Application of clustering methods to anomaly detection in fibrous media

Abstract

The paper considers the problem of anomaly detection in 3D images of fibre materials. The spatial Stochastic Expectation Maximisation algorithm and Adaptive Weights Clustering are applied to solve this problem. The initial 3D grey scale image was divided into small cubes subject to clustering. For each cube clustering attributes values were calculated: mean local direction and directional entropy. Clustering is conducted according to the given attributes. The proposed methods are tested on the simulated images and on real fibre materials. Introduction.Nowadays, there exists a large amount of novel materials with interesting physical properties. For instance, reinforcement of polymers with fibres significantly increases the mechanical properties of the materials. The materials' performance is determined mostly by their composition as well as by allocation and directions of the reinforcing fibres.Due to the production process, an anomaly region may be formed in the material. We define it as an area where the distribution of fibre directions differs from the remaining material. To keep the stated material's properties, it is necessary to identify regions with untypical fibre distribution. For this purpose, high-resolution microcomputer tomography reaching a level of microns [1,2] is used to observe the fibre system in a composite sample, cf. Figure 1 (right).Our main task is then to find the areas with anomalous directional properties of fibres in the 3D image. This is done by means of cluster analysis dividing the whole image volume into two clusters: the smaller "anomaly" region and the bigger "normal" material.

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 [45] and it was the object of studies in [15] and [16], 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 [21].…”

“…We denote by J W the collection of indexes k such that Y k is non-empty. In the considered data set |J W | = 430741 and its precise construction is in [15]. The estimating procedure of directions in MAVI software produces vectors on a unit sphere which are not necessarily symmetrically distributed.…”

Detecting anomalies in fibre systems using 3-dimensional image data

“…However, the spatial SAEM approach yields better results, cf. [21]. Moreover, it does not require a complex parameter tuning and operates fast.…”

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).…”

“…We denote by J W the collection of indexes k such that Y k is non-empty. In the considered data set |J W | = 430741 and its precise construction is in (Dresvyanskiy et al, 2019).…”