# 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}
}
• Published 2004
• Computer Science, Physics
• International Journal of Computer Vision
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
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#### References

SHOWING 1-10 OF 89 REFERENCES
Geometry and photometry in three-dimensional visual recognition
• Mathematics
• 1993
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
• Mathematics, Computer Science
• Comput. Vis. Image Underst.
• 1997
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?
• Mathematics, Computer Science
• Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition
• 1996
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?
• Mathematics, Computer Science
• International Journal of Computer Vision
• 2004
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
• J. Oliensis
• Mathematics, Computer Science
• International Journal of Computer Vision
• 2004
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
• Mathematics, Medicine
• Object Representation in Computer Vision
• 1996
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
• Computer Science
• Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231)
• 1998
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.
• Computer Science, Medicine
• Journal of the Optical Society of America. A, Optics and image science
• 1991
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