For several applications in Medicine, it is fundamental to determine the spatial tracking, along the time, of structure parts such as the apex of heart. The objective of this work is to present a robust technique for pointwise tracking of contours. Given two n-dimensional closed contours (S, D) derived from two consecutive image scenes, the basic idea is to find the cheapest path that connects each point in S to a point in D. The critical steps are the definition of the cost function and the numerical approach for the global discrete minimization. For the cost function, we have used the minimum distance to the contours and curvature of a level set function. The global discrete optimization can be achieved using dynamic programming on a constrained region with privileged tracks. A privileged path is associated to all elements that form destination contour D and a point of this contour is set as seed for the dynamic programming. By this artifice, all paths can be obtained. Simulations with several polygons showed encouraging results. For instance, for 10 prominent points and distortion of 15 degree(s) plus 20% of expansion, in a 400 x 400 pixels image, the mean distance error was below 2 pixels.