In this paper we have presented some geometric techniques to characterize and parametrize surfaces of industrial parts in range images. The surfaces are characterized to one of plane, sphere, cylinder and cone, because they form the majority of object surfaces in man-made industrial parts. The problem has been studied for two different situations. In the first case,a priori knowledge about the surface shape is assumed. In such a situation the problem of surface characterization reduces to that of surface parameter estimation. The standard deviations of the estimated parameters give a measure of uncertainty of characterizing a surface patch to one of the four surface types. In the second case, noa priori information regarding the shape of a surface is available. This includes partially visible surfaces also. To deal with such a situation, a fuzzy classifier is designed using the uncertainty values. The fuzzy classifier classifies the unknown surface patch (including partially visible surfaces) to one of the four surface types. Experimental results with synthetic range images are presented to highlight the distinctive features of our technique.