The Bas-Relief Ambiguity

@article{Belhumeur2004TheBA,
  title={The Bas-Relief Ambiguity},
  author={Peter N. Belhumeur and David J. Kriegman and Alan Loddon Yuille},
  journal={International Journal of Computer Vision},
  year={2004},
  volume={35},
  pages={33-44}
}
AbstractWhen an unknown object with Lambertian reflectance is viewed orthographically, there is an implicit ambiguity in determining its 3-d structure: we show that the object's visible surface f(x, y) is indistinguishable from a “generalized bas-relief” transformation of the object's geometry, $$ {\bar f} $$ (x, y) = λf(x, y) + μx + νy, and a corresponding transformation on the object's albedo. For each image of the object illuminated by an arbitrary number of distant light sources, there… Expand

Figures and Topics from this paper

Isotropy, Reciprocity and the Generalized Bas-Relief Ambiguity
TLDR
An algorithm for recovering full Euclidean geometry from a set of uncalibrated photometric stereo images is presented, and it is shown that the GBR ambiguity is resolved by any non-Lambertian reflectance function that is isotropic and spatially invariant. Expand
The KGBR viewpoint-lighting ambiguity.
TLDR
A novel viewpoint-lighting ambiguity called the KGBR is obtained that corresponds to a group of three-dimensional affine transformations on the object or scene geometry combined with transformations onThe object orscene albedo. Expand
Resolving the Generalized Bas-Relief Ambiguity by Entropy Minimization
TLDR
A new prior on the albedo distribution is proposed : that the entropy of the distribution should be low, justified by the fact that many objects in the real-world are composed of a small finite set of albeda values. Expand
Bas-Relief Ambiguity Reduction in Shape from Shadowgrams
Coplanar shadowgrams provide an affordable mean to retrieve the 3d shape of an object especially when classical stereopsis fails (eg:textureless objects). Its principles are similar to the conceptsExpand
Reflections on the generalized bas-relief ambiguity
TLDR
It is shown that for general nonconvex surfaces, interreflections completely resolve the GBR ambiguity, and the full Euclidean geometry can be recovered from uncalibrated photometric stereo for which the light source directions and strengths are unknown. Expand
3-D Reconstruction of Shaded Objects from Multiple Images Under Unknown Illumination
TLDR
A new model that explicitly enforces positivity in the light sources with the assumption that the object is Lambertian and its albedo is piecewise constant is developed and it is shown that the new model significantly improves the accuracy and robustness relative to existing approaches. Expand
Material — Illumination Ambiguities and the Perception of Solid Objects
TLDR
No evidence for ‘material constancy’ for perception of smooth rendered spheres despite vast quantitative and qualitative differences in illumination and in BRDF between the stimuli is found. Expand
Chapter 16 The Statistics of Shape , Reflectance , and Lighting in Real-World Scenes
Visual perception is a statistical problem par excellence. If the goal of vision is to give a reliable reconstruction of the scenes and objects in the external world from 2D images on the retinas,Expand
A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima
TLDR
This work proposes exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction, and demonstrates several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. Expand
Specularities Reduce Ambiguity of Uncalibrated Photometric Stereo
TLDR
It is shown that if object reflectance is a sum of Lambertian and specular terms, the ambiguity reduces into a 2dof group of transformations (compositions of isotropic scaling, rotation around the viewing vector, and change in coordinate frame handedness). Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 89 REFERENCES
Geometry and photometry in three-dimensional visual recognition
This thesis addresses the problem of visual recognition under two sources of variability: geometric and photometric. The geometric deals with the relation between 3D objects and their views underExpand
Surface Curvature and Shape Reconstruction from Unknown Multiple Illumination and Integrability
TLDR
It is shown that deriving these gradient ratio constants provides just enough calibration information about incident illumination geometry to compute the viewer-centered curvature matrix at each object point, up to a scalar multiple. Expand
What is the set of images of an object under all possible lighting conditions?
  • P. Belhumeur, D. Kriegman
  • Mathematics, Computer Science
  • Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition
  • 1996
TLDR
It is proved that the set of n-pixel images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a conveX polyhedral cone in IR/sup n/ and that the dimension of this illumination cone equals the number of distinct surface normals. Expand
A computer algorithm for reconstructing a scene from two projections
A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the twoExpand
What Is the Set of Images of an Object Under All Possible Illumination Conditions?
TLDR
It is proved that the set of n-pixel images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a conveX polyhedral cone in IRn and that the dimension of this illumination cone equals the number of distinct surface normals. Expand
Photometric stereo under a light source with arbitrary motion
A new photometric-stereo method for estimating the surface normal and the surface reflectance of objects without a priori knowledge of the light-source direction or the light-source intensity isExpand
Uniqueness in shape from shading
  • J. Oliensis
  • Mathematics, Computer Science
  • International Journal of Computer Vision
  • 2004
TLDR
It is argued that most images are effectively impossible, with no corresponding physically reasonable surface, and that any image can be rendered effectively impossible by a small perturbation of its intensities. Expand
Shape Constancy in Pictorial Relief
TLDR
It is concluded that shape constancy under changes in illumination is dominant throughout, but that the (small) deviations from true constancy reveal the effect of cues such as shading in a natural setting. Expand
Illumination cones for recognition under variable lighting: faces
TLDR
This method is both an implementation and extension (an extension in that it models cast shadows) of the illumination cone representation proposed in Belhumeur and Kriegman (1996), and the results exceed those of popular existing methods. Expand
Affine structure from motion.
TLDR
It is indicated how solutions of the structure-from-motion problem can be stratified in such a way that one explicitly knows at which stages various a priori assumptions enter and specific geometrical expertise is required. Expand
...
1
2
3
4
5
...