Name
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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1137/100815104 | SIAM J. Imaging Sciences |
Keywords | Field | DocType |
underlying partial differential equation,ambiguity analysis,various numerical test,perspective shape,semi-lagrangian discretization,numerical approximation,numerical result,finite difference discretization,constituting equation,convergence result,numerical approximations,perspective model,iterative approximation scheme,shape from shading,finite difference methods | Convergence (routing),Discretization,Boundary value problem,Mathematical optimization,Mathematical analysis,Viscosity,Finite difference method,Ambiguity,Partial differential equation,Photometric stereo,Mathematics | Journal |
Volume | Issue | ISSN |
5 | 1 | 1936-4954 |
Citations | PageRank | References |
14 | 0.71 | 22 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Breuß | 1 | 168 | 25.45 |
| Emiliano Cristiani | 2 | 132 | 12.58 |
| Jean-Denis Durou | 3 | 273 | 20.42 |
| Maurizio Falcone | 4 | 235 | 19.89 |
| Oliver Vogel | 5 | 95 | 10.68 |