A Hardware Oriented Approximate Convex Hull Algorithm and its FPGA Implementation

抄録

The convex hull is the minimum convex surrounding a given set of points. Since the process of finding convex hulls has various practical application fields including embedded real-time systems, efficient acceleration of convex hull algorithms is an important problem in computer geometry. In this paper, we discuss an FPGA acceleration approach to address this problem. In order to compute the convex hull of an unsorted point set, it is necessary to store all the points during the computation, and thus the capacity of a on-chip memory is likely to be a major constraint for efficient FPGA implementation. On the other hand, approximate convex hulls are often sufficient for practical applications. Therefore, we propose a hardware oriented approximate convex hull algorithm, which can process the input points as a stream without storing all the points in the memory. We also propose some computation reduction techniques for efficient FPGA implementation. Then, we present FPGA implementation of the proposed algorithm, which is parallelized both in temporal and spatial domains, and evaluate its effectiveness in terms of performance and accuracy. As a result, we demonstrated 11 to 30 times faster performance compared to the widely-used convex hull software library Qhull. In addition, accuracy assessment revealed that the maximum approximation error normalized to the diameters of point sets was 0.038%, which was reasonably small for practical use cases.