Stefan Simon

Stefan Simon
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Mathematics - Numerical Analysis (4)

Publications Authored By Stefan Simon

We present a generalized optimal transport model in which the mass-preserving constraint for the $L^2$-Wasserstein distance is relaxed by introducing a source term in the continuity equation. The source term is also incorporated in the path energy by means of its squared $L^2$-norm in time of a functional with linear growth in space. This extension of the original transport model enables local density modulation, which is a desirable feature in applications such as image warping and blending. Read More

We consider the problem of an optimal distribution of soft and hard material for nonlinearly elastic planar beams. We prove that under gravitational force the optimal distribution involves no microstructure and is ordered, and we provide numerical simulations confirming and extending this observation. Read More

In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying Riemannian metric measures the rate of transport cost and the rate of viscous dissipation. Read More

B\'ezier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of B\'ezier 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. Read More