High-Speed Calculation of Convex Hull in 2D Images Using FPGA

Given a set of points, a convex hull is the smallest convex polygon containing all the points. In this paper, we describe a high-speed method for calculating the convex hull of 2D images based on Andrew's monotone chain algorithm using FPGA. This algorithm arranges input points in ascending order, according to their y-coordinates, and repeatedly checks for convexity using every group of three subsequent points by calculating the cross product of the vectors they generate. In order to arrange the points in ascending order, they must be sorted by their y-coordinates, which tends to significantly increase the total execution time when calculating the convex hull in larger images. In our method, (1) all the points on a row in a given image are acquired in parallel, (2) only the points that can compose the convex hull are selected, and (3) the convex hull is concurrently built from the selected points during the previous steps. These three steps are successively executed until all rows in the image have been processed. The FPGA implementation of our method produces throughput 23.2 times faster than the GPU implementation.