Shepe from Shading with perspective projection and camera calibration

Hasegawa, Júlio Kiyoshi; Tozzi, Clésio Luis

doi:10.1016/0097-8493(96)00004-0

Cited by 27 publications

(25 citation statements)

References 8 publications

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“…They minimize a cost functional based on a local linear approximation of the reflectance map. Hasegawa and Tozzi (1996) suggest to combine SFS with photogrammetry to reconstruct the surface and calibrate the camera. Their method consists in solving large systems of linear equations and seems to be suitable only for small images.…”

Section: Introductionmentioning

confidence: 99%

A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras

Prados

Faugeras

2005

Int J Comput Vision

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We describe a mathematical and algorithmic study of the Lambertian "Shape-From-Shading" problem for orthographic and pinhole cameras. Our approach is based upon the notion of viscosity solutions of HamiltonJacobi equations. This approach provides a mathematical framework in which we can show that the problem is well-posed (we prove the existence of a solution and we characterize all the solutions). Our contribution is threefold. First, we model the camera both as orthographic and as perspective (pinhole), whereas most authors assume an orthographic projection (see Horn and Brooks (1989) for a survey of the SFS problem up to 1989 andZhang et al. (1999), Kozera (1998 for more recent ones); thus we extend the applicability of shape from shading methods to more realistic acquisition models. In particular it extends the work of Prados et al. (2002a) and Rouy and Tourin (1992). We provide some novel mathematical formulations of this problem yielding new partial differential equations. Results about the existence and uniqueness of their solutions are also obtained. Second, by introducing a "generic" Hamiltonian, we define a general framework allowing to deal with both models (orthographic and perspective), thereby simplifying the formalization of the problem. Thanks to this unification, each algorithm we propose can compute numerical solutions corresponding to all the modeling. Third, our work allows us to come up with two new generic algorithms for computing numerical approximations of the "continuous solution of the "Shape-From-Shading" problem as well as a proof of their convergence toward that solution. Moreover, our two generic algorithms are able to deal with discontinuous images as well as images containing black shadows.

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Section: Introductionmentioning

confidence: 99%

A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras

Prados

Faugeras

2005

Int J Comput Vision

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“…Some SFS approaches using perspective projection were found in the literature (e.g. [17], [18]). However, most of these approaches ignore the camera extrinsic parameters, hence cannot provide metric information of the depth.…”

Section: Shape From Shading Using a Calibrated Imagementioning

confidence: 99%

Novel Image-Based 3D Reconstruction of the Human Jaw using Shape from Shading and Feature Descriptors

Abdelrahim

Abdelrahman

Abdelmunim

et al. 2011

Procedings of the British Machine Vision Conference 2011

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In this paper, we propose a novel approach for 3D surface reconstruction of the human jaw. Due to the difficulties of setting up a data acquisition system inside the mouth, we use an intra-oral camera to capture a sequence of calibrated images. These images are registered together to build a panoramic view of the jaw. We incorporate a shape from shading(SFS) algorithm that benefits from camera calibration parameters to build a 3D model from the panoramic image obtained from the previous stage. Our approach results in a 3D surface which has more fine details compared with those resulting from other literature techniques. We will demonstrate different artificial jaws surfaces reconstruction to show the efficiency of our system.

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“…3 to be convinced that the assumption of orthogonal projection is not realistic with regard to our application, that is, the correction of photographs of skew documents, since the text lines are not parallel. The consideration of perspective projection in SFS has been the object, until recently, of only very few works [9,6,3]; moreover, none of these works have proposed a new modeling of SFS. Recently, three groups of authors have simultaneously established a new modeling for perspective SFS [10,12,2].…”

Section: Eikonal Equationmentioning

confidence: 99%