<p>Topology optimization is a method that achieves optimal structural performance by optimizing material distribution and has been widely applied in fields such as aerospace, automotive manufacturing, and biomedical engineering. Although various methods have been developed to address numerical instability issues in topology optimization, such as checkerboard patterns, gray-scale phenomena, and mesh dependence, effectively selecting an appropriate filtering radius remains a key challenge. To address this, this paper proposes a quantitative method based on gray-scale analysis, conducting frequency domain analysis via 2D discrete Fourier transform (DFT) and combining clustering ratio and clustering index. This method systematically investigates the impact of the filtering radius on numerical instability issues and precisely determines the optimal filtering radius. The effectiveness of the proposed method is validated through numerical experiments, where a comprehensive evaluation index <i>S</i> is defined to determine the optimal filtering radius value under different application scenarios. Unlike traditional empirical rules, the method proposed in this paper improves the precision of filtering radius selection through frequency domain feature analysis, significantly reduces numerical instability, and ensures the accuracy and stability of the optimization results. The research results show that the filtering radius selection method based on gray-scale analysis enhances computational efficiency, optimizes structural performance and manufacturability, and avoids the additional costs that may arise from improper filtering radius selection. This study provides a theoretical foundation and quantitative guidance for the parameter selection of filtering techniques in topology optimization, offering significant engineering application value.</p>