Providing mobile robots with autonomous capabilities is advantageous. It allows one to
dispense with the intervention of human operators, which may prove beneficial in economic …

This monograph reviews both the theory and practice of the numerical computation of
geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows …

We describe and implement an algorithm for computing the set of reachable states of a
continuous dynamic game. The algorithm is based on a proof that the reachable set is the …

A wide range of computer vision applications require an accurate solution of a particular
Hamilton-Jacobi (HJ) equation, known as the Eikonal equation. In this paper, we propose an …

We present a novel approach to direct and control virtual crowds using navigation fields. Our
method guides one or more agents toward desired goals based on guidance fields. The …

The computation of global invariant manifolds has seen renewed interest in recent years.
We survey different approaches for computing a global stable or unstable manifold of a …

Convergent numerical schemes for degenerate elliptic partial differential equations are
constructed and implemented. Simple conditions are identified which ensure that nonlinear …

Recent advances in Autonomous Underwater Vehicle (AUV) technology have facilitated the
collection of oceanographic data at a fraction of the cost of ship‐based sampling methods …

We construct high order fast sweeping numerical methods for computing viscosity solutions
of static Hamilton–Jacobi equations on rectangular grids. These methods combine high …

Invariance to geometric transformations is a highly desirable property of automatic classifiers
in many image recognition tasks. Nevertheless, it is unclear to which extent state-of-the-art …