A Viscosity Solution Method for Shape-from-shading without Image Boundary Data
نویسندگان
چکیده
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”; 2) it unifies the works of Rouy et al. [18, 25], Falcone et al. [12], Prados et al. [21, 24], based on the notion of viscosity solutions and the work of Dupuis and Oliensis [11] dealing with classical solutions. AMS Subject Classification. — Please, give AMS classification codes —.
منابع مشابه
Shape from Shading with discontinuous image brightness
The Shape–from–Shading models in image analysis lead to first order Hamilton– Jacobi equations which may have several weak solutions (in the viscosity sense). Moreover, for real images, these equations are highly discontinuous in the space variable. The lack of uniqueness and the irregularity of the coefficients involve some troubles when we try to compute a solution. In order to avoid these di...
متن کاملNumerical Solution of the Perspective Shape-from-Shading Problem
We study the Perspective Shape from Shading problem from the numerical point of view presenting a simple algorithm to compute its solution. The scheme is based on a semi-Lagrangian approximation of the first order Hamilton-Jacobi equation related to the problem. The scheme is converging to the weak solution (in the viscosity sense) of the equation and allows to compute accurately regular as wel...
متن کاملUnifying Approaches and Removing Unrealistic Assumptions in Shape from Shading: Mathematics Can Help
This article proposes a solution of the Lambertian Shape From Shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solutions. 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. Note that, in the previous SFS work of Rouy et al. [23, 15], Falcone et ...
متن کاملA Unified Approach to the Well-Posedness of Some Non-Lambertian Models in Shape-from-Shading Theory
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 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....
متن کاملA New Shape from Shading Approach for Specular Surfaces
Shape recovery is a basic problem in computer vision. Shape from shading (SFS) is an approach to get the 3D shape from a single shading image. Diffuse model is usually used to approximate the surface reflectance property. For specular surfaces, however, it is not suitable. In this paper, we propose a new SFS approach for specular surfaces. The Blinn-Phong reflectance model is applied to charact...
متن کامل