  The effects of many physical processes in the intracluster medium of galaxy
clusters imprint themselves in X-ray surface brightness images. It is therefore
important to choose optimal methods for extracting information from and
enhancing the interpretability of such images. We describe in detail a gradient
filtering edge detection method that we previously applied to images of the
Centaurus cluster of galaxies. The Gaussian gradient filter measures the
gradient in the surface brightness distribution on particular spatial scales.
We apply this filter on different scales to Chandra X-ray observatory images of
two clusters with AGN feedback, the Perseus cluster and M87, and a merging
system, A3667. By combining filtered images on different scales using radial
filters spectacular images of the edges in a cluster are produced. We describe
how to assess the significance of features in filtered images. We find the
gradient filtering technique to have significant advantages for detecting many
kinds of features compared to other analysis techniques, such as
unsharp-masking. Filtering cluster images in this way in a hard energy band
allows shocks to be detected.
