A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory

Fabio Camilli; Silvia Tozza

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arXiv · 1603.06336

A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory

Fabio Camilli·Silvia Tozza

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Abstract

In this paper we show that the introduction of an attenuation factor in the %image irradiance brightness equations relative to various perspective Shape from Shading models allows to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solution 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.

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Fabio Camilli, Silvia Tozza. 2016-03-21. A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory. https://arxiv.org/abs/1603.06336

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