Multi-Resolution algorithms for

Multi-resolution methods applied to active contour models can speed up processes and improve results. In order to estimate those improvements, we describe and compare in this paper two models using such algorithms. First we propose a multi-resolution algorithm of an improved snake model, the balloon model. Convergence is achieved on an image pyramid and parameters are automatically modiied so that, at each scale, the maximal length of the curve is proportional to the image size. This algorithm leads to an important saving in computational time without decreasing the accuracy of the result at the full scale. Then we present a multi-resolution parametrically deformable model using Fourier descriptors in which the curve is rst described by a single harmonic; then harmonics of higher frequencies are used so that precision increases with the resolution. We show that boundary nding using this multi-resolution algorithm leads to more stability. These models illustrate two diierent ways of using multi-resolution methods: the rst one uses multi-resolution data, the second one applies multi-resolution to the model itself.