Directional Diffusion Probabilistic Modelling With Fuzzy Similarity Fields for Multipolarized Petrographic Registration

Accurate registration of multipolarized petrographic thin‐section images is essential for quantitative characterization of rock microstructures under plane‐polarized and cross‐polarized illumination. However, conventional diffusion probabilistic models struggle with the pronounced uncertainty arising from birefringence, textural heterogeneity, illumination variations, and blurred mineral boundaries. To address this, we propose an intuitionistic fuzzy set–guided diffusion probabilistic model for robust registration of multipolarized thin‐section images. We derive an IFS‐based fuzzy similarity field to drive a directional diffusion process and enable semantically consistent propagation of correspondence probabilities. In parallel, a membership‐adaptive diffusion coefficient modulates the diffusion strength according to local correspondence confidence, enhancing propagation in reliable regions while suppressing it in uncertain areas, and an IFS‐weighted loss emphasizes high‐confidence pixels while penalizing high‐hesitancy regions to stabilize optimization in structurally ambiguous zones. Experiments on a benchmark dataset of 2634 rock thin‐section images spanning sedimentary, metamorphic, and igneous lithologies demonstrate that IFS‐DPM preserves mineral grain boundaries, fracture networks, and pore structures under complex textures and multipolarized conditions, providing a robust registration framework for petrographic analysis.