PDE Acceleration for Active Contours

Abstract

Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are either inapplicable or impractical. Accelerated gradient descent converges faster and performs a more robust local search of the parameter space by initially overshooting then oscillating back into minimizers which have a basis of attraction large enough to contain the overshoot. Recent work has demonstrated how a broad class of accelerated schemes can be cast in a variational framework leading to continuum limit ODE's. We extend their formulation to the PDE framework, specifically for the infinite dimensional manifold of continuous curves, to introduce acceleration, and its added robustness, into the broad range of PDE based active contours.