The active contours approach is an oft-used family of techniques in image analysis. This work presents a comparative study between two active contour approaches for image segmentation. The level sets method and deformable contours under B-spline representation are compared. These image segmentation methods have different features and are difficult to compare in terms of performance, accuracy and initialization conditions. Both are implemented and a way to calculate the approximation error is developed. As a conclusion of this work a theoretical comparison and a comparative characterization of the approximation error for each method are presented.