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的任务，在生物医学领域具有广泛应用。人体具有双侧对称性，且器官位置存在一定变异。这使我们预期，在卷积神经网络中引入旋转与反演不变层将对生物医学分割产生积极影响。本研究展示了权重对称性对执行三维网格分割的神经网络的影响。我们分析了病理性血管结构（动脉瘤）和常规解剖结构（心室心内膜与心外膜）的三维网格分割问题。局部几何特征通过有符号距离函数采样进行编码，神经网络对每个网格节点执行预测。研究表明，权重对称性可带来1%至3%的额外精度提升，并且在神经网络至少包含三个卷积层时，可将可训练参数数量减少最多8倍而不会造成性能损失。这一特性在训练集极小的情况下同样有效。