A tensor technique for determining three-dimensional object orientation using images from several viewing angles (robot vision, object recognition, sequence analysis)

Abstract

The research documented in this thesis was directed towards finding a method for the determination of the 3-D geometric transformation that relates two 3-D object orientations where the only available information is a set of 2-D images describing the object from several viewing angles. A tensor technique which does not rely on any type of feature correspondence information or differential object motion has been developed and implemented. The basis for this technique is the property that the moments of an object in some arbitrary orientation form the components of a tensor associated with that orientation. Therefore, 3-D Cartesian absolute moment tensors may be constructed from projections for each 3-D object orientation and may be used to form a simple linear system of equations which determines a unique solution for the 3-D transformation relating two 3-D object orientations. The rule giving the minimum number of projections as a function of the highest order of the tensor used in the calculations has also been found. The technique is developed for the case of objects described by sets of point mass arbitrarily distributed in 3-Space, but has application to more general object types.