Markus Brunk

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We present an approach for automatic bone age classification from hand x-ray images using the Discriminative Generalized Hough Transform (DGHT). To this end, a region, characteristic for the bone age (e.g. an epiphyseal plate), is localized and subsequently classified to determine the corresponding age. Both steps are realized using the DGHT, whereat the(More)
Coupled systems of differential-algebraic equations (DAEs) may suffer from instabilities during a dynamic iteration. For a general dynamic iteration, we extend the existing analysis on recursion estimates, error transport and stability to a general DAE setting. In this context, we discuss the influence of certain coupling structures and the computational(More)
An efficient and accurate numerical method is presented for the solution of highly oscillatory differential equations. While standard methods would require a very fine grid to resolve the oscillations, the presented approach uses first an analytic (second order) WKB-type transformation, which filters out the dominant oscillations. The resulting ODE is much(More)
A computationally efficient a posteriori error estimator is introduced and analyzed for collocation solutions to linear index-1 DAEs with properly stated leading term. The procedure is based on a modified defect correction principle, extending an established technique from the ODE context to the DAE case. We prove that the resulting error estimate is(More)
The paper consists of two parts. In the first part of the paper, we proposed a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index-1 differential-algebraic equations (DAEs). Based on the idea of Defect Correction we developed local error estimates for the case(More)
A coupled semiconductor–circuit model including thermal effects is proposed. The charged particle flow in the semiconductor devices is described by the energy-transport equations for the electrons and the drift-diffusion equations for the holes. The electric circuit is modeled by the network equations from modified nodal analysis. The coupling is realized(More)
A hierarchy of diffusive partial differential equations is derived by a moment method and a Chapman-Enskog expansion from the semiconductor Boltzmann equation assuming dominant collisions. The moment equations are closed by employing the entropy maximization principle of Levermore. The new hierarchy contains the well-known drift-diffusion model, the(More)