# Benefits of mirror weight symmetry for 3D mesh segmentation in biomedical applications

arXiv: https://arxiv.org/abs/2309.17076 · HTML: https://mlsanity.com/paper/2309.17076/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Rotation-invariant convolutional neural networks for galaxy morphology prediction](https://mlsanity.com/paper/1503.07077/) (2015)
- [CubeNet: Equivariance to 3D Rotation and Translation](https://mlsanity.com/paper/1804.04458/) (2018)
- [IntrA: 3D Intracranial Aneurysm Dataset for Deep Learning](https://mlsanity.com/paper/2003.02920/) (2020)
- [Deep-HiTS: Rotation Invariant Convolutional Neural Network for Transient Detection](https://mlsanity.com/paper/1701.00458/) (2017)
- [Exploring Weight Symmetry in Deep Neural Networks](https://mlsanity.com/paper/1812.11027/) (2018)
- [Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods](https://mlsanity.com/paper/2108.13993/) (2021)

## Abstract (arXiv)

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.