This work presents a novel approach for curve tracing and user-steered boundary tracking in image segmentation, named Bandeirantes. The proposed approach was devised using Image Foresting Transform with unexplored and dynamic connectivity functions, which incorporate the internal energy of the paths, at any curvature scale, resulting in better segmentation of smooth-shaped objects and leading to a better curve tracing algorithm. We analyze its theoretical properties and discuss its relations with other popular methods, such as riverbed, live wire and G-wire. We compare the methods in a curve tracing task of an automatic grading system. The results show that the new method can significantly increase the system accuracy.