You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Most conventional photometric stereo algorithms inversely solve a BRDF-based image formation model. However, the actual imaging process is often far more complex due to the global light transport on the non-convex surfaces. This paper presents a photometric stereo network that directly learns relationships between the photometric stereo input and surface normals of a scene. For handling unordered, arbitrary number of input images, we merge all the input data to the intermediate representation called observation map that has a fixed shape, is able to be fed into a CNN. To improve both training and prediction, we take into account the rotational pseudo-invariance of the observation map that is derived from the isotropic constraint. For training the network, we create a synthetic photometric stereo dataset that is generated by a physics-based renderer, therefore the global light transport is considered. Our experimental results on both synthetic and real datasets show that our method outperforms conventional BRDF-based photometric stereo algorithms especially when scenes are highly non-convex.

Cited Abstract(s):
[1]: This paper presents a robust photometric stereo method that effectively compensates for various non-Lambertian corruptions such as specularities, shadows, and image noise. We construct a constrained sparse regression problem that enforces both Lambertian, rank-3 structure and sparse, additive corruptions. A solution method is derived using a hierarchical Bayesian approximation to accurately estimate the surface normals while simultaneously separating the non-Lambertian corruptions. Extensive evaluations are performed that show state-of-the-art performance using both synthetic and real-world images.

[2]: This paper tackles the photometric stereo problem in the presence of inaccurate lighting, obtained either by calibration or by an uncalibrated photometric stereo method. Based on a precise modeling of noise and outliers, a robust variational approach is introduced. It explicitly accounts for self-shadows, and enforces robustness to cast-shadows and specularities by resorting to redescending M-estimators. The resulting non-convex model is solved by means of a computationally efficient alternating reweighted least-squares algorithm. Since it implicitly enforces integrability, the new variational approach can refine both the intensities and the directions of the lighting.

[3]: 

[4]: 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.
Many photometric stereo algorithms recover surface normals of a scene via a simple diffuse reflectance modeling ( , Lambertian) while treating other effects as outliers. For instance, Wu al [4] have proposed a rank-minimization based approach to decompose images into the low-rank Lambertian image and non-Lambertian sparse corruptions. Ikehata al extended their method by constraining the rank-3 Lambertian structure [1] (or the general diffuse structure [3] ) for better computational stability. Recently, Queau al [2] have presented a robust variational approach for inaccurate lighting as well as various non-Lambertian corruptions. While effective, a drawback of this approach is that if it were not for dense diffuse inliers, the estimation fails.