In this paper we study a perspective model for shape from shading and its numerical approximation. We show that an ambiguity still persists, although the model with light attenuation factor has previously been shown to be well-posed under appropriate assumptions. Analytical results revealing the ambiguity are complemented by various numerical tests. Moreover, we present convergence results for two iterative approximation schemes. The first is based on a finite difference discretization, whereas the second is based on a semi-Lagrangian discretization. The convergence results are obtained in the general framework of viscosity solutions of the underlying partial differential equation. In addition to these theoretical and numerical results, we propose an algorithm for reconstructing discontinuous surfaces, making it possible to obtain results of reasonable quality even for complex scenes. To this end, we solve the constituting equation on a previously segmented input image, using state constraint boundary conditions at the segment borders.

Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations / Michael, Breuss; Cristiani, Emiliano; Jean Denis, Durou; Falcone, Maurizio; Oliver, Vogel. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - ELETTRONICO. - 5:1(2012), pp. 311-342. [10.1137/100815104]

Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations

CRISTIANI, Emiliano;FALCONE, Maurizio;
2012

Abstract

In this paper we study a perspective model for shape from shading and its numerical approximation. We show that an ambiguity still persists, although the model with light attenuation factor has previously been shown to be well-posed under appropriate assumptions. Analytical results revealing the ambiguity are complemented by various numerical tests. Moreover, we present convergence results for two iterative approximation schemes. The first is based on a finite difference discretization, whereas the second is based on a semi-Lagrangian discretization. The convergence results are obtained in the general framework of viscosity solutions of the underlying partial differential equation. In addition to these theoretical and numerical results, we propose an algorithm for reconstructing discontinuous surfaces, making it possible to obtain results of reasonable quality even for complex scenes. To this end, we solve the constituting equation on a previously segmented input image, using state constraint boundary conditions at the segment borders.
2012
finite difference methods; shape-from-shading; semi-lagrangian schemes; numerical approximation; hamilton-jacobi equations; ambiguity analysis; shape from shading; ambiguities and ill-posedness
01 Pubblicazione su rivista::01a Articolo in rivista
Perspective Shape from Shading: Ambiguity Analysis and Numerical Approximations / Michael, Breuss; Cristiani, Emiliano; Jean Denis, Durou; Falcone, Maurizio; Oliver, Vogel. - In: SIAM JOURNAL ON IMAGING SCIENCES. - ISSN 1936-4954. - ELETTRONICO. - 5:1(2012), pp. 311-342. [10.1137/100815104]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/443554
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