In this paper, we investigate the problems that Convolutional Neural Networks (CNN)-based pose estimators have with symmetric objects. We considered the value of the CNN's output representation when continuously rotating the object and found that it has to form a closed loop after each step of symmetry. Otherwise, the CNN (which is itself a continuous function) has to replicate an uncontinuous function. On a 1-DOF toy example we show that commonly used representations do not fulfill this demand and analyze the problems caused thereby. In particular, we find that the popular min-over-symmetries approach for creating a symmetry-aware loss tends not to work well with gradient-based optimization, i.e. deep learning. We propose a representation called "closed symmetry loop" (csl) from these insights, where the angle of relevant vectors is multiplied by the symmetry order and then generalize it to 6-DOF. The representation extends our algorithm from [Richter-Klug, ICVS, 2019] including a method to disambiguate symmetric equivalents during the final pose estimation. The algorithm handles continuous rotational symmetry (e.g. a bottle) and discrete rotational symmetry (e.g. a 4-fold symmetric box). It is evaluated on the T-LESS dataset, where it reaches state-of-the-art for unrefining RGB-based methods.
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