On the well-posedness of uncalibrated photometric stereo under general lighting

Uncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem under directional lighting are well-established, there is a lack of mathematical evidence for the uniqueness of a solution under general lighting. On the other hand, stable and accurate heuristical solutions of uncalibrated photometric stereo under such general lighting have recently been proposed. The quality of the results demonstrated therein tends to indicate that the problem may actually be well-posed, but this still has to be established. The present paper addresses this theoretical issue, considering first-order spherical harmonics approximation of general lighting. Two important theoretical results are established. First, the orthographic integrability constraint ensures uniqueness of a solution up to a global concave-convex ambiguity , which had already been conjectured, yet not proven. Second, the perspective integrability constraint makes the problem well-posed, which generalizes a previous result limited to directional lighting. Eventually, a closed-form expression for the unique least-squares solution of the problem under perspective projection is provided , allowing numerical simulations on synthetic data to empirically validate our findings

Solving the Uncalibrated Photometric Stereo Problem using Total Variation

International audienceIn this paper we propose a new method to solve the problem of uncalibrated photometric stereo, making very weak assumptions on the properties of the scene to be reconstructed. Our goal is to solve the generalized bas-relief ambiguity (GBR) by performing a total variation regularization of both the estimated normal field and albedo. Unlike most of the previous attempts to solve this ambiguity, our approach does not rely on any prior information about the shape or the albedo, apart from its piecewise smoothness. We test our method on real images and obtain results comparable to the state-of-the-art algorithms

Overcoming shadows in 3-source photometric stereo

Light occlusions are one of the most significant difficulties of photometric stereo methods. When three or more images are available without occlusion, the local surface orientation is overdetermined so that shape can be computed and the shadowed pixels can be discarded. In this paper, we look at the challenging case when only two images are available without occlusion, leading to a one degree of freedom ambiguity per pixel in the local orientation. We show that, in the presence of noise, integrability alone cannot resolve this ambiguity and reconstruct the geometry in the shadowed regions. As the problem is ill-posed in the presence of noise, we describe two regularization schemes that improve the numerical performance of the algorithm while preserving the data. Finally, the paper describes how this theory applies in the framework of color photometric stereo where one is restricted to only three images and light occlusions are common. Experiments on synthetic and real image sequences are presented

Unbiased Photometric Stereo for Colored Surfaces: A Variational Approach

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by IEEE.3D shape recovery using photometric stereo (PS) gained increasing attention in the computer vision community in the last three decades due to its ability to recover the thinnest geometric structures. Yet, the reliability of PS for color images is difficult to guarantee, because existing methods are usually formulated as the sequential estimation of the colored albedos, the normals and the depth. Hence, the overall reliability depends on that of each subtask. In this work we propose a new formulation of color photometric stereo, based on image ratios, that makes the technique independent from the albedos. This allows the unbiased 3D- reconstruction of colored surfaces in a single step, by solving a system of linear PDEs using a variational approach