This paper presents an efficient technique for extracting closed contours from range images' edge points. Edge points are assumed to be given as input to the algorithm (i.e., previously computed by an edge-based range image segmentation technique). The proposed approach consists of three steps. Initially, a partially connected graph is generated from those input points. Then, the minimum spanning tree of that graph is computed. Finally, a postprocessing technique generates a single path through the regions' boundaries by removing noisy links and closing open contours. The novelty of the proposed approach lies in the fact that, by representing edge points as nodes of a partially connected graph, it reduces the contour closure problem to a minimum spanning tree partitioning problem plus a cost function minimization stage to generate closed contours. Experimental results with synthetic and real range images, together with comparisons with a previous technique, are presented.