Semi-Unsupervised Microscopy Segmentation with Fuzzy Logic and Spatial Statistics for Cross-Domain Analysis Using a GUI

Brightfield microscopy of unstained live cells is challenging due to low contrast, dynamic morphology, uneven illumination, and lack of labels. Deep learning achieved SOTA performance on stained, high-contrast images but needs large labeled datasets, expensive hardware, and fails under uneven illumination. This study presents a low-cost, lightweight, annotation-free segmentation method by introducing one-time calibration-assisted unsupervised framework adaptable across imaging modalities and image type. The framework determines background via spatial standard deviation from the local mean. Uncertain pixels are resolved using fuzzy logic, cumulative squared shift of nodal intensity, statistical features, followed by post-segmentation denoising calibration which is saved as a profile for reuse until noise pattern or object type substantially change. The program runs as a script or graphical interface for non-programmers. The method was rigorously evaluated using \textit{IoU}, \textit{F1-score}, and other metrics, with statistical significance confirmed via Wilcoxon signed-rank tests. On unstained brightfield myoblast (C2C12) images, it outperformed \textit{Cellpose 3.0} and \textit{StarDist}, improving IoU by up to 48\% (average IoU = 0.43, F1 = 0.60). In phase-contrast microscopy, it achieved a mean IoU of 0.69 and an F1-score of 0.81 on the \textit{LIVECell} dataset ($n = 3178$), with substantial expert agreement ($\kappa > 0.75$) confirming cross-modality robustness. Successful segmentation of laser-affected polymer surfaces further confirmed cross-domain robustness. By introducing the \textit{Homogeneous Image Plane} concept, this work provides a new theoretical foundation for training-free, annotation-free segmentation. The framework operates efficiently on CPU, avoids cell staining, and is practical for live-cell imaging and biomedical applications.