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The volume of data that will be produced by the next generation of astrophysical instruments represents a significant opportunity for making unplanned and unexpected discoveries. Conversely, finding unexpected objects or phenomena within such large volumes of data presents a challenge that may best be solved using computational and statistical approaches. We present the application of a coarse-grained complexity measure for identifying interesting observations in large astronomical data sets. This measure, which has been termed apparent complexity, has been shown to model human intuition and perceptions of complexity. Apparent complexity is computationally efficient to derive and can be used to segment and identify interesting observations in very large data sets based on their morphological complexity. We show, using data from the Australia Telescope Large Area Survey, that apparent complexity can be combined with clustering methods to provide an automated process for distinguishing between images of galaxies which have been classified as having simple and complex morphologies. The approach generalizes well when applied to new data after being calibrated on a smaller data set, where it performs better than tested classification methods using pixel data. This generalizability positions apparent complexity as a suitable machine-learning feature for identifying complex observations with unanticipated features. [ABSTRACT FROM AUTHOR]