46 citations · 95 across the 9 of their papers we have counts for
10 papers
The Pólya-Szegő inequality for smoothing rearrangements
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
A basic version of the Pólya-Szegő inequality states that if is a Young function, the -Dirichlet energy -- the integral of -- of a suitable function $f\in…
On a partition with a lower expected -discrepancy than classical jittered sampling
Markus Kiderlen, Florian Pausinger
We prove that classical jittered sampling of the -dimensional unit cube does not yield the smallest expected -discrepancy among all stratified samples with $N=m^d…
Discrepancy of stratified samples from partitions of the unit cube
Markus Kiderlen, Florian Pausinger
We extend the notion of jittered sampling to arbitrary partitions and study the discrepancy of the related point sets. Let be a partition of a…
Rearrangement and polarization
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on . Rearrangements are map…
Dilation volumes of sets of finite perimeter
Markus Kiderlen, Jan Rataj
This paper analyzes the first order behavior (that is, the right sided derivative) of the volume of the dilation as converges to zero. Here and are subsets…
Voronoi-based estimation of Minkowski tensors from finite point samples
Daniel Hug, Markus Kiderlen, Anne Marie Svane
Intrinsic volumes and Minkowski tensors have been used to describe the geometry of real world objects. This paper presents an estimator that allows to approximate these quantities…
Surface tensor estimation from linear sections
Astrid Kousholt, Markus Kiderlen, Daniel Hug
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The…
Efficient calculation of local dose distribution for response modelling in proton and ion beams
S. Greilich, U. Hahn, M. Kiderlen +2
We present an algorithm for fast and accurate computation of the local dose distribution in MeV beams of protons, carbon ions or other heavy-charged particles. It uses compound Poi…
Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms
Gabriele Bianchi, Richard J. Gardner, Markus Kiderlen
We propose strongly consistent algorithms for reconstructing the characteristic function 1_K of an unknown convex body K in R^n from possibly noisy measurements of the modulus of i…
Convergence of algorithms for reconstructing convex bodies and directional measures
Richard J. Gardner, Markus Kiderlen, Peyman Milanfar
We investigate algorithms for reconstructing a convex body in from noisy measurements of its support function or its brightness function in directions $u_1,…