surface and their end points in space near the surface e g voxels these vectors are hereinafter referred to as shape vectors and the above points in space e g voxels take on the values of the shape vectors the shape vector is a kind of position vector having a range component and a directional component a potential value is used as the range component and a potential direction as the directional component further a lot of voxels are provided in a space including the shape surface each having the value of a shape vector in fig1 as for part of voxels shape vectors v 1 of the partial shape data 10 are indicated by the white arrows and shape vectors v 2 of the partial shape data 20 are indicated by the black arrows as a result of registration the partial shape data 10 and 20 in fig1 have different potential directions i e their vectors have different directional components the details of an overlapping portion x between the partial shape data 10 and 20 in fig1 are illustrated in fig1 as shown the partial shape data 10 and 20 have different surfaces in the stage of registration so their shape vectors v 1 and v 2 are independent of each other while the conventional merging method has a problem of inaccurate merging when the partial shape data have different potential directions since the merging is performed through arithmetic operations such as addition of the potential range values i e scalar quantities.