# Detecting anomalies in fibre systems using 3-dimensional image data

## TL;DR

This paper introduces a novel method for detecting anomalies in 3D fibre images by classifying local regions based on fibre direction attributes and applying statistical tests, validated on simulated and real data.

## Contribution

It proposes a new spatial SAEM algorithm and a change point test for anomaly detection in 3D fibre systems, combining clustering and significance testing.

## Key findings

- Effective anomaly detection in simulated 3D images
- Successful application to real fibre reinforced polymer data
- New spatial SAEM algorithm improves classification accuracy

## Abstract

We consider the problem of detecting anomalies in the directional distribution of fibre materials observed in 3D images. We divide the image into a set of scanning windows and classify them into two clusters: homogeneous material and anomaly. Based on a sample of estimated local fibre directions, for each scanning window we compute several classification attributes, namely the coordinate wise means of local fibre directions, the entropy of the directional distribution, and a combination of them. We also propose a new spatial modification of the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. Besides the clustering we also consider testing the significance of anomalies. To this end, we apply a change point technique for random fields and derive the exact inequalities for tail probabilities of a test statistics. The proposed methodology is first validated on simulated images. Finally, it is applied to a 3D image of a fibre reinforced polymer.