Measuring and evaluating the compactness of superpixels

Superpixel segmentation has become a popular preprocessing step in computer vision with a great variety of existing algorithms. Almost all algorithms claim to compute compact superpixels, but no one showed how to measure compactness and no one investigated the implications. In this paper, we propose a novel metric to measure superpixel compactness. With this metric, we show that there is a trade-off between compactness and boundary recall. In addition, we propose an algorithm that allows to precisely control this trade-off and that outperforms the current state-of-the-art. As a demonstration, we show the importance of considering compactness with the help of an example application.