Active contour models are among the most popular PDE-based tools in computer vision. In this paper we present a new algorithm for the fast evolution of geodesic active contours and compare it with other established numerical schemes. The new algorithm employs a full time-implicit and unconditionally stable numerical scheme and applies multigrid methods for the efficient solution of the occurring sparse linear system. When we utilize very big time-steps for the numerical evolution of the front, the proposed scheme has increased accuracy and better rotational invariance properties compared with the alternative AOS scheme. This allows for the rapid evolution and convergence of the contour to its final configuration after only very few iterations. Standard pyramidal and/or narrowband techniques can be easily integrated into our algorithm and further accelerate the curve evolution. Experimental results in object boundary detection demonstrate the power of the method.