This thesis introduces a novel variational approach to uncalibrated photometric stereo for robust recovery of 3D surface shape, reflectance properties, and lighting from multiple images captured under varying and unknown illumination. Building on recent advances in physically-aware piecewise regularization, the proposed method incorporates a specialized depth regularizer acting separately on interior regions and object boundaries, substantially improving stability and accuracy in the estimation of depth and albedo compared to conventional methods. Unlike classical photometric stereo techniques that require strict calibration or prior knowledge of lighting conditions, the presented framework formulates the simultaneous recovery of normals, diffuse and specular albedo, and lighting parameters as an unsupervised joint optimization problem. Optimization is carried out via a lagged block coordinate descent scheme, alternately updating surface depth, normal maps, lighting coefficients, and albedo, with robust M-estimators and adaptive Huber-TV regularization applied to both diffuse and specular reflectance components. The effectiveness of this approach is validated through extensive experiments on both synthetic datasets—with known ground truth—and real-world multi-illumination image collections. In the synthetic setting, the method accurately reconstructs detailed surfaces and reflectance from controlled geometric and photometric configurations, demonstrating strong quantitative improvements over classical and learning based baselines, especially near object boundaries and in challenging regions with specular highlights. Crucially, when applied to real image datasets, the model retains its robustness, offering high-fidelity 3D reconstruction even in the presence of noise, missing data, or imperfect segmentation, thus evidencing its practical potential beyond laboratory conditions. Overall, this work advances the state of the art in uncalibrated photometric stereo by demonstrating that a variational, physically-motivated framework with piecewise regularization can faithfully recover geometry and reflectance from both synthetic and real uncalibrated multi-illumination images. The results lay the foundation for future efforts toward even more adaptive regularization and application to uncontrolled, in-the-wild photometric datasets, promising safer and more flexible geometry reconstruction for complex materials and scenes.

Treball fi de màster de: Master in Intelligent Interactive Systems

Supervisor: Dr. Antonio Agudo