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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.
 An analysis of a large image dataset of aesthetic artworks (the JenAesthetics dataset) and other categories of images reveals that artworks, on average, show a relatively high WSS. Similarly, high values for WSS were obtained for images of natural patterns that can be described as being fractal (for example, images of clouds, branches or lichen growth patterns). The analysis of the JenAesthetics dataset, which consists of paintings of Western provenance, yielded similar values of WSS for different art styles. In conclusion, self-similarity is uniformly high across different levels of spatial resolution in the artworks analyzed in the present study.