MEASUREMENT OF CURVED OBJECTS USING GRADIENT BASED FITTING AND CSG MODELS
Johan W. H. Tangelder · 2000
Since curved objects often contain no points that can be identified in overlapping images, it is difficult to apply a photogrammetric technique based on point identification. However, curved objects can very well be represented using 3D parameterized CSG (Constructive Solid Geometry) models. In this approach the shape and the pose of a curved object are given by the parameters of its CSG model. An initial measurement of the pose and the shape of a curved object can be obtained by the selection of a CSG model from a database and the approximate alignment of the object with the projections of the CSG model in a collection of images. These images are taken with a calibrated camera of which the interior and exterior orientations are known. In this paper we focus on the precise measurement of the pose and the shape of the curved object by fitting the projections of the CSG model precisely onto the edges of the curved object in the images. Observation equations are formulated relating the adaptation of the pose and shape parameters to the distance between pixels with high gray value gradients and edges of the projected CSG model. The model is fitted to the object in the images by estimating the changes to the pose and shape parameters by the least squares solution of these observation equations. The efficiency of the fitting algorithm is significantly improved by (a) the computation of a limited number of gradient strengths in a buffer around the projected model edges and (b) the elimination of gradients that are not perpendicular to the projected model edges. The practical application of the fitting algorithm is illustrated for images containing straight and curved pipes. The convergence behaviour and the robustness of the fitting algorithm are evaluated.