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.