Minimum description length clustering to measure meaningful image complexity

We present a new image complexity metric. Existing complexity metrics cannot distinguish meaningful content from noise, and give a high score to white noise images, which contain no meaningful information. We use the minimum description length principle to determine the number of clusters and designate certain points as outliers and, hence, correctly assign white noise a low score. The presented method is a step towards humans' ability to detect when data contain a meaningful pattern. It also has similarities to theoretical ideas for measuring meaningful complexity. We conduct experiments on seven different sets of images, which show that our method assigns the most accurate scores to all images considered. Additionally, comparing the different levels of the hierarchy of clusters can reveal how complexity manifests at different scales, from local detail to global structure. We then present ablation studies showing the contribution of the components of our method, and that it continues to assign reasonable scores when the inputs are modified in certain ways, including the addition of Gaussian noise and the lowering of the resolution. Code is available at https://github.com/Lou1sM/meaningful_image_complexity.