Activation functions are fundamental components in neural networks, enabling non-linear transformations essential for tasks like signal processing, control systems, image analysis, economics, and robotics. They play a crucial role in facilitating processes such as noise reduction, segmentation, and decision-making across various applications. Splines offer an alternative approach to traditional activation functions (e.g., ReLU or Sigmoid), providing flexibility and adaptability to enhance function approximation. In this work a specific spline, the Piecewise Linear Fractional Function (PLRF), is introduced and proposed as a re-scoring mechanism for soft Non-Maximum Suppression (NMS) in object detection pipelines. The PLRF is parametrized with up to four hyperparameters within the range (0, 1) and the paper presents two black-box optimization techniques, GridFib and HybridNM, to refine hyperparameters. Experimental results on two different datasets indicate that the PLRF achieves higher scores compared to Greedy-NMS and Soft-NMS methods. Furthermore, the number of function evaluations needed with the proposed optimization methods reduces computational evaluations needed relative to the Bayesian optimization technique commonly used in this context.