Alexander Belyaev

Aljosha Köcher, Alexander Belyaev, Jesko Hermann et al.

In manufacturing, many use cases of Industry 4.0 require vendor-neutral and machine-readable information models to describe, implement and execute resource functions. Such models have been researched under the terms capabilities and skills. Standardization of such models is required, but currently not available. This paper presents a reference model developed jointly by members of various organizations in a working group of the Plattform Industrie 4.0. This model covers definitions of most important aspects of capabilities and skills. It can be seen as a basis for further standardization efforts.

Alexander Belyaev, Boris Khesin, Serge Tabachnikov

We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a general construction for obtaining discrete spherical means of directional derivatives. The construction is based on using the Minkowski's existence theorem and Veronese maps. Approximating the directional derivatives by appropriate finite differences allows one to obtain finite difference operators with good rotation invariance properties. In particular, we use discrete circular and spherical means to derive discrete approximations of various linear and nonlinear first- and second-order differential operators, including discrete Laplacians. A practical potential of our approach is demonstrated by considering applications to nonlinear filtering of digital images and surface curvature estimation.

Alexander Belyaev, Pierre-Alain Fayolle, Michael Cohen

We introduce a simple and efficient method to enhance and clarify images. More specifically, we deal with low light image enhancement and clarification of hazy imagery (hazy/foggy images, images containing sand dust, and underwater images). Our method involves constructing an image filter to simulate low-light or hazy conditions and deriving approximate reverse filters to minimize distortions in the enhanced images. Experimental results show that our approach is highly competitive and often surpasses state-of-the-art techniques in handling extremely dark images and in enhancing hazy images. A key advantage of our approach lies in its simplicity: Our method is implementable with just a few lines of MATLAB code.

Alexander Belyaev, Pierre-Alain Fayolle

Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for both the schemes, accuracy improvements are proposed and evaluated. Asymptotics of Laplace integrals and Taylor series extrapolations are used to achieve the improvements.