Symmetric Cross-Entropy: A Novel Multi-Level Thresholding Method and Comprehensive Study of Entropy for High-Precision Arctic Ecosystem Segmentation

Arctic sea ice is a critical indicator of global climate dynamics, directly influencing maritime navigation, polar biodiversity, and offshore engineering safety. The precise mapping of diverse ice types, such as frazil ice, slush, melt ponds, and open water, is essential for environmental monitoring; however, it remains a formidable challenge in satellite remote sensing. These difficulties arise from low-contrast imagery, overlapping spectral signatures, and the subtle textural nuances characteristic of polar regions. Traditional entropy-based thresholding techniques often falter when segmenting these complex scenes, as they typically rely on Gaussian distribution assumptions that do not align with the stochastic nature of Arctic data. To address these limitations, this paper presents a novel unsupervised segmentation framework based on symmetric cross-entropy (SCE). Unlike standard directional measures, SCE provides a more robust objective function for multi-level thresholding by simultaneously maximizing intra-class cohesion and minimizing inter-class ambiguity. The proposed method uses an optimized search strategy to identify intensity levels that best delineate complex Arctic features. We conducted an extensive entropy-based comparative study that benchmarked SCE against 25 state-of-the-art entropy measures, including Shannon, Kapur, Rényi, Tsallis, and Masi entropies. Our experimental results demonstrate that the SCE method: (i) achieves superior accuracy by consistently outperforming established models in segmentation precision and boundary definition; (ii) provides visual clarity by producing segments with significantly reduced noise, making them ideal for identifying small-scale melt ponds and slush zones; and (iii) demonstrates computational robustness by providing stable threshold values even in datasets with non-Gaussian class distributions and poor illumination. Ultimately, these improvements deliver high-quality ice feature data that enhance risk assessment, operational planning, and predictive modeling. This research marks a major step forward in Arctic sea studies and introduces a valuable new tool for wider image processing and computer vision communities.