Content-based analysis and retrieval of digital images found in scientific articles is often hindered by images consisting of multiple subfigures (compound figures). We address this problem by proposing a method to automatically classify and separate compound figures, which consists of two main steps: (i) a supervised compound figure classifier (CFC) discriminates between compound and non-compound figures using task-specific image features; and (ii) an image processing algorithm is applied to predicted compound images to perform compound figure separation (CFS). Our CFC approach is shown to achieve state-of-the-art classification performance on a published dataset. Our CFS algorithm shows superior separation accuracy on two different datasets compared to other known automatic approaches. Finally, we propose a method to evaluate the effectiveness of the CFC-CFS process chain and use it to optimize the misclassification loss of CFC for maximal effectiveness in the process chain.