Identification of 3-D objects from three orthogonal silhouettes using normalized linear quad-octrees

Abstract

Linear octrees offer a volume representation of 3-D objects, which is quite compact and lends itself to traditional object processing operations. However, the linear octree structure for generating the representation of 3-D objects from three orthogonal silhouettes by using the volume intersection technique is dependent on viewpoints. The recognition achieved from matching object representations to model representations requires that the representations of objects are independent of viewpoints. In order to obtain independent representations of viewpoints, the three principal axes of the object should be obtained from the moment of inertia matrix by computing its eigenvectors. The linear octree is projected onto the image planes of the three principal views (along the principal axes) to obtain the three normalized linear quadtrees. The object matching procedure has two phases: the first phase is to match the normalized linear quadtrees of the unknown object to a subset of models contained in a library utilizing a measure of symmetric difference; the second phase is to generate the normalized linear octrees of the object and these selected models and then to match the normalized linear octree of the unknown object with the model having the minimum symmetric difference.