Photometric stereo under perspective projection

Tankus, Ariel; Kiryati, Nahum

doi:10.1109/iccv.2005.190

Cited by 56 publications

(60 citation statements)

References 24 publications

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“…A similar formulation has been given in [11], however in that paper the authors propose a two step procedure, computing explicitly the partial derivatives in the perspective variables (ξ, η). In other words, they do not treat the system (8) as a PDE system, but rather as a linear system, where the unknowns i.e.…”

Section: Direct Surface Reconstruction Using Multiple Images and Shadowsmentioning

confidence: 99%

“…In order to understand the idea behind the proofs of Lemma 1 and Theorem 1 we refer to [16] where the same results are proved in the case with only two images. We emphasize once more the advantages of this new formulation with respect to [11]. The first is obviously the direct computation of the height of the surface, without passing through the preliminary computation of the partial derivatives.…”

Section: Theorem 1 Let γ(T) Be a Regular Curve Of Discontinuity For mentioning

confidence: 99%

“…We start with 3 images, which is the minimal number of images that allow a computation of the boundary condition without a-priori knowing the albedo [11]. We start by writing the PDEs (5) resulting from each image pair…”

Section: Direct Surface Reconstruction Using Multiple Images and Shadowsmentioning

confidence: 99%

“…Most of the works which addressed the PS problem, for example [1,5,10,11], reconstruct the surface in two steps:…”

Section: Introductionmentioning

confidence: 99%

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Perspective Photometric Stereo with Shadows

Mecca

Rosman

Kimmel

et al. 2013

Lecture Notes in Computer Science

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Abstract. High resolution reconstruction of 3D surfaces from images remains an active area of research since most of the methods in use are based on practical assumptions that limit their applicability. Furthermore, an additional complication in all active illumination 3D reconstruction methods is the presence of shadows, whose presence cause loss of information in the image data. We present an approach for the reconstruction of surfaces via Photometric Stereo, based on the perspective formulation of the Shape from Shading problem, solved via partial differential equations. Unlike many photometric stereo solvers that use computationally costly variational methods or a two-step approach, we use a novel, well-posed, differential formulation of the problem that enables us to solve a first order partial differential equation directly via an alternating directions raster scanning scheme. The resulting formulation enables surface computation for very large images and allows reconstruction in the presence of shadows.

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Section: Direct Surface Reconstruction Using Multiple Images and Shadowsmentioning

confidence: 99%

Section: Theorem 1 Let γ(T) Be a Regular Curve Of Discontinuity For mentioning

confidence: 99%

Section: Direct Surface Reconstruction Using Multiple Images and Shadowsmentioning

confidence: 99%

“…Most of the works which addressed the PS problem, for example [1,5,10,11], reconstruct the surface in two steps:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Perspective Photometric Stereo with Shadows

Mecca

Rosman

Kimmel

et al. 2013

Lecture Notes in Computer Science

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show abstract

“…It is for example impractical to acquire images of a statue. The use of an orthographic model also introduces errors that can be avoided with a perspective model [15]. Perspective cameras allow different kinds of lenses to be used (e.g.…”

Section: Problem Statementmentioning

confidence: 99%

Image-Based Acquisition of Shape and Spatially Varying Reflectance

Haber¹,

Bekaert

2008

Procedings of the British Machine Vision Conference 2008

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The shape and reflectance of complex objects, for use in computer graphics applications, cannot always be acquired using specialized equipment due to cost or pratical considerations. We want to provide an easy and cost-effective way for the approximate recovery of both shape and spatially-varying reflectance of objects using commodity hardware.In this paper, we present an image-based technique for recovering 3D shape and spatially-varying reflectance properties from a sparse set of photographs, taken under varying illumination. Our technique models the reflectance with a set of low-parameter BRDFs without knowledge of the location of the light-sources or camera. This results an a flexible and portable system that can be used in the field.We successfully apply the approach to several objects (synthetic and real), recovering shape and reflectance. The acquired information can then be used to render the object with modifications to geometry and lighting via traditional rendering methods.

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Shape from Shading

Tankus

Sochen

Yeshurun

2009

Wiley Encyclopedia of Computer Science and Engineering

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Shape‐from‐shading (SfS) is a fundamental problem in computer vision. Its goal is reconstruction of surface depth (i.e., distance from camera plane) based on a single image of the surface. The problem was introduced in the early 1970s by Horn. A very common assumption in this field is that image projection is orthographic. We will present the orthographic shape‐from‐shading problem and an algorithm for its solution: the fast marching method of Kimmel and Sethian. We shall than reexamine the basis of SfS, which is the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but on its natural logarithm, and as such it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then described; it is a modification of the aforementioned orthographic fast marching method. Then, a comparison of the orthographic fast marching, perspective fast marching, and the perspective algorithm of Prados and Faugeras on synthetic images is are presented. The two perspective methods equate with each other and show better reconstruction results than the orthographic. We then compare the orthographic and perspective versions of the fast marching method on endoscopic images. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real‐life applications in fields such as endoscopy.

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Photometric stereo under perspective projection

Abstract: Abstract

Cited by 56 publications

References 24 publications

Perspective Photometric Stereo with Shadows

Perspective Photometric Stereo with Shadows

Image-Based Acquisition of Shape and Spatially Varying Reflectance

Shape from Shading

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