3D mesh segmentation is an important task with many biomedical applications. The human body has bilateral symmetry and some variations in organ positions. It allows us to expect a positive effect of rotation and inversion invariant layers in convolutional neural networks that perform biomedical segmentations. In this study, we show the impact of weight symmetry in neural networks that perform 3D mesh segmentation. We analyze the problem of 3D mesh segmentation for pathological vessel structures (aneurysms) and conventional anatomical structures (endocardium and epicardium of ventricles). Local geometrical features are encoded as sampling from the signed distance function, and the neural network performs prediction for each mesh node. We show that weight symmetry gains from 1 to 3% of additional accuracy and allows decreasing the number of trainable parameters up to 8 times without suffering the performance loss if neural networks have at least three convolutional layers. This also works for very small training sets.

翻译：三维网格分割是一项重要任务，具有众多生物医学应用。人体具有双侧对称性，且器官位置存在一定变异，这使得我们预期在卷积神经网络中应用旋转和反转不变层会对生物医学分割产生积极效果。本研究展示了神经网络中权重对称性对三维网格分割的影响。我们分析了病理性血管结构（动脉瘤）和常规解剖结构（心室心内膜和心外膜）的三维网格分割问题。局部几何特征通过有符号距离函数的采样进行编码，神经网络对每个网格节点进行预测。结果表明，当神经网络至少包含三个卷积层时，权重对称性可提升1%至3%的额外准确率，并允许将可训练参数数量减少多达8倍且不损失性能。这一结论同样适用于非常小的训练集。