and make our models compatible with existing deep learning models. Experiments on both synthetic and real-world data show that the proposed QPU is beneficial for the learning tasks requiring rotation robustness.