  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.
