A new outlier rejection approach for non-Lambertian photometric stereo

Photometric stereo (PS) has garnered increasing attention due to its adeptness in restoring local fine textures. However, non-Lambertian reflections present in almost all real-world objects limit the effectiveness of the Lambertian model for surface normal vector estimation. Although BRDF-based and deep learning-based methods have become mainstream, recent research shows that comparable accuracy can also be achieved through simple filtering of observed intensity values. Nevertheless, these methods only consider the relative bias of pixel values and require manual specification of the number of pixels to be culled and the number of iterations. To address these issues, this paper proposes corresponding improvement methods. Firstly, a weighted inter-relationship function (IRF) fused with Huber loss is introduced to robustly and effectively evaluate the abnormal degree of pixel value. Secondly, based on the IRF curve and histogram statistical analysis, the number of excluded pixels is adaptively calculated. Thirdly, linear equations are then constructed based on the photometric equations, and the maximum between-class variance method is employed to achieve a high degree of sparsity, enabling fast and effective normal vector estimation. Finally, to verify the effectiveness of the proposed algorithm for non-Lambertian PS vision, quantitative verification tests on the synthetic dataset and the open-source datasets “DiLiGenT” and “DiLiGenT-PI” in real-world scenarios, and qualitative assessment experiments on real metal roughness samples are conducted. The experimental results demonstrate that, compared with the position threshold and IRF methods, our algorithms not only significantly enhance the accuracy of normal vector solutions but also markedly improve the operational efficiency of the algorithm, laying a solid foundation for practical online applications. These results fully validate the correctness and effectiveness of the proposed algorithm and provide a reference for the further development of outlier removal algorithms.