The measurement of the 3-d position of the polyhedra

The scene containing polyhedra has been studied as one of the interesting subjects in research on robot vision, and several methods for extracting the line drawing of the polyhedron have been proposed. However, few have dealt with estimation of the location and orientation of the polyhedron in 3-D space. This paper proposes a method for measuring the 3-D position (location and orienation) of the known polyhedron by effectively utilizing the shade information. In other words, the relations among the polyhedron, its image and shadow image are analyzed, by which the 3-D coordinates of four noncoplanar vertices of the polyhedron, are determined. The candidates for mapping of the measured vertices to those of the polyhedron are found by the distance search method or by the feature reference method. Using the coordinates of the candidates, the polyhedron is reconstructed, together with its shadow. By comparing these reconstructed shadows SR' with the original shadow SP', the one providing the best fit is adopted as the solution. The method is applicable even if there is no difference among the brightness of the surfaces. The experiment shows that the error in measurement of the 3-D location and orientation by the proposed method are within 2 and 5 percent of the visual field, respectively.