An adaptive multi-scale spatial fuzzy C-means algorithm for unsupervised segmentation of multispectral remote sensing imagesUn algorithme adaptatif multi-échelle de type fuzzy C-means spatial pour la segmentation non supervisée d’images de télédétection multispectrales

Unsupervised segmentation of multispectral remote sensing images remains challenging due to spectral variability, noise contamination, and complex spatial structures. Conventional fuzzy C-means (FCM) clustering relies solely on spectral information and is sensitive to noise, whereas spatial FCM variants with fixed neighborhood regularization may suffer from oversmoothing and loss of fine structural details. To address these limitations, this paper proposes an adaptive multi-scale spatial fuzzy C-means (AM-SFCM) algorithm for multispectral remote sensing image segmentation. The proposed framework integrates adaptive spatial weighting and multi-scale neighborhood fusion into the classical FCM formulation, enabling spatial contextual information to be dynamically adjusted according to local image characteristics. Consequently, AM-SFCM improves spatial coherence while preserving important boundaries and heterogeneous structures. Extensive experiments were conducted on Sentinel-2 multispectral datasets acquired over Hanoi (Vietnam), Paris (France), and New York City (USA). Quantitative evaluations using the partition coefficient, partition entropy, and Xie–Beni indices demonstrate that AM-SFCM consistently achieves competitive or superior clustering performance compared with FCM, SFCM, and fuzzy local information C-means. Qualitative analyses further show that the proposed method produces more coherent segmentation maps, sharper object boundaries, and more reliable confidence distributions. Additional sensitivity and runtime analyses confirm the robustness of the proposed multi-scale design and its stable convergence behavior. The experimental results suggest that AM-SFCM provides a promising framework for unsupervised multispectral remote sensing image segmentation across diverse urban environments.