Robust photometric stereo via low-rank matrix completion and recovery

Authors:
Lun Wu;Arvind Ganesh;Boxin Shi;Yasuyuki Matsushita;Yongtian Wang;Yi Ma
Affiliations:
School of Optics and Electronics, Beijing Institute of Technology, Beijing;Coordinated Science Lab, University of Illinois at Urbana-Champaign;Key Laboratory of Machine Perception, Peking University, Beijing;Microsoft Research Asia, Beijing;School of Optics and Electronics, Beijing Institute of Technology, Beijing;Coordinated Science Lab, University of Illinois at Urbana-Champaign and Microsoft Research Asia, Beijing
Venue:
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Year:
2010

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Abstract

We present a new approach to robustly solve photometric stereo problems. We cast the problem of recovering surface normals from multiple lighting conditions as a problem of recovering a low-rank matrix with both missing entries and corrupted entries, which model all types of non-Lambertian effects such as shadows and specularities. Unlike previous approaches that use Least-Squares or heuristic robust techniques, our method uses advanced convex optimization techniques that are guaranteed to find the correct low-rank matrix by simultaneously fixing its missing and erroneous entries. Extensive experimental results demonstrate that our method achieves unprecedentedly accurate estimates of surface normals in the presence of significant amount of shadows and specularities. The new technique can be used to improve virtually any photometric stereo method including uncalibrated photometric stereo.