This work introduces a novel variational approach to uncalibrated photometric stereo for robustly recovering 3D surface shape, reflectance, and lighting from images under unknown illumination. Unlike classical methods that require calibration, this framework formulates the task as an unsupervised joint optimization problem for both diffuse and specular reflectance. The proposed method incorporates a specialized depth regularizer that acts separately on interior regions and object boundaries, substantially improving depth and albedo estimation. Optimization is performed via a lagged block coordinate descent scheme, alternately updating surface depth, normals, lighting, and albedo components. The effectiveness of this approach is validated on both synthetic and real-world datasets, where it demonstrates strong quantitative improvements over baselines, especially near object boundaries and in regions with specular highlights. The results show that a physically-motivated variational framework can faithfully recover geometry and reflectance from uncalibrated multi-illumination images, advancing the state of the art.