We address the problem of finding a set of contour curves in a 2D or 3D image. We consider the problem of perceptual grouping and contour completion, where the data is an unstructured set of regions in the image. A new method to find complete curves from a set of edge points is presented. Contours are found as minimal paths between connected components, using the fast marching algorithm. We find the minimal paths between each of these components, until the complete set of these "regions" is connected. The paths are obtained using back propagation from the saddle points to both components. We then extend this technique to 3D. The data is a set of connected components in a 3D image. We find 3D minimal paths that link together these components. Using a potential based on vessel detection, we illustrate the capability of our approach to reconstruct tree structures in a 3D medical image dataset.