Graph-Based Relaxation for Over-Normalization Avoidance in Reflectance Normalization of Multi-Temporal Satellite Imagery

Reflectance normalization is critical for minimizing temporal discrepancies and facilitating reliable multi-temporal satellite analysis. However, this process is challenged by the risks of under-normalization and over-normalization, which stem from the inherent complexities of varying atmospheric conditions, data acquisition, and environmental dynamics. Under-normalization occurs when multi-temporal variations are insufficiently corrected, resulting in temporal reflectance inconsistencies. Over-normalization arises when overly aggressive adjustments suppress meaningful variability, such as seasonal and phenological patterns, thereby compromising data integrity. Effectively addressing these challenges is essential for preserving the spatial and temporal fidelity of satellite imagery, which is crucial for applications such as environmental monitoring and long-term change analysis. This study introduces a novel graph-based relaxation for reflectance normalization aimed at addressing issues of under- and over-normalization through a two-stage structural normalization strategy: intra-normalization and inter-normalization. A graph structure represents adjacency and similarity among image instances, enabling an iterative relaxation process to adjust reflectance values. In the proposed framework, the intra-normalization stage aligns images within the same reflectance group to preserve temporally local reflectance patterns, while the inter-normalization stage harmonizes reflectance across different groups, ensuring smooth temporal transitions and maintaining essential temporal variability. Experimental results with the metrics root mean squared error (RMSE) and Structural Similarity Index Measure (SSIM) demonstrate the effectiveness of the proposed method. Specifically, the proposed method achieves around 37% improvement measured by RMSE in the transition of two adjacent image groups compared with related normalization methods. Graph-based relaxation preserves seasonal dynamics, ensures smooth transitions, and improves vegetation indices, making it suitable for both short-term and long-term environmental change analysis.