Well Convergent and Computationally Efficient Quaternion Loss

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


Rotation estimation, i.e. the ability to predict angles describing 3D positioned object, is an omnipresent problem in computer vision, computer graphics and 3D object detection task in automotive industry. Deep learning algorithms usually parameterise rotation using only the yaw angle. This paper presents detailed comparison of several 3D rotation distance functions using quaternions. We propose a computationally efficient quaternion loss function for neural network training. We conclude that function respects the topology of SO(3) and is bi-invariant. We also show the geometrical representation of presented functions. Lastly, we evaluate the effectiveness of the proposed loss function and compare its performance with other methods using a public large-scale dataset.


Optimization Quaternions Sensors Neural networks Automotive 



Research was funded by Polish Ministry of Science and Higher Education Project No. 0014/DW/2018/02 and carried out in cooperation of Aptiv Services Poland S.A. - Technical Center Kraków and AGH University of Science and Technology - Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Automatic Control and RoboticsAGH University of Science and TechnologyKrakówPoland
  2. 2.APTIV Services Poland S.A.KrakówPoland

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