An edge detection and classification scheme for range images which produces a multiscale representation in terms of well-localized depth and orientation edges is presented. The extraction is accomplished by detecting the presence of significant edges at a coarse scale and then determining their precise location by tracking them over decreasing scale. An adaptive multiscale thresholding is applied during this focusing process ro inhibit the attraction of insignificant details. Once focused, the edges are classified into the categories of true edge and diffuse edge by invoking classification rules derived from a mathematical analysis of edge displacement and branching over scale-space. Experimental results illustrate the robustness of the approach in the presence of noise and its performance with synthetic and real images of varying complexity. Comparisons with recently published techniques point out the improved performance of the approach, especially when the images contain substantially overlapping objects.>