How self-similar are artworks at different levels of spatial resolution?

Recent research has shown that a large variety of aesthetic paintings are highly self-similar. The degree of self-similarity seen in artworks is close to that observed for complex natural scenes, to which low-level visual coding in the human visual system is adapted. In this paper, we introduce a new measure of self-similarity, which we will refer to as the Weighted Self-Similarity (WSS). Using PHOG, which is a state-of-the-art technique from computer vision, WSS is derived from a measure that has been previously linked to aesthetic paintings and represents self-similarity on a single level of spatial resolution. In contrast, WSS takes into account the similarity values at multiple levels of spatial resolution. The values are linked to each other by using a weighting factor so that the overall self-similarity of an image reflects how self-similarity changes at different spatial levels. Compared to the previously proposed metric, WSS has the advantage that it also takes into account differences between self-similarity at different levels of spatial resolution with respect to one another.