On the well-posedness of uncalibrated photometric stereo under general lighting - Normandie Université Access content directly
Book Sections Year : 2020

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

Abstract

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.
Fichier principal
Vignette du fichier
Brahimi2020_uncalibrated_PS.pdf (671.25 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02297643 , version 1 (26-09-2019)
hal-02297643 , version 2 (06-04-2020)

Identifiers

Cite

Mohammed Brahimi, Yvain Quéau, Bjoern Haefner, Daniel Cremers. On the well-posedness of uncalibrated photometric stereo under general lighting. Durou, Jean-Denis; Falcone, Maurizio; Queau, Yvain; Tozza, Silvia. Advances in Photometric 3D-Reconstruction, Springer International Publishing, pp.147--176, 2020, Advances in Computer Vision and Pattern Recognition, ⟨10.1007/978-3-030-51866-0_5⟩. ⟨hal-02297643v2⟩
261 View
298 Download

Altmetric

Share

Gmail Facebook X LinkedIn More