Extracting Geometric Primitives

Extracting geometric primitives is an important task in model-based computer vision. The Hough transform is the most common method of extracting geometric primitives. Recently, methods derived from the field of robust statistics have been used for this purpose. We show that extracting a single geometric primitive is equivalent to finding the optimum value of a cost function which has potentially many local minima. Besides providing a unifying way of understanding different primitive extraction algorithms, this model also shows that for efficient extraction the true global minimum must be found with as few evaluations of the cost function as possible. In order to extract a single geometric primitive we choose a number of minimal subsets randomly from the geometric data. The cost function is evaluated for each of these, and the primitive defined by the subset with the best value of the cost function is extracted from the geometric data. To extract multiple primitives, this process is repeated on the geometric data that do not belong to the primitive. The resulting extraction algorithm can be used with a wide variety of geometric primitives and geometric data. It is easily parallelized, and we describe some possible implementations on a variety of parallel architectures. We make a detailed comparison with the Hough transform and show that it has a number of advantages over this classic technique.