# A Semi-Lagrangian Approximation of the Oren–Nayar PDE for the Orthographic Shape–from–Shading Problem

### Silvia Tozza, Maurizio Falcone

#### Abstract

Several advances have been made in the last ten years to improve the Shape–from–Shading model in order to allow its use on real images. The classic Lambertian model, suitable to reconstruct 3D surfaces with uniform reflection properties has shown to be unsuitable for other types of surfaces, for example for rough objects consisting of materials such as clay. Other models have been proposed but it is still unclear what would be the best model. For this reason, we start our analysis for non-Lambertian surfaces. The goal being to find a unique model which should be flexible enough to deal with many kinds of real images. As a starting point for this big project, we consider the non-Lambertian Oren–Nayar reflectance model. In this paper we construct a semi-Lagrangian approximation scheme for its nonlinear partial differential equation and we compare its performances with the classical model in terms of some error indicators on series of benchmarks images.

#### References

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#### Paper Citation

#### in Harvard Style

Tozza S. and Falcone M. (2014). **A Semi-Lagrangian Approximation of the Oren–Nayar PDE for the Orthographic Shape–from–Shading Problem** . In *Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2014)* ISBN 978-989-758-009-3, pages 711-716. DOI: 10.5220/0004855007110716

#### in Bibtex Style

@conference{visapp14,

author={Silvia Tozza and Maurizio Falcone},

title={A Semi-Lagrangian Approximation of the Oren–Nayar PDE for the Orthographic Shape–from–Shading Problem},

booktitle={Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2014)},

year={2014},

pages={711-716},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004855007110716},

isbn={978-989-758-009-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2014)

TI - A Semi-Lagrangian Approximation of the Oren–Nayar PDE for the Orthographic Shape–from–Shading Problem

SN - 978-989-758-009-3

AU - Tozza S.

AU - Falcone M.

PY - 2014

SP - 711

EP - 716

DO - 10.5220/0004855007110716