Symmetry-Based Center and Rotation Refinement for Fiber Diffraction Patterns

X-ray fiber diffraction patterns exhibit four-fold symmetry that can be exploited, through folding and averaging, to improve signal-to-noise ratio. Accurate folding requires a precise sub-pixel estimate of the symmetry center and precise orientation of the meridional pattern axis to the fiber axis: small center or angular errors blur diffraction features, reduce layer-line sharpness, and introduce errors in spacing measurements. A pixel-level estimate is often too imprecise for this purpose, and detector gaps further complicate the alignment objective. We formulate the masked quadrant-folding problem, define a four-quadrant symmetry loss that consistently excludes invalid pixels, and evaluate several refinement strategies: hierarchical coarse-to-fine grid search; ECC-based rigid registration with global center/orientation correction fitting; ECC registration followed by local gradient refinement; and a hybrid that appends a local grid search on a cropped pattern. Direct gradient optimization from the rough QF alignment was found to be unreliable. Grid search provides a robust, interpretable baseline that directly minimizes the folding objective but is substantially slower than registration; ECC gives a fast near-correct alignment, and the hybrid closes the accuracy gap to brute-force search at a fraction of its runtime. On real datasets with calibration data, applying a calibration center with optimized rotation is effectively optimal. The hybrid center-refinement method has been integrated into the MuscleX package.