On the basis of a semi-realistic SIR microsimulation for Germany and Poland, we show that the R ₀ parameter interval for which the COVID-19 epidemic stays overcritical but below the capacity limit of the health care system to reach herd immunity is so narrow that a successful implementation of this strategy is likely to fail, which is in contrast to results obtained from classical differential equation models. Our microsimulation is based on official census data and involves household composition and age distribution as the main population structure variables. Outside household contacts are characterised by an out-reproduction number R ^* which is the only free parameter of the model. For a subcritical domain we compute the time till extinction and prevalence as a function of the initial number of infected individuals and R ^* . For the Polish city of Wrocław we also discuss the combined impact of testing coverage and contact reduction. For both countries we estimate R ^* for disease progression until 20th of March 2020.

Local Correlation and Entropy Maps as Tools for Detecting Defects in Industrial Images: 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.

In this paper we present a fast and easy method of quality monitoring for processes observed by cameras. A process of combustion in an industrial gas burner is used as an example. It is shown that we can observe only a small randomly chosen part of subsequent camera images. We propose a few, working in parallel manner, quality control charts. These Shewart type charts operate on squared norms of sparse partial image projections. Each chart is used for monitoring only a part of the whole camera image. The charts provide a partial decision about the state of the monitored system. A final decision is the logical product of these partial decisions. A simulation study based on 144 images of a working gas burner is presented.

In this paper we propose a method of object classification based on the sequences of Zernike moments. The method makes use of the pattern recognition properties of Zernike moments and expands it to the problem of classification. Since the distinctive features of the classified objects are carried over to the Zernike moments, the proposed method allows for a robust, rotation and translation invariant classification of complex objects in grayscale images. In this approach, each object class has defined a reference Zernike moment sequence that is used as the prototype of the class. The object’s affiliation to the class is decided with the MSE criterion calculated for the object’s Zernike moments sequence and the reference Zernike moments sequence of the class. The method is tested using grayscale images of handwritten digits and microscopic sections.