The Gaussian curvature is taken as a characteristic function. All points of the surface that belong to an equivalent class are represented as a node of the Reeb graph. The object surface is divided in five regions in accordance with the value of Gaussian curvature. The Reeb graphs of these five regions are constructed and then compared with the five regions of the recognizing objects. The examples of the Reeb graph construction for human faces, forks and knives are given.
Some additional work has to be done when the camera moves and generates a series of range data.
A corresponding Reeb graph is constructed for each frame. After the matching is done, a translation vector and a rotational matrix can be computed to establish geometric matching of range data. Although the recognition part is not covered in details, the general approach seems to be promising for many applications. Since the proposed surface is a locus of cross product normal vectors, it coincides to the origin where the degenerate normal vector occurs. This can be detected by a proposed subdivision algorithm.