Contour tting using an adaptive spline model

This paper presents a new segmentation algorithm by tting active contour models (or snakes) to objects using adaptive splines. The adaptive spline model describes the contour of an object by a set of piecewisely interpolating C polynomial spline patches which are locally controlled. Thus the resulting description of the object contour is continuous and smooth. Polynomial splines provide a fast and e cient way for interpolating the object contour and allow us to compute its internal energy due to bending and elasticity deformations analytically. The adaptive spline model can be represented by its spline control points. The accuracy of the model is gradually increased during the segmentation process by inserting new control points. For estimating the optimal position of the control points, two di erent relaxation techniques based on Markov{Random{Fields (MRFs) have been combined and evaluated: Simulated Annealing (SA), which is a stochastic relaxation technique, and Iterated Conditional Modes (ICM), which is a probabilistic relaxation technique. We have studied convergence behavior and performance on arti cial and medical images. The results show that the combination of both relaxation techniques provides very robust and initialization independent segmentation results.