We present the SWAP Filter: an azimuthally varying, radial normalizing filter specifically developed for EUV images of the solar corona. We discuss the origins of our technique, its implementation and key user-configurable parameters, and highlight its effects on data via a series of examples. We discuss the filter's strengths in a data environment in which wide field-of-view observations that specifically target the low signal-to-noise middle corona are newly available and expected to grow in the coming years.