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Robust, fast and flexible symmetry plane detection based on differentiable symmetry measure

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Abstract

Reflectional symmetry is a potentially very useful feature which many real-world objects exhibit. It is instrumental in a variety of applications such as object alignment, compression, symmetrical editing or reconstruction of incomplete objects. In this paper, we propose a novel differentiable symmetry measure, which allows using gradient-based optimization to find symmetry in geometric objects. We further propose a new method for symmetry plane detection in 3D objects based on this idea. The method performs well on perfectly as well as approximately symmetrical objects, it is robust to noise and to missing parts. Furthermore, it works on discrete point sets and therefore puts virtually no constraints on the input data. Due to flexibility of the symmetry measure, the method is also easily extensible, e.g., by adding more information about the input object and using it to further improve its performance. The proposed method was tested with very good results on many objects, including incomplete objects and noisy objects, and was compared to other state-of-the-art methods which it outperformed in most aspects.

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Acknowledgements

This work was supported by Ministry of Education, Youth and Sports of the Czech Republic, project PUNTIS (LO1506) under the program NPU I and University specific research project SGS-2019-016 Synthesis and Analysis of Geometric and Computing Models. We would also like to thank the authors of [35] for providing us the implementation of their method together with all the information needed for its comparison to our method. Furthermore, we want to thank the authors of [27] for providing us the results of their method shown in Table 4.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Lukáš Hruda & Ivana Kolingerová

  2. NTIS, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Libor Váša

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  1. Lukáš Hruda
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Hruda, L., Kolingerová, I. & Váša, L. Robust, fast and flexible symmetry plane detection based on differentiable symmetry measure. Vis Comput 38, 555–571 (2022). https://doi.org/10.1007/s00371-020-02034-w

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