Computing volume descriptions from sparse 3-D data

Abstract

An approach is presented to describing objects as generalized cones (GCs) starting from sparse, imperfect 3-D data, such as may be obtained from stereo. Though some previous systems have been developed for generalized cone descriptions, they are not good at handling imperfect and sparse data. In our approach, we first label the boundaries of the generalized cone as axial contour generators and terminators. We examine the general properties of these labels/features. In addition, we note that for aLinearStraightHomogeneousGeneralizedCone (LSHGC), the axial contour generators are coplanar. We use these properties in our search for labeling the GC boundaries; the search is based on the hypothesize and verify paradigm. The axis, cross-section, and cross-section function of the GC are then deduced from the labeled boundaries. The system described has been tested on a number of synthetic and real scenes of LSHGCs and some results are presented. We conclude by indicating how the system could be extended to more complex objects.