Name
Abstract | ||
|---|---|---|
This article proposes a solution of the Lambertian shapefrom shading (SFS) problem in the case of a pinhole cameramodel (performing a perspective projection). Our approachis based upon the notion of viscosity solutions of Hamilton-Jacobiequations. This approach allows us to naturallydeal with nonsmooth solutions and provides a mathematicalframework for proving correctness of our algorithms.Our work extends previous work in the area in three aspects.First, it models the camera as a pinhole whereasmost authors assume an orthographic projection (see [15]for a panorama of the SFS problem up to 1989 and [29, 17]for a recent survey), thereby extending the applicability ofshape from shading methods to more realistic images. Inparticular it extends the work of [24] and [26]. Second, byadapting the brightness equation to the perspective problem,we obtain a new partial differential equation (PDE).Results about the existence and uniqueness of its solutionare also obtained. Third, it allows us to come up with a newapproximation scheme and a new algorithm for computingnumerical approximations of the "continuous" solution aswell as a proof of their convergence toward that solution. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1109/ICCV.2003.1238433 | Nice, France |
Keywords | Field | DocType |
lambertian shapefrom shading,solution aswell,new partial differential equation,brightness equation,perspective shape,perspective problem,viscosity solutions,new algorithm,viscosity solution,previous work,nonsmooth solution,sfs problem,shading,partial differential equation,computer vision,partial differential equations,approximation theory,machine vision,pinhole camera model,convergence,shape from shading,perspective projection | Convergence (routing),Applied mathematics,Orthographic projection,Computer science,Mathematical analysis,Correctness,Artificial intelligence,Computer vision,Uniqueness,Perspective (graphical),Partial differential equation,Photometric stereo,Pinhole camera model | Conference |
ISBN | Citations | PageRank |
0-7695-1950-4 | 58 | 2.12 |
References | Authors | |
9 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Emmanuel Prados | 1 | 450 | 20.47 |
| Olivier D. Faugeras | 2 | 9364 | 2568.69 |