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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.

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.

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.

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.

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.

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