29 citations · 45 across the 5 of their papers we have counts for
3 papers · 1 filter
Average-distance problem with curvature penalization for data parameterization: regularity of minimizers
Xinyang Lu, Dejan Slepcev
We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functio…
Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
Antonio Esposito, Francesco S. Patacchini, André Schlichting +1
We consider dynamics driven by interaction energies on graphs. We introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with…
Mumford-Shah functionals on graphs and their asymptotics
Marco Caroccia, Antonin Chambolle, Dejan Slepčev
We consider adaptations of the Mumford-Shah functional to graphs. These are based on discretizations of nonlocal approximations to the Mumford-Shah functional. Motivated by applica…