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. 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.

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 $I=n\cdot L$, where $I$ is a (known) vector of $m$ observed intensities, $n$ is the (unknown) surface normal, and $L$ is a (known) $3\times m$ 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. Current research aims to make the method work in the presence of projected shadows, highlights, and non-uniform lighting.

See also

• Photometry
• Stereo vision
• 3D scanner

References

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