The Evolutionary Map of the Universe (EMU) large-area radio continuum survey will detect tens of millions of radio galaxies, giving an opportunity for the detection of previously unknown classes of objects. To maximise the scientific value and make new discoveries, the analysis of this data will need to go beyond simple visual inspection. We propose the coarse-grained complexity, a simple scalar quantity relating to the minimum description length of an image, that can be used to identify images that contain complex and unusual structures. The complexity can be computed without reference to the ensemble or existing catalogue data, making the computation efficient on surveys at very large scales (such as the full EMU survey). We apply our coarse-grained complexity measure to data from the EMU Pilot Survey to detect and confirm anomalous objects in this data set and produce an anomaly catalogue. Rather than work with existing catalogue data using a specific source detection algorithm, we perform a blind scan of the area, computing the complexity using a sliding square aperture. The effectiveness of the complexity measure for identifying anomalous objects is evaluated using crowd-sourced labels generated via the Zooniverse.org platform. We find that the complexity scan captures unusual sources, such as odd radio circles, in the high-value tail of the complexity distribution. We use this distribution to produce catalogues of the 5%, 1% and 0.5% most complex frames with the largest catalogue estimated to be 86% complete and the smallest catalogue 94% pure.