Detecting anomalies in fibre systems using 3-dimensional image data

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.

Statistical tests based on Rényi entropy estimation

“…The experiment is repeated for a random sample from the P 3 (γ) distribution with γ = 3, and the value of W P 1000,1 (3, γ) computed for different values of γ in the range [1,6]. The results are shown in Figure 11, where we see that the statistic reaches a minimum value at approximately γ = 3.…”

“…An entropy-based goodness-of-fit test for generalized Gaussian distributions is presented by [3]. A recent application to image processing can be found in [6].…”

The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

“…4b (left). The detailed description of the material can be found in (Wirjadi et al, 2014) and it was the object of studies in (Dresvyanskiy et al, 2019) and (Dresvyanskiy et al, 2020), where the regions of anomaly behaviour of the fibres were found. The data set is provided by Prof. Claudia Redenbach (TU Kaiserslautern) and consists of local direction of fibres estimated by the tools of MAVI software (Fraunhofer ITWM, Department of Image Processing, 2005).…”

“…Directional distributions characterize randomness in unit vectors (directions). Spherical data sets appear in a wide range of problems arising from Earth sciences (Pischiutta et al, 2013), oceanography (Wyatt et al, 1997;Shabani et al, 2016), biology (Mouritsen & Mouritsen, 2000), physics (Torrance et al, 1966), material science (Dresvyanskiy et al, 2020).…”

A Riemannian Newton trust-region method for fitting Gaussian mixture models

“…Besides the goal of density approximation, the possibility of modeling latent features by the underlying components make it also a strong tool for soft clustering tasks. Typical applications are to be found in the area of image analysis (Alfò et al 2008;Dresvyanskiy et al 2020;Zoran and Weiss 2012), pattern recognition (Wu et al 2012;Bishop 2006), econometrics (Articus and Burgard 2014;Compiani and Kitamura 2016 and many others).…”