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A method to segment and describe visible surfaces of three-dimensional (3-D) objects is presented by first segmenting the surfaces into simple surface patches and then using these patches and their boundaries to describe the 3-D surfaces. First, distinguished points are extracted which will comprise the edges of segmented surface patches, using the zero-crossings and extrema of curvature along a given direction. Two different methods are used: if the sensor provides relatively noise-free range images, the principal curvatures are computed at only one resolution, otherwise, a multiple scale approach is used and curvature is computed in four directions 45° apart to facilitate interscale tracking. These points are then grouped into curves and these curves are classified into different classes which correspond to significant physical properties such as jump boundaries, folds, and ridge lines (or smooth extrema). Then jump boundaries and folds are used to segment the surfaces into surface patches, and a simple surface is fitted to each patch to reconstruct the original objects. These descriptions not only make explicit most of the salient properties present in the original input, but are more suited to further processing, such as matching with a given model. The generality and robustness of this approach is illustrated on scene images with different available range sensors.