An algorithm for segmenting range images of industrial parts is presented in this paper. Range images, are unique in that they directly approximate the physical surfaces of a real world 3-D scene. The segmentation of images ( range or intensity ) is based on edge detection or region growing techniques. The algorithm presented in this paper segments the range images by detecting discontinuities. There are three types of discontinuities in range images: jump, crease and smooth edges. The detection of a jump edge is relatively easy and can be obtained using edge detection techniques used for intensity images. The crease and smooth edges are difficult to detect especially in the presence of noise. Our approach is based on the analysis of the difference between the input and the filtered images. We show that, at an edge, the difference after Gaussian smoothing has a maxima in a direction perpendicular to the edge. The close connected regions are then obtained by eroding the image once and an iterative region growing least square fit is used to obtain the final segmented image. The performance of the proposed algorithm on a number of range images is presented.