Computing 3-D Location and Shape Parameters of Cones Using Structured Lights

The paper proposes a simple method to determine the 3-D location and shape parameters of a right circular cone using structured lights. A vital concept in the proposed method is to convert the complex curved stripe pattern into an equivalent, but simpler, linear stripe pattern. The conic surface patch lying between two visible silhouette edges is replaced by the plane defined by the two silhouette edges that cut the cone. The appropriate geometric models are given to compute the cone axis and shape parameters representing the height of the cone and the radius of the cone base. For successful application of the proposed measurement method, the sensing environment must be in a proper geometric configuration such that the required cone cutting plane and the two silhouette edges can be constructed. It is pointed out that in terms of a Gaussian sphere representation, there always exists such a right geometric configuration for the cone measurement. Experimental results are given for the measurement of three cones of different sizes. The results show that the method is reasonably accurate and robust against noise in the extracted stripe data.