Skip to Main content Skip to Navigation
Reports

A rigorous and realistic Shape From Shading method and some of its applications

Emmanuel Prados 1 Olivier Faugeras
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : This article proposes a rigorous and realistic solution of the Lambertian Shape From Shading (SFS) problem. The power of our approach is threefolds. First, our work is based on a rigorous mathematical method: we define a new notion of weak solutions (in the viscosity sense) which does not necessarily requires boundary data (contrary to the work of [rouy-tourin:92,prados-faugeras-etal:02,prados-faugeras:03,camilli-falcone:96,falcone-sagona-etal:01]) and which allows to define a solution as soon as the image is (Lipschitz) continuous (contrary to the work of [oliensis:91,dupuis-oliensis:94]). We prove the existence and uniqueness of this (new) solution and we approximate it by using a provably convergent algorithm. Second, it improves the applicability of the SFS to real images: we complete the realistic work of [prados-faugeras:03,tankus-sochen-etal:03], by modeling the problem with a pinhole camera and with a single point light source located at the optical center. This new modelization appears very relevant for applications. Moreover, our algorithm can deal with images containing discontinuities and black shadows. It is very robust to pixel noise and to errors on parameters. It is also generic: i.e. we propose a unique algorithm which can compute numerical solutions of the various perspective and orthographic SFS models. Finally, our algorithm seems to be the most efficient iterative algorithm of the SFS literature. Third, we propose three applications (in three different areas) based on our SFS method.
Document type :
Reports
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download

https://hal.inria.fr/inria-00071450
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 5:34:36 PM
Last modification on : Thursday, February 7, 2019 - 3:50:18 PM
Document(s) archivé(s) le : Sunday, April 4, 2010 - 8:27:29 PM

Identifiers

  • HAL Id : inria-00071450, version 1

Collections

Citation

Emmanuel Prados, Olivier Faugeras. A rigorous and realistic Shape From Shading method and some of its applications. RR-5133, INRIA. 2004. ⟨inria-00071450⟩

Share

Metrics

Record views

565

Files downloads

400