Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image

Abstract

To say that beauty is in the eye of the beholder means that beauty is largely subjective so varies from person to person. While the subjectivity view is commonly held, there is also an objectivity view that seeks to measure beauty or aesthetics in some quantitative manners. Christopher Alexander has long discovered that beauty or coherence highly correlates to the number of subsymmetries or substructures and demonstrated that there is a shared notion of beauty—structural beauty—among people and even different peoples, regardless of their faiths, cultures, and ethnicities. This notion of structural beauty arises directly out of living structure or wholeness, a physical and mathematical structure that underlies all space and matter. Based on the concept of living structure, this paper develops an approach for computing the structural beauty or life of an image (L) based on the number of automatically derived substructures (S) and their inherent hierarchy (H). To verify this approach, we conducted a series of case studies applied to eight pairs of images including Leonardo da Vinci’s Mona Lisa and Jackson Pollock’s Blue Poles. We discovered among others that Blue Poles is more structurally beautiful than the Mona Lisa, and traditional buildings are in general more structurally beautiful than their modernist counterparts. This finding implies that goodness of things or images is largely a matter of fact rather than an opinion or personal preference as conventionally conceived. The research on structural beauty has deep implications on many disciplines, where beauty or aesthetics is a major concern such as image understanding and computer vision, architecture and urban design, humanities and arts, neurophysiology, and psychology.

Making a Building Smart with a Co-Created and Continuously Evolving Enjoyable Service Entity—Insights from a Collaborative Study

“…Alexander has showed how a city has a complex structure of overlaps, redundancies, ambiguity, and interactive relationships that allows combining sub-units similar to words of a sentence to form coherent wholes through design [13]. Under the notion of living structure even a mathematical model has been developed to characterize the degree of livingness or structural beauty and the verification findings further supporting the notion that goodness of things or images is largely a matter of fact rather than an opinion or personal preference as commonly conceived [14].…”

Soft Assets Consideration in Smart and Resilient City Development

“…Given many small items that constitute one 'beautiful' image, classifying the inherent scaling hierarchy is useful by thorough (computational) analysis of Jiang and de Rijke's research [17,18]. This paper adopted this analysis to examine municipal decision-making and the level of consideration, and the balancing between soft asset capitals to draw some common patterns for later research.…”

“…There are guiding theories relevant to identifying soft assets and their value creation Jiang and de Rijke [17] explained the idea of a 'Living structure' that was originally prom ulgated by Christopher Alexander. They explain how notions/images, such as 'beauty are largely judged by subjective view but also explained by objective manner [17]. Jian also explained concepts, such as wholeness, '… which can be defined mathematically.…”

“…In Table 1, each soft asset has the properties and values that are created in an organi There are guiding theories relevant to identifying soft assets and their value creation. Jiang and de Rijke [17] explained the idea of a 'Living structure' that was originally promulgated by Christopher Alexander. They explain how notions/images, such as 'beauty', are largely judged by subjective view but also explained by objective manner [17].…”

“…By examining the relations between large and small node relations by node degree distribution, it was understood that the two fundamental laws of living structure were quite relevant to the case of soft assets. This paper did not take a computational approach that was ably undertaken by Jiang and Rijke [17]. However, the idea of living structure is not fully subjective, but still possible to present objectively, and the evolution of an organic process is something in common and very insightful for this paper.…”