Photometric stereo

[1] By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited.

[2] 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.

[3] Photometric stereo has since been generalized to many other situations, including 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.

Photometric stereo is widely used in various fields, ranging from archaeology[4] to quality control.

[6] 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

This model can easily be extended to surfaces with non-uniform albedo, while keeping the problem linear.

is square (there are exactly 3 lights) and non-singular, it can be inverted, giving: Since the normal vector is known to have length 1,

is not square (there are more than 3 lights), a generalisation of the inverse can be obtained using the Moore–Penrose pseudoinverse,[8] by simply multiplying both sides with

The classical photometric stereo problem concerns itself only with Lambertian surfaces, with perfectly diffuse reflection.

This is unrealistic for many types of materials, especially metals, glass and smooth plastics, and will lead to aberrations in the resulting normal vectors.

In practice, all of these require many light sources to obtain reliable data.

Some progress has been made towards modelling an even more general surfaces, such as Spatially Varying Bidirectional Distribution Functions (SVBRDF), Bidirectional surface scattering reflectance distribution functions (BSSRDF), and accounting for interreflections.