A viscosity solution method for Shape-From-Shading without image boundary data

Emmanuel Prados; Fabio Camilli; Olivier Faugeras

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 2, page 393-412
  • ISSN: 0764-583X

Abstract

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In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884], [Lions et al., Numer. Math.64 (1993) 323–353], [Falcone and Sagona, Lect. Notes Math.1310 (1997) 596–603], [Prados et al., Proc. 7th Eur. Conf. Computer Vision2351 (2002) 790–804; Prados and Faugeras, IEEE Comput. Soc. Press2 (2003) 826–831], based on the notion of viscosity solutions and the work of [Dupuis and Oliensis, Ann. Appl. Probab.4 (1994) 287–346] dealing with classical solutions.

How to cite

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Prados, Emmanuel, Camilli, Fabio, and Faugeras, Olivier. "A viscosity solution method for Shape-From-Shading without image boundary data." ESAIM: Mathematical Modelling and Numerical Analysis 40.2 (2006): 393-412. <http://eudml.org/doc/249696>.

@article{Prados2006,
abstract = { In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884], [Lions et al., Numer. Math.64 (1993) 323–353], [Falcone and Sagona, Lect. Notes Math.1310 (1997) 596–603], [Prados et al., Proc. 7th Eur. Conf. Computer Vision2351 (2002) 790–804; Prados and Faugeras, IEEE Comput. Soc. Press2 (2003) 826–831], based on the notion of viscosity solutions and the work of [Dupuis and Oliensis, Ann. Appl. Probab.4 (1994) 287–346] dealing with classical solutions. },
author = {Prados, Emmanuel, Camilli, Fabio, Faugeras, Olivier},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Shape-from-shading; boundary data; unification of SFS theories; singular viscosity solutions; states constraints.; states constraints},
language = {eng},
month = {6},
number = {2},
pages = {393-412},
publisher = {EDP Sciences},
title = {A viscosity solution method for Shape-From-Shading without image boundary data},
url = {http://eudml.org/doc/249696},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Prados, Emmanuel
AU - Camilli, Fabio
AU - Faugeras, Olivier
TI - A viscosity solution method for Shape-From-Shading without image boundary data
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/6//
PB - EDP Sciences
VL - 40
IS - 2
SP - 393
EP - 412
AB - In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884], [Lions et al., Numer. Math.64 (1993) 323–353], [Falcone and Sagona, Lect. Notes Math.1310 (1997) 596–603], [Prados et al., Proc. 7th Eur. Conf. Computer Vision2351 (2002) 790–804; Prados and Faugeras, IEEE Comput. Soc. Press2 (2003) 826–831], based on the notion of viscosity solutions and the work of [Dupuis and Oliensis, Ann. Appl. Probab.4 (1994) 287–346] dealing with classical solutions.
LA - eng
KW - Shape-from-shading; boundary data; unification of SFS theories; singular viscosity solutions; states constraints.; states constraints
UR - http://eudml.org/doc/249696
ER -

References

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