A Bayesian refinement method incorporating geometric prior and LLM-guided hyperprior for measurement-grade overhang analysis in X-ray electrode inspection

Accurate electrode instance identification from X-ray images is essential for reliable overhang analysis in lithium-ion battery electrode inspection. However, industrial X-ray radiographs often exhibit blurred edges, contrast attenuation, and structural occlusions caused by layer overlap, leading to discontinuous or distorted segmentation masks requiring post refinement. Existing mask refinement methods struggle in such low-contrast and densely packed patterns because they mostly rely on data-driven training without explicit physical knowledge. This paper presents a Bayesian refinement method that corrects coarse electrode masks through probabilistic inference with context-aware geometric priors. The proposed model integrates curvature, lattice, and global assembly priors with the image-based likelihood to derive a maximum a posteriori formulation, while an additional language-conditioned hyperprior estimated by an LLM adaptively modulates the strength of each prior according to morphological context. Importantly, Bayesian MAP inference remains the core optimization engine, and the LLM only provides auxiliary hyperparameter guidance rather than direct mask generation. This design enables training-free, interpretable, and physically consistent restoration of electrode boundaries across diverse imaging conditions. Experiments on real X-ray datasets of cylindrical cells demonstrate that the proposed approach significantly improves the mask quality especially boundary accuracy and continuity compared with existing refinement methods in practical battery inspection. Beyond segmentation fidelity, the refined masks improve measurement-grade overhang analysis, reducing the standard deviation of electrode height and spacing by approximately 18\\% and 22\\%, respectively.