# 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

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topPrados, 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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