Fast Sphere Detection Based on Polytope Method Using One-Dimensional Histogram

We propose a method for fast extraction of sphere. Basically, main algorithms of the extraction in 3D figure are the same as 2D method we reported in previous research. The proposed method utilizes the one-dimensional histogram as search space, and the polytope method which is one of the minimization algorithms for search parameters in target figure. The histogram has two characteristics: (a) The distribution of the histogram changes if the parameters of representing the sphere changes. (b) The value of highest frequency of histogram becomes maximum if the best parameters are obtained. Therefore, the maximum value of highest frequency of histogram is searched to obtain the best parameters of the sphere by using the polytope method. By using the polytope method, the proposed method can extract the sphere from 3D vertex data without a large memory space or long processing time.