Radon Institute of Computational and Applied Mathematics

Linz, Austria

Radon Institute of Computational and Applied Mathematics

Linz, Austria

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Abhau J.,University of Innsbruck | Scherzer O.,University of Innsbruck | Scherzer O.,Radon Institute of Computational and Applied Mathematics
International Journal of Computer Vision | Year: 2010

In this paper we propose an efficient algorithm for topology adaptation of evolving surface meshes in 3D. This system has two novel features: First, a spatial hashing technique is used to detect self-colliding triangles of the evolving mesh. Secondly, for the topology adaptation itself, we use formulas which are derived from homology. In view of this the advantages of our algorithm are that it does not require global mesh re-parameterizations and the topology adaptation can be performed in a stable way via a rather coarse mesh. We apply our algorithm to segmentation of three-dimensional synthetic and ultrasound data. © 2009 Springer Science+Business Media, LLC.


Constantin A.,University of Vienna | Kalimeris K.,Radon Institute of Computational and Applied Mathematics | Scherzer O.,Radon Institute of Computational and Applied Mathematics | Scherzer O.,University of Vienna
Nonlinear Analysis: Real World Applications | Year: 2015

We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed. © 2015 Elsevier Ltd. All rights reserved.


Bastl B.,University of West Bohemia | Juttler B.,Johannes Kepler University | Lavicka M.,University of West Bohemia | Schicho J.,Radon Institute of Computational and Applied Mathematics | Sir Z.,University of West Bohemia
Computer Aided Geometric Design | Year: 2011

We consider special rational triangular Bézier surfaces of degree two on the sphere in standard form and show that these surfaces are parameterized by chord length. More precisely, it is shown that the ratios of the three distances of a point to the patch vertices and the ratios of the distances of the parameter point to the three vertices of the (suitably chosen) domain triangle are identical. This observation extends an observation of Farin (2006) about rational quadratic curves representing circles to the case of surfaces. In addition, we discuss the relation to tripolar coordinates. © 2010 Elsevier B.V. All rights reserved.


Poschl C.,University Pompeu Fabra | Resmerita E.,Johannes Kepler University | Scherzer O.,University of Vienna | Scherzer O.,Radon Institute of Computational and Applied Mathematics
Inverse Problems | Year: 2010

Consider a nonlinear ill-posed operator equation F(u) = y, where Fis defined on a Banach space X. In this paper we analyze finite-dimensional variational regularization, which takes into account operator approximations and noisy data. As shown in the literature, depending on the setting, convergence of the regularized solutions of the finite-dimensional problems can be with respect to the strong or just a weak topology. In this paper our contribution is twofold. First, we derive convergence rates in terms of Bregman distances in the convex regularization setting under appropriate sourcewise representation of a solution of the equation. Secondly, for particular regularization realizations in nonseparable Banach spaces, we discuss the finite-dimensional approximations of the spaces and the type of convergence, which is needed for the convergence analysis. These considerations lay the fundament for efficient numerical implementation. In particular, we emphasize on the space X of finite total variation functions and analyze in detail the cases when X is the space of the functions of finite bounded deformation and the L∞-space. The latter two settings are of interest in numerous problems arising in optimal control, machine learning and engineering. © 2010 IOP Publishing Ltd.


Zangerl G.,University of Vienna | Scherzer O.,University of Vienna | Scherzer O.,Radon Institute of Computational and Applied Mathematics
Mathematical Methods in the Applied Sciences | Year: 2010

Illuminating tissue with pulsed electromagnetic waves generates acoustic waves inside an object which can be measured and converted into a three-dimensional (3d) image. This text is concerned with a two-step reconstruction method where the acoustic pressure is measured with circular integrating detectors. In the first step, reconstruction formulas for some kind of projection of the source distribution are derived; in the second step, an inversion formula for a circular radon transform on the sphere is developed. Copyright © 2010 John Wiley & Sons, Ltd.


Kalimeris K.,Radon Institute of Computational and Applied Mathematics | Scherzer O.,Radon Institute of Computational and Applied Mathematics | Scherzer O.,University of Vienna
Mathematical Methods in the Applied Sciences | Year: 2013

In this paper, we derive time reversal imaging functionals for two strongly causal acoustic attenuation models, which have been proposed recently. The time reversal techniques are based on recently proposed ideas of Ammari et al. for the thermo-viscous wave equation. Here and there, an asymptotic analysis provides reconstruction functionals from first order corrections for the attenuating effect. In addition, we present a novel approach for higher order corrections. Copyright © 2013 John Wiley & Sons, Ltd.


Elbau P.,Radon Institute of Computational and Applied Mathematics | Scherzer O.,Radon Institute of Computational and Applied Mathematics | Scherzer O.,University of Vienna | Schulze R.,Radon Institute of Computational and Applied Mathematics | Schulze R.,University of Vienna
Inverse Problems | Year: 2012

The literature on reconstruction formulas for photoacoustic tomography is vast. The various reconstruction formulas differ in the measurement devices used and geometry on which the data are sampled. In standard photoacoustic imaging (PAI), the object under investigation is illuminated uniformly. Recently, sectional PAI techniques, using focusing techniques for initializing and measuring the pressure along a plane, appeared in the literature. This paper surveys existing and provides novel exact reconstruction formulas for sectional PAI. © 2012 IOP Publishing Ltd.


Grasmair M.,University of Vienna | Scherzer O.,University of Vienna | Scherzer O.,Radon Institute of Computational and Applied Mathematics | Vanhems A.,Toulouse Business School
Inverse Problems | Year: 2013

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition. © 2013 IOP Publishing Ltd.

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