In the machine vision research, the image segmentation problem, that partitions the sensed image into meaningful regions corresponding to physical scene surfaces, is an important and difficult one. Recently, with the development of accurate and fast range finding systems, range images which provide more reliable information about three-dimensional geometry of object surfaces than intensity images sensed by such as TV camera become available. The thesis proposes a method of range image segmentation, which is capable of extracting the smooth surface primitives of 3-D objects from the range image and applying to intensity images for image coding. Under the smoothness assumption that the range image of interest has been formed with smoothly varying surfaces of objects, we can view the range image segmentation problem as the range image approximation problem to which the function approximation idea can be applied well. The proposed method consists of a surface type labeling stage and a region merging stage, where both stages are based on polynomial function approximation. In the first stage, one of the six surface type labels is assigned to each pixel of the range image according to the sign of the two principal curvatures, obtained by the theory of differential geometry and two-dimensional quadratic function approximation. The equally labeled and connected regions are localized and then the iterative region merging operation is performed based on the biquadratic function approximation to detect more reliable surface regions in the second stage. The experimental results show good performance of the proposed method in range image segmentation. In addition, the proposed one applied to intensity images for image coding has some advantages such as singgle pixel-width boundaries, a lower approximation error, and the reduced processing time and memory, when compared with Kocher-Leonaldi``s method[Koch86].