In this paper we show that the introduction of an attenuation factor in the brightness equations relative to various perspective shape-from-shading models allows us to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solutions and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton–Jacobi equations associated to these models.

A unified approach to the well-posedness of some non-lambertian models in shape-from-shading theory / Camilli, Fabio; Tozza, Silvia. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - STAMPA. - 10:1(2017), pp. 26-46. [10.1137/16M1066397]

A unified approach to the well-posedness of some non-lambertian models in shape-from-shading theory

CAMILLI, FABIO;TOZZA, SILVIA
2017

Abstract

In this paper we show that the introduction of an attenuation factor in the brightness equations relative to various perspective shape-from-shading models allows us to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solutions and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton–Jacobi equations associated to these models.
2017
Maximum principle; Non-Lambertian models; Perspective model; Shape-from-shading; Stationary Hamilton–Jacobi equations; Viscosity solution; Mathematics (all); Applied Mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
A unified approach to the well-posedness of some non-lambertian models in shape-from-shading theory / Camilli, Fabio; Tozza, Silvia. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - STAMPA. - 10:1(2017), pp. 26-46. [10.1137/16M1066397]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/949589
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