This paper addresses the problem of photometric stereo for non-Lambertian surfaces. Existing approaches often adopt simplified reflectance models to make the problem more tractable, but this greatly hinders their applications on real-world objects. In this paper, we propose a deep fully convolutional network, called PS-FCN, that takes an arbitrary number of images of a static object captured under different light directions with a fixed camera as input, and predicts a normal map of the object in a fast feed-forward pass. Unlike the recently proposed learning based method, PS-FCN does not require a pre-defined set of light directions during training and testing, and can handle multiple images and light directions in an order-agnostic manner. Although we train PS-FCN on synthetic data, it can generalize well on real datasets. We further show that PS-FCN can be easily extended to handle the problem of uncalibrated photometric stereo.Extensive experiments on public real datasets show that PS-FCN outperforms existing approaches in calibrated photometric stereo, and promising results are achieved in uncalibrated scenario, clearly demonstrating its effectiveness.
In this section, we briefly review representative non-Lambertian photometric stereo techniques. More comprehensive surveys of photometric stereo algorithms can be found in @cite_23 @cite_7 . Non-Lambertian photometric stereo methods can be broadly divided into four categories, namely outlier rejection based methods, sophisticated reflectance model based methods, exemplar based methods, and learning based methods.
@cite_7 @cite_23
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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. This paper provides an introduction to photometric methods for image-based 3D shape reconstruction and a survey of photometric stereo techniques. We begin with taxonomy of active and passive shape acquisition techniques. Then we describe the methodical background of photometric 3D reconstruction, define the canonical setting of photometric stereo (Lambertian surface reflectance, parallel incident light, known illumination direction, known surface albedo, absence of cast shadows), discuss the 3D reconstruction of surfaces from local gradients, summarize the concept of the bidirectional reflectance distribution function (BRDF), and outline several important empirically and physically motivated reflectance models. We provide a detailed treatment of several generalizations of the canonical setting of photometric stereo, namely non-distant light sources, unknown illumination directions, and, in some detail, non-Lambertian surface reflectance functions. An important special case is purely specular reflections, where an extended light source allows capturing a surface that consists of perfectly specular surface patches. Linear combinations of purely Lambertian and purely specular reflectance components are favorably used for reconstructing smooth surfaces and also human skin. Nonuniform surface reflectance properties are estimated based on a simultaneous 3D reconstruction and determination of the locally variable parameters of the reflectance function based on a multitude of images. Assuming faceted surfaces, the effective resolution of the 3D reconstruction result can be increased to some extent beyond that of the underlying images. Other approaches separate specular and diffuse reflectance components based on polarization data or color information. The specular reflections can be used additionally to estimate the direction from which the surface is illuminated. Finally, we describe methods to combine photometric 3D reconstruction techniques with active and passive triangulation-based approaches. 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. This paper addresses the problem of photometric stereo for non-Lambertian surfaces. Existing approaches often adopt simplified reflectance models to make the problem more tractable, but this greatly hinders their applications on real-world objects. In this paper, we propose a deep fully convolutional network, called PS-FCN, that takes an arbitrary number of images of a static object captured under different light directions with a fixed camera as input, and predicts a normal map of the object in a fast feed-forward pass. Unlike the recently proposed learning based method, PS-FCN does not require a pre-defined set of light directions during training and testing, and can handle multiple images and light directions in an order-agnostic manner. Although we train PS-FCN on synthetic data, it can generalize well on real datasets. We further show that PS-FCN can be easily extended to handle the problem of uncalibrated photometric stereo. Extensive experiments on public real datasets show that PS-FCN outperforms existing approaches in calibrated photometric stereo, and promising results are achieved in uncalibrated scenario, clearly demonstrating its effectiveness.