In particular when using high-resolution DEM for archaeological prospection and mapping, we are interested in very subtle relief features: Many traces of former human activities (e.g. field boundaries) differ from their surroundings only by centimetres. Over periods of centuries and millenia, formerly distinct anthropogenic features such as burial mounds or fortifications become smoothed by erosion, infilling, ploughing or intentional levelling. As a result, archaeological relief features are often subtle in comparison with the natural topography on which they are superimposed.
A simple method to extract small-scale relief features is trend removal. Just as in the two-dimensional case (e.g. removing the long-term trend from a time series to find anomalies), the three-dimensional case of removing the trend from a DEM is based on smoothing the data and then subtracting the smoothed data set from the original data set.
For smoothing the DEM, a (simple or weighted) average is computed for a moving window surrounding each pixel. For weighted averaging, a Gaussian function is commonly used. The intensity of DEM smoothing when applying such a low-pass filter depends on the size of the filter window and the standard deviation of the Gaussian filter. Subtracting the low-pass filtered DEM from the original DEM effectively means applying a high-pass filter.
The result is a raster map which contains positive and negative values for local bumps and depressions, respectively. To display this raster map as an image, greyscale or colour coding can be applied. Care has to be taken when interpreting such images. All convex and concave terrain edges are highlighted as relative positive and negative relief features, but this does not mean that they are positive and negative relief features in an absolute sense: the dark fringes surrounding the burial mounds in the example do not show actual ring ditches.