A Variational Method Based Post-Processing Framework for High-Fidelity EBSD Grain-Detection Refinement

Existing grain detection algorithms for EBSD data primarily identify grains based on predefined boundary criteria, leading to poor fidelity of grain detection. Significant deviations may exist between the mean orientation of a grain and the orientations of individual pixels. Here, we propose a variational method based post-processing framework that refines an existing grain detection and addresses this issue by framing the problem as a piecewise constant Mumford-Shah problem, and solving it using a variational method grounded in energy minimization principles. The algorithm employs an iterative thresholding method to enhance pixel orientation similarity within grains while balancing grain boundary length. Compared to existing grain detection algorithms, this approach demonstrates superior fidelity of grain detection, as evidenced by validation on a high-strength low-alloy bainitic steel EBSD map. Setting the threshold misorientation angle as 5° for grain detection, the fraction of pixels with orientation deviation angle from grain mean orientation larger than 5° were reduced from 0.186 for the conventional flood fill algorithm to 0.009 for the proposed one. The detected grain number even decreases from 1093 to 1033. In addition, the influences of different grain detection results on texture analysis and parent phase reconstruction were discussed. Based on the grains detected by the proposed algorithm, the orientation distribution function and pole figure textures characteristic aligns better with those of the EBSD data, and more physically reasonable parent phase reconstruction results were obtained for the case examined here, compared with those based on the conventional flood fill algorithm. This proposed framework offers a powerful tool for grain-detection refinement from EBSD data, and enables more reliable subsequent crystallographic analysis.