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The paper deals with the automatic geometrical testing of three-dimensional objects from profile range images. This involves a scheme for automatically aligning, comparing and best fitting profile range images of a component with a corresponding model. Profile range images are directly obtained using range finding equipment. After an alignment process, these are then compared with mathematical models of the component generated in a computer aided design (CAD) system by emanating normals from the model and determining where they intersect the image surface. A Gaussian least square best fit of the model to the measured component is then computed to two degrees of freedom which takes the overall surface differences into account. Surface differences are expressed by two translation terms. This method can be extended to a maximum of six degrees of freedom.