Determining 3-D Shape from the Distribution of Normal Vector on a Curved Surface

Abstract

This paper describes the shape representation of 3-D objects which utilizes the normal vector obtained from 2-D images.
It is proposed to use the 2-D plane which is obtained by projecting the Gaussian sphere perspectively as the characteristic space for representing 3-D objects, and the shape of the surface of any 3-D object is corresponding to the figure on this plane. As for some basic curved surfaces, the characteristic figures on the plane are shown and these are extracted in the characteristic space. Each of them is easily extracted using techniques for image processing. The method for the detection of ellipses in the characteristic space is described in detail. And, it is experimentaly clarified that the detection of two or more ellipses in the same characteristic space is possible. Since the extraction of the 2-D figure is carried out all over the plane, overall region analysis without an effect of the positional error becomes possible.
Moreover, the technique, by which the curvature of the curved surface is presumed by using the ratio of the area of the curved surface in the scene and the density of the normal vector in this characteristic space, is obtained. The method, by which both principal curvature and the tangential line vector are used, is proposed for representing the object which can not be satisfactorily represented only in the distribution of the normal vector. It is also shown that the characteristic space proposed earlier is also applicable to the method, because the change of the vector is shown as the figure in this characteristic space.