Loading...
Please wait, while we are loading the content...
Similar Documents
"Perspective Shape from Shading" and Viscosity Solutions (2003)
| Content Provider | CiteSeerX |
|---|---|
| Author | Prados, E. Ens, Inria Faugeras, O. |
| Abstract | This article proposes a solution of the Lambertian shape from shading (SFS) problem in the case of a pinhole camera model (performing a perspective projection). Our approach is based upon the notion of viscosity solutions of Hamilton-Jacobi equations. This approach allows us to naturally deal with nonsmooth solutions and provides a mathematical framework 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 whereas most authors assume an orthographic projection (see [2] for a panorama of the SFS problem up to 1989 and [10, 3] for a recent survey), thereby extending the applicability of shape from shading methods to more realistic images. In particular it extends the work of [7] and [8]. Second, by adapting the brightness equation to the perspective problem, we obtain a new partial differential equation (PDE). Results about the existence and uniqueness of its solution are also obtained. Third, it allows us to come up with a new approximation scheme and a new algorithm for computing numerical approximations of the "continuous" solution as well as a proof of their convergence toward that solution. |
| File Format | |
| Publisher Date | 2003-01-01 |
| Access Restriction | Open |
| Subject Keyword | Realistic Image Pinhole Whereas Pinhole Camera Model Perspective Problem Brightness Equation Perspective Projection Sfs Problem Continuous Solution Orthographic Projection New Partial Differential Equation Perspective Shape Lambertian Shape New Approximation Scheme |
| Content Type | Text |
| Resource Type | Article |
