Abstract: Although deep learning based object detection is of great significance for various applications, it faces challenges when deployed on edge devices due to the computation and energy limitations.Post-training quantization (PTQ) can improve inference efficiency through integer computing. However, they suffer from severe performance degradation when performing full quantization due to overlooking the unique characteristics of regression tasks in object detection. In this paper, we are the first to explore regression-friendly quantization and evaluate full quantization on various detectors. We reveal the intrinsic reason behind the difficulty of quantizing regressors with empirical and theoretical justifications, and introduce a novel Regression-specialized Post-Training Quantization (Reg-PTQ) scheme. It includes Filtered Global Loss Integration Calibration to combine the global loss with a two-step filtering mechanism, mitigating the adverse impact of false positive bounding boxes; and Learnable Logarithmic-Affine Quantizer tailored for the non-uniform distributed parameters in regression structures. Extensive experiments on prevalent detectors showcase the effectiveness of the well-designed Reg-PTQ. Notably, our Reg-PTQ achieves $7.6\times$ and $5.4\times$ reduction in computation and storage consumption under INT4 with little performance degradation, which indicates the immense potential of fully quantized detectors in real-world object detection applications.