Online deep Bingham network for probabilistic orientation estimation

Orientation estimation is one of the core problems in several computer vision tasks. Recently deep learning techniques combined with the Bingham distribution have attracted considerable interest towards this problem when considering ambiguities and rotational symmetries of objects. However, existing works suffer from two issues. First, the computational overhead for calculating the normalisation constant of the Bingham distribution is relatively high. Second, the choice of loss functions is uncertain. In light of these problems, we present an online deep Bingham network to estimate the orientation of objects. We sharply reduce the computational overhead of the normalisation constant by directly applying a numerical integration formula. Additionally, we are the first to give theorems on the convexity and Lipschitz continuity of the Bingham distribution's negative log-likelihood, which formally indicates that it is a proper choice of the loss function. We test our method on three public datasets, namely the UPNA, the T-LESS and Pascal3D+, showing that our method outperforms the state-of-the-art in terms of orientation accuracy and time efficiency, which can reduce the runtime by more than 6 h compared to the offline methods. The ablation experiments further demonstrate the effectiveness and robustness of our model.