Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

Mohammed Brahimi 1 Yvain Quéau 2 Bjoern Haefner 1 Daniel Cremers 1
2 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [45 references]  Display  Hide  Download

https://hal-normandie-univ.archives-ouvertes.fr/hal-02297643
Contributor : Yvain Queau <>
Submitted on : Thursday, September 26, 2019 - 12:11:16 PM
Last modification on : Wednesday, April 8, 2020 - 1:44:15 AM
Long-term archiving on: : Monday, February 10, 2020 - 3:18:14 AM

File

Springer_chapter_UPS.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02297643, version 1

Citation

Mohammed Brahimi, Yvain Quéau, Bjoern Haefner, Daniel Cremers. On the well-posedness of uncalibrated photometric stereo under general lighting. 2019. ⟨hal-02297643v1⟩

Share

Metrics

Record views

83

Files downloads

160