Patrick W. Dondl, Patrina S. P. Poh, Martin Rumpf and Stefan Simon Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227): 20180718 2019 10.1098/rspa.2018.0718
2017
Matthias Erbar, Martin Rumpf, Bernhard Schmitzer and Stefan Simon Computation of Optimal Transport on Discrete Metric Measure Spaces Unknown https://arxiv.org/abs/1707.06859
Jan Maas, Martin Rumpf and Stefan Simon Transport based image morphing with intensity modulation In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision
Publisher: Springer, Cham
2017 http://dx.doi.org/10.1007/978-3-319-58771-4_45
2016
Peter Hornung, Martin Rumpf and Stefan Simon Material Optimization for Nonlinearly Elastic Planar Beams 2016 http://arxiv.org/abs/1604.02267
Jan Maas, Martin Rumpf and Stefan Simon Generalized optimal transport with singular sources 2016 http://arxiv.org/abs/1607.01186
2015
Alexander Effland, Martin Rumpf, Stefan Simon, Kirsten Stahn and Benedikt Wirth Bézier curves in the space of images In Proceedings Scale Space and Variational Methods in Computer Vision, Volume 9087 of Lecture Notes in Computer Science
page 372-384.
Publisher: Springer International
2015 http://dx.doi.org/10.1007/978-3-319-18461-6_30
Abstract: Bézier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bézier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model by Miller and Younes. Bézier curves are then computed via the Riemannian version of de Casteljau's algorithm, which is based on a hierarchical scheme of convex combination along geodesic curves. Geodesics are approximated using a variational discretization of the Riemannian path energy. This leads to a generalized de Casteljau method to compute suitable discrete Bézier curves in image space. Selected test cases demonstrate qualitative properties of the approach. Furthermore, a Bézier approach for the modulation of face interpolation and shape animation via image sketches is presented.