  Ground based Cherenkov telescope systems measure astrophysical gamma-ray
emission against a background of cosmic-ray induced air showers. The
subtraction of this background is a major challenge for the extraction of
spectra and morphology of gamma-ray sources. The unprecedented sensitivity of
the new generation of ground based very-high-energy gamma-ray experiments such
as H.E.S.S. has lead to the discovery of many previously unknown extended
sources. The analysis of such sources requires a range of different background
modelling techniques. Here we describe some of the techniques that have been
applied to data from the H.E.S.S. instrument and compare their performance.
Each background model is introduced and discussed in terms of suitability for
image generation or spectral analysis and possible caveats are mentioned. We
show that there is not a single multi-purpose model, different models are
appropriate for different tasks. To keep systematic uncertainties under control
it is important to apply several models to the same data set and compare the
results.
