Multi-Channel Functional Gradient–Entropy Model for Robust Road Boundary Detection in Complex Visual Environments

Accurate and consistent road boundary detection remains a fundamental requirement in autonomous driving, traffic surveillance, and intelligent transportation systems, particularly under diverse lighting and environmental conditions.To address the limitations of classical edge detectors in complex outdoor scenarios, a novel multi-channel edge detection framework is proposed, termed the Multi-Channel Functional Gradient-Entropy (MC-FGE) model.This model has been specifically designed for colour road imagery and incorporates a mathematically principled architecture to enhance structural clarity and semantic relevance.The initial phase involves channel-wise normalization of RGB data, followed by the computation of a fused gradient magnitude that preserves edge information across heterogeneous spectral distributions.Two original mathematical constructs are introduced: the Spectral Curvature Function (SCF), which quantifies local geometric sharpness by leveraging first-and second-order differential operators while exhibiting resilience to noise; and the Colour Entropy Potential Function, which captures local texture complexity and intensity-driven irregularity through entropy analysis of chromatic distributions.These functions are combined into a unified Functional Edge Strength Map (FESM), designed to emphasize semantically meaningful road-related boundaries while suppressing irrelevant background textures.A central innovation is the Log-Root Adaptive Thresholding Function (LRATF), which adaptively modulates threshold sensitivity by integrating curvature and entropy cues in a logarithmic-root formulation, thereby improving robustness to illumination variability, occlusions, and shadow interference.The final binary edge map is derived through precision thresholding of the FESM and refined using morphological post-processing to ensure topological continuity and suppress artefactual edge fragments.Quantitative and qualitative evaluations conducted across varied outdoor datasets demonstrate that the MC-FGE model consistently outperforms conventional edge detectors such as Canny, Sobel, and Laplacian of Gaussian, particularly in scenarios involving texture-rich road surfaces, poor lighting, and partial occlusion.The model not only exhibits enhanced detection accuracy and edge coherence but also offers improved interpretability of road features, contributing both a rigorous theoretical foundation and a scalable computational framework for adaptive edge-based scene understanding in road environments.