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The potential of edge-based complete image segmentation into regions has not gained the due attention in the literature thus far. The present paper attempts to explore this potential by proposing an adaptive grouping algorithm to solve the contour closure problem that is the key to a successful edge-based complete image segmentation. The effectiveness of the proposed algorithm is extensively tested in the range image domain and compared to several region-based segmentation methods within a rigorous comparison framework. On three range image databases of varying quality acquired by different range scanners, it is shown that the proposed approach is able to achieve very appealing performance with respect to both segmentation quality and computation time.