6 research outputs found
Automatic differentiation of non-holonomic fast marching for computing most threatening trajectories under sensors surveillance
We consider a two player game, where a first player has to install a
surveillance system within an admissible region. The second player needs to
enter the the monitored area, visit a target region, and then leave the area,
while minimizing his overall probability of detection. Both players know the
target region, and the second player knows the surveillance installation
details.Optimal trajectories for the second player are computed using a
recently developed variant of the fast marching algorithm, which takes into
account curvature constraints modeling the second player vehicle
maneuverability. The surveillance system optimization leverages a reverse-mode
semi-automatic differentiation procedure, estimating the gradient of the value
function related to the sensor location in time N log N
Generalized fast marching method for computing highest threatening trajectories with curvature constraints and detection ambiguities in distance and radial speed
Work presented at the 9th Conference on Curves and Surfaces, 2018, ArcachonWe present a recent numerical method devoted to computing curves that globally minimize an energy featuring both a data driven term, and a second order curvature penalizing term. Applications to image segmentation are discussed. We then describe in detail recent progress on radar network configuration, in which the optimal curves represent an opponent's trajectories
Ground Metric Learning on Graphs
Optimal transport (OT) distances between probability distributions are
parameterized by the ground metric they use between observations. Their
relevance for real-life applications strongly hinges on whether that ground
metric parameter is suitably chosen. Selecting it adaptively and
algorithmically from prior knowledge, the so-called ground metric learning GML)
problem, has therefore appeared in various settings. We consider it in this
paper when the learned metric is constrained to be a geodesic distance on a
graph that supports the measures of interest. This imposes a rich structure for
candidate metrics, but also enables far more efficient learning procedures when
compared to a direct optimization over the space of all metric matrices. We use
this setting to tackle an inverse problem stemming from the observation of a
density evolving with time: we seek a graph ground metric such that the OT
interpolation between the starting and ending densities that result from that
ground metric agrees with the observed evolution. This OT dynamic framework is
relevant to model natural phenomena exhibiting displacements of mass, such as
for instance the evolution of the color palette induced by the modification of
lighting and materials.Comment: Fixed sign of gradien
Proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress
Published proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress, hosted by York University, 27-30 May 2018