Wall Stress Estimation of Cerebral Aneurysm based on Zernike Convolutional Neural Networks

TL;DR

This paper introduces ZerNet, a novel geometric convolutional neural network designed to accurately estimate wall stress in cerebral aneurysms by effectively handling manifold-structured data, outperforming existing geometric ConvNets.

Contribution

The paper presents ZerNet, a new geometric ConvNet that generalizes convolution and pooling on manifolds, addressing limitations of traditional ConvNets for manifold-structured data.

Findings

ZerNet outperforms existing geometric ConvNets in accuracy.

The method effectively handles data on arbitrary manifolds.

Application to aneurysm wall stress estimation demonstrates clinical relevance.

Abstract

Convolutional neural networks (ConvNets) have demonstrated an exceptional capacity to discern visual patterns from digital images and signals. Unfortunately, such powerful ConvNets do not generalize well to arbitrary-shaped manifolds, where data representation does not fit into a tensor-like grid. Hence, many fields of science and engineering, where data points possess some manifold structure, cannot enjoy the full benefits of the recent advances in ConvNets. The aneurysm wall stress estimation problem introduced in this paper is one of many such problems. The problem is well-known to be of a paramount clinical importance, but yet, traditional ConvNets cannot be applied due to the manifold structure of the data, neither does the state-of-the-art geometric ConvNets perform well. Motivated by this, we propose a new geometric ConvNet method named ZerNet, which builds upon our novel mathematical generalization of convolution and pooling operations on manifolds. Our study shows that the ZerNet outperforms the other state-of-the-art geometric ConvNets in terms of accuracy.