Applications Using Photometric Stereo (PS)

Rough surface description

The description and modelling of rough surfaces is important in the study of friction, scattering theory, computer graphics, texture analysis and many other fields. In this section we first describe the classical techniques used to discriminate and simulate rough surfaces. We then show how techniques from texture analysis can be used to extend the scope of surface description.

A rough surface can be treated as a series of discrete points. The heights of these points are modelled as a random variable. The distribution of heights gives important information about about the surface---a rough surface will have a large standard deviation. A large number parameters have been proposed, however the most common of these, rms roughness is the standard deviation of surface heights.

Measuring surface profile allows the statistical signal processing technologies to be applied

Although there is a degree of randomness at work, adjacent points do have some influence over each other. If the height distribution is Gaussian, then the interaction between different points on the surface can be completely described using the power spectrum or the autocorrelation function. Because two Gaussian surfaces that have the same power spectrum look like different examples of the same type we can use the power spectrum to model surfaces. A series of parametric models of the power spectrum have been proposed: Sayles and Thomas proposed a fractal model, Mulvaney proposed a model of the surface spectrum that is white below a cut-off wavenumber, and fractal above it.