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Local correlation and entropy maps as tools for detecting defects in industrial images

100%
Skubalska-Rafajłowicz E.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 1
41-47
EN
The aim of this paper is to propose two methods of detecting defects in industrial products by an analysis of gray level images with low contrast between the defects and their background. An additional difficulty is the high nonuniformity of the background in different parts of the same image. The first method is based on correlating subimages with a nondefective reference subimage and searching for pixels with low correlation. To speed up calculations, correlations are replaced by a map of locally computed inner products. The second approach does not require a reference subimage and is based on estimating local entropies and searching for areas with maximum entropy. A nonparametric estimator of local entropy is also proposed, together with its realization as a bank of RBF neural networks. The performance of both methods is illustrated with an industrial image.
2
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Random projections and hotelling's T² statistics for change detection in high-dimensional data streams

100%
Skubalska-Rafajłowicz E.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 2
447-461
EN
The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of Rn . We examine the random projection method using artificial noisy image sequences as examples.
3
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Random projection RBF nets for multidimensional density estimation

100%
Skubalska-Rafajłowicz E.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 4
455-464
EN
The dimensionality and the amount of data that need to be processed when intensive data streams are observed grow rapidly together with the development of sensors arrays, CCD and CMOS cameras and other devices. The aim of this paper is to propose an approach to dimensionality reduction as a first stage of training RBF nets. As a vehicle for presenting the ideas, the problem of estimating multivariate probability densities is chosen. The linear projection method is briefly surveyed. Using random projections as the first (additional) layer, we are able to reduce the dimensionality of input data. Bounds on the accuracy of RBF nets equipped with a random projection layer in comparison to RBF nets without dimensionality reduction are established. Finally, the results of simulations concerning multidimensional density estimation are briefly reported.
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