Other researchers have put forward some improved RANSAC methods. However, the traditional RANSAC has high computational complexity and relatively high time consumption. It has high detection accuracy and can suppress the effect of noise. This method can effectively detect spherical regions in a point cloud. proposed the RANSAC method for 3D sphere detection. Three-dimensional point cloud sphere detection includes the 3D Hough transform, registration, random sample consensus (RANSAC), region growing, and other methods. In order to improve the efficiency and accuracy of coordinate system unification during measurement, many studies have been devoted to improving the sphere detection accuracy and shortening the calculation time. īecause the sphere is used as the target of detection, any error of the sphere center that it determines will be propagated as an error in the coordinate system transformation. Three-dimensional structured light scanning technology is often used as the terminal measurement device in combined measurements due to its good collimation, non-contact mode, high accuracy, and fast measurement. Its key principle is to transform the terminal scan data from different locations into a unified global coordinate reference system with the help of auxiliary targets. Combined measurement is a method to select a measurement method with large-scale precision characteristics to achieve global measurement and control and to select a precise and an efficient morphology measurement method as the terminal measurement to collect high-density point clouds. Because of the sizeable measurement space range and the complex structure of measured parts, they need to be measured by a combined measurement method. The experimental results demonstrate that the method outperforms the conventional RANSAC algorithm in terms of accuracy and detection speed in estimating sphere parameters.ĭuring the maintenance of aircraft landing gear, it is necessary to detect assembly errors, such as parallelism of the front and rear axles of the frame and axiality between the shock absorber prop and sleeve. The total least squares method is used to estimate the inner point set of spherical objects obtained by the RANSAC algorithm. Secondly, the RANSAC method is combined with the total least squares method. Combined with the k-d nearest neighbor search algorithm, the principal curvature constraint of random sampling points is implemented to improve the quality of sample points selected by RANSAC and increase the detection speed. Firstly, the principal curvature of point cloud data is calculated. The method is based on the RANSAC algorithm. For this reason, a novel method of spherical object detection and parameter estimation based on an improved random sample consensus (RANSAC) algorithm is proposed. However, point cloud sphere detection has the disadvantages of errors and slow detection time. Through its central coordinates, scanned point cloud data from different locations can be converted into a unified coordinate reference system. Im not quite sure how we easily get this from the determinant.Spherical targets are widely used in coordinate unification of large-scale combined measurements. However, a statement is made that since the principle directions are orthogonal, it is easy to see that a necessary and sufficient condition for a parameterized curve to be a line of curvature is $F=f=0$. I have followed his argument in detail myself and derived the determinant in equation (8).
Do Carmo entitled Differential Geometry of Curves and Surfaces, an analysis of the principle directions is made near a non umbilic point on pp 160-161.
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