Multi-scale structural complexity as a quantitative measure of visual complexity

TL;DR

This work tackles the challenge of objectively quantifying visual complexity and critiques purely informational metrics. It introduces multi-scale structural complexity ($MSSC$), a coarse-graining framework that quantifies scale-wise dissimilarity and aggregates it into ${\cal C}$ via $${\cal C} = \sum_k {\cal C}_k,$$ with ${\cal C}_k = \frac{1}{2} \int_D ( f_{(k+1)d\lambda}(x) - f_{kd\lambda}(x) )^2 dx$, implemented through Fourier-domain processing. Applying $MSSC$ to the SAVOIAS dataset yields correlations with subjective complexity that are comparable to or exceed other computational measures, notably in natural-scene categories, and reveals how complexity emerges at different spatial scales. The study also identifies where $MSSC$ diverges from human judgments, particularly for symbolic art, motivating domain-aware interpretations and future work on informational vs effective complexity, physiological plausibility, and practical design applications. These insights pave the way for hypothesis-driven exploration of visual complexity in perception, aesthetics, and design engineering.

Abstract

While intuitive for humans, the concept of visual complexity is hard to define and quantify formally. We suggest adopting the multi-scale structural complexity (MSSC) measure, an approach that defines structural complexity of an object as the amount of dissimilarities between distinct scales in its hierarchical organization. In this work, we apply MSSC to the case of visual stimuli, using an open dataset of images with subjective complexity scores obtained from human participants (SAVOIAS). We demonstrate that MSSC correlates with subjective complexity on par with other computational complexity measures, while being more intuitive by definition, consistent across categories of images, and easier to compute. We discuss objective and subjective elements inherently present in human perception of complexity and the domains where the two are more likely to diverge. We show how the multi-scale nature of MSSC allows further investigation of complexity as it is perceived by humans.

Figures (11)

• Figure 1: Descriptive measures of complexity tend to prioritize pure randomness over structure, ranking noise as more complex than meaningful images.
• Figure 2: from (Bagrov et al., 2020): schematic representation of the idea behind the coarse graining method. The difference between versions of the image at each step of coarse graining determines partial complexity contributed by the spatial scale removed at that step.
• Figure 3: Coarse graining performed with Fourier Transform, the graph on the right shows partial complexity for each step.
• Figure 4: Categories in the SAVOIAS dataset (Saraee et al.,2018)
• Figure 5: Natural scenes