Normalized-Gradient-Entropy-Guided Dynamic-Window Error Function Fitting for Subpixel Edge Localization in Monocular Distance Measurement

Monocular distance measurement estimates the target distance from the apparent size of a known target, and its accuracy is strongly affected by edge localization accuracy. Conventional pixel-level edge detectors provide only integer-pixel positions, which may introduce considerable errors when the target is small or far from the camera. To improve subpixel localization accuracy for blurred edges and the adaptability of fixed sampling windows, this study proposes a normalized-gradient-entropy-guided dynamic-window error-function (ERF) fitting method. An ERF model is used to describe the gray-level transition of a Gaussian-blurred step edge, and gray-level samples are collected along the local gradient direction of each Canny edge candidate. Normalized gradient entropy is introduced to characterize the local gradient distribution and adaptively select 5-, 7-, 9-, or 11-point fitting windows. Synthetic experiments show that the proposed four-parameter dynamic ERF method achieves the lowest overall RMSE and MAE among the compared localization methods, namely 0.163 pixel and 0.124 pixel, respectively. Real monocular distance-measurement experiments show that the proposed method achieved the lowest mean absolute error of 0.976 cm and the lowest mean relative error of 0.504%, demonstrating improved target-edge size extraction and ranging stability.