3 research outputs found
Variational Uncalibrated Photometric Stereo under General Lighting
Photometric stereo (PS) techniques nowadays remain constrained to an ideal
laboratory setup where modeling and calibration of lighting is amenable. To
eliminate such restrictions, we propose an efficient principled variational
approach to uncalibrated PS under general illumination. To this end, the
Lambertian reflectance model is approximated through a spherical harmonic
expansion, which preserves the spatial invariance of the lighting. The joint
recovery of shape, reflectance and illumination is then formulated as a single
variational problem. There the shape estimation is carried out directly in
terms of the underlying perspective depth map, thus implicitly ensuring
integrability and bypassing the need for a subsequent normal integration. To
tackle the resulting nonconvex problem numerically, we undertake a two-phase
procedure to initialize a balloon-like perspective depth map, followed by a
"lagged" block coordinate descent scheme. The experiments validate efficiency
and robustness of this approach. Across a variety of evaluations, we are able
to reduce the mean angular error consistently by a factor of 2-3 compared to
the state-of-the-art.Comment: Haefner and Ye contributed equall
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
Photometric Depth Super-Resolution
This study explores the use of photometric techniques (shape-from-shading and
uncalibrated photometric stereo) for upsampling the low-resolution depth map
from an RGB-D sensor to the higher resolution of the companion RGB image. A
single-shot variational approach is first put forward, which is effective as
long as the target's reflectance is piecewise-constant. It is then shown that
this dependency upon a specific reflectance model can be relaxed by focusing on
a specific class of objects (e.g., faces), and delegate reflectance estimation
to a deep neural network. A multi-shot strategy based on randomly varying
lighting conditions is eventually discussed. It requires no training or prior
on the reflectance, yet this comes at the price of a dedicated acquisition
setup. Both quantitative and qualitative evaluations illustrate the
effectiveness of the proposed methods on synthetic and real-world scenarios.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence
(T-PAMI), 2019. First three authors contribute equall