The Push-Relabel algorithm is recognized as one of the efficient algorithms in the field of graph cut, finding widespread applications in computer vision. While its pixel-level parallel implementations are prevalent, existing methods predominantly rely on checkerboard scheduling, imposing inherent constraints on neighborhood size, limited to four. This limitation compro-mises both algorithm precision and efficiency, hindering real-time and high-precision applications. To address these issues, this paper introduces a novel approach to accelerate Push-Relabel algorithm implementation on FPGA in a more universal and efficient manner, supporting variable-sized image block opera-tions. Firstly, by introducing the deferred update strategy, we realize the Pulse-Enhanced Parallel Push-Relabel (PEPPR) algo-rithm to address data contention and conflict in parallel pro-cessing. Secondly, the Simultaneous Weighted Push method is proposed, further enhancing parallel operations. Lastly, we in-troduce the efficient Diffusion Wave Search (DWS) algorithm to expedite algorithm convergence and reduce redundancy. While achieving a modest 1.7x acceleration compared to state-of-the-art implementations, the proposed algorithm (PEPPR-DWS) suc-cessfully overcomes the inherent limitations of checkerboard scheduling in full pixel-level parallelism. In the test based on Middlebury Benchmark V3, the proposed 8-neighborhood im-plementation exhibits a reduction of error rate by over 1% com-pared to the typical 4-neighborhood implementation. It provides a versatile and efficient solution for high-precision and real-time applications, holding substantial potential for practical applica-tions.