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

Semi-Calibrated Near-Light Photometric Stereo

International audienceWe tackle the nonlinear problem of photometric stereo under close-range pointwise sources, when the intensities of the sources are unknown (so-called semi-calibrated setup). A variational approach aiming at robust joint recovery of depth, albedo and intensities is proposed. The resulting nonconvex model is numerically resolved by a provably conver-gent alternating minimization scheme, where the construction of each subproblem utilizes an iteratively reweighted least-squares approach. In particular, manifold optimization technique is used in solving the corresponding subproblems over the rank-1 matrix manifold. Experiments on real-world datasets demonstrate that the new approach provides not only theoretical guarantees on convergence, but also more accurate geometry

Photometric Stereo-Based 3D Reconstruction Method for the Objective Evaluation of Fabric Pilling

Fabric pilling evaluation has been considered as an essential element for textile quality inspection. Traditional manual method is still based on human eyes and brain, which is subjective with low efficiency. This paper proposes an objective evaluation method based on semi-calibrated near-light Photometric Stereo (PS). Fabric images are digitalized by self-developed image acquisition system. The 3D depth information of each point could be obtained by PS algorithm and then mapped to 2D grayscale image. After that, the non-textured image could be filtered by using the Gaussian low-pass filter. The pilling segmentation is conducted by using global iterative threshold segmentation method, and then K-Nearest Neighbor (KNN) is finally selected as a tool for the grade classification of fabric pilling. Our experimental results show that the proposed evaluation system could achieve excellent judging performance for the objective pilling evaluation