Thick curves arise naturally in certain applications such as magnetic resonance imaging of the brain; they can also arise in computer vision problems through morphological dilation of boundaries of objects. In this paper we describe two new adaptive active contour algorithms for the extraction and mapping of the skeleton of a thick curve. They are based on conditions that have been derived in previous work which guarantee uniqueness and fidelity of the solution. Both algorithms modify the regularization constant Ko in attempt to maintain convexity of the energy function while simultaneously improving the fidelity of the result. The first algorithm changes Ko over time while the second adapts Ko spatially. We evaluate both algorithms on experiments with synthetic curves; both demonstrate an improved performance compared to a fixed parameter active contour algorithm.