View source for Carmichael's totient function conjecture

'''Photometric stereo''' is a technique in [[computer vision]] for estimating the [[surface normals]] of objects by observing that object under different lighting conditions.

The technique was originally introduced by Woodham in 1980.<ref name="Woodham1980">Woodham, R.J. 1980. Photometric method for determining surface orientation from multiple images.  Optical Engineerings 19, I, 139-144.</ref>  The special case where the data is a single image is known as '''shape from shading''', and was analyzed by B. K. P. Horn in 1989.<ref name="BKPHorn89">B. K. P. Horn, 1989. Obtaining shape from shading information. In B. K. P. Horn and M. J. Brooks, eds., Shape from Shading, pages 121–171. MIT Press.</ref>

==Methods==
Under Woodham's original assumptions — [[Lambertian reflectance]], known point-like distant light sources, and uniform [[albedo]] — the problem can be solved by inverting the linear equation <math>I = n \cdot L</math>, where <math>I</math> is a (known) vector of <math>m</math> observed intensities, <math>n</math> is the (unknown) surface normal, and <math>L</math> is a (known) <math>3 \times m</math> matrix of normalized light directions.

Photometric stereo has since been generalized to many other situations, including non-uniform albedo, extended light sources, and non-Lambertian surface finishes.<ref>{{cite web 
  |url=http://www1.uwe.ac.uk/et/mvl/projects/facerecognition.aspx
  |title=A Photometric Stereo Approach to Face Recognition 
  |publisher=University of the West of England
  |accessdate=2011-03-27
}}</ref>  Current research aims to make the method work in the presence of projected shadows, highlights, and non-uniform lighting.

==See also==

* [[Photometry (optics)|Photometry]]
* [[Stereo vision]]
* [[3D scanner]]

==References ==
{{Reflist}}

[[Category:Computer graphics]]
[[Category:Computer vision]]
[[Category:3D imaging]]

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