Ultra-Fast FPGA Implementation of Graph Cut Algorithm With Ripple Push and Early Termination

Abstract

Graph cut has been a popular approach widely used to solve the minimum cut problem, which is prevalent in computer vision tasks, although not limited to this field. Push-relabel is considered as one of the promising algorithms of graph cut due to its good potential to be parallelized. However, existing implementations often not only fail to fully exploit the available parallelism but also fail to make full use of the application context to reduce redundant computations. Therefore, they are not competent for application scenarios with high resolution and real-time requirements. To address the issue, we propose three novel techniques to achieve an ultra-fast and efficient FPGA implementation of a push-relabel algorithm. First, we propose a ripple push technique that significantly parallelizes push operations so as to accelerate the push-relabel convergence process. Second, we propose an early-termination technique that effectively removes redundant computations of the push-relabel algorithm. We also theoretically prove the correctness of our early-termination technique. Third, we propose a highly parallelized search technique called flood irrigation search (FIS). It quickly judges early termination conditions based on a pixel parallel architecture. Our implementation focuses on performance-sensitive applications that divide large images into small graph tiles with a specific size. Compared to the state-of-the-art FPGA implementations of push-relabel algorithms, experimental results show that our method can at least achieve <inline-formula> <tex-math notation="LaTeX">$8.93\times $ </tex-math></inline-formula> improvement of execution time.