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The complexity of an image tells many aspects of the image content and is an important factor in the selection of source material for testing various image processing methods. We explore objective measures of complexity that are based on compression. We show that spatial information (SI) measures strongly correlate with compression-based complexity measures. Among the commonly used SI measures, the mean of the edge magnitude is shown to be the best predictor. Moreover, we find that compression-based complexity of an image normally increases with decreasing resolution.