A parallel algorithm for solving the Eikonal equation

A large variety of methods based on partial differential equations (PDE) use the interface propagation. For their flexibility these methods are being more and more applied to various problems ranging from physics, fluid mechanics to control theory and computer vision. The solution of the PDE-based interface evolution is in itself a complex iterative computational task involving a great number of iterations (unknown a priori). Therefore, these applications are very demanding on the hardware and their real-time implementation is still a challenging problem. An efficient implementation could be done by using a specific parallel architecture. This paper proposes an original, entirely parallel algorithm to solve the Eikonal equation. Which is the base of applications using a weighted distance function. This algorithm allows the parallel implementation of active contours methods or continuous watershed on a specific hardware.