Structural stability and thermodynamics of artistic composition

Chan, San To; Fried, Eliot

doi:10.51094/jxiv.858

##article.authors##

Chan, San To 沖縄科学技術大学院大学力学と材料科学ユニット
Fried, Eliot 沖縄科学技術大学院大学力学と材料科学ユニット https://groups.oist.jp/mmmu/eliot-fried

DOI:

https://doi.org/10.51094/jxiv.858

キーワード:

デジタル絵、画像解析、エントロピー、複雑性、安定性

抄録

Inspired by the way that digital artists zoom out of the canvas to assess the clarity of their works, we introduce a conceptually simple yet effective metric for quantifying the visual clarity of digital images. This metric contrasts original images with progressively ``melted'' counterparts, produced by randomly flipping adjacent pixel pairs. It measures the presence of stable structures, assigning the value zero to completely uniform or random images and finite values for those with discernible patterns. This metric respects the color diversity of the original image and withstands image compression and color quantization. Its suitability for diverse image analysis problems is demonstrated through its effective evaluation of visual textures, the identification of structural transitions in physical systems like the Potts and XY models, and its consistency with color theory in digital arts. This allows us to demonstrate that colors in visual art function as a state variable, akin to the spin configuration in magnets, driving artistic designs to transition between states having distinct visual stability. When combined with the Shannon entropy, which quantifies color diversity, the structural stability metric can serve as a navigation tool for artists to explore pathways on the complex structural information landscape toward the completion of their artwork. As a practical demonstration, we apply our metric to refine and optimize an emote design for a video game. The structural stability metric emerges as a versatile tool for extracting nuanced structural information from digital images, enhancing decision-making and data analysis across scientific and creative domains.

利益相反に関する開示

本著者には申告すべき利益相反はありません

ダウンロード *前日までの集計結果を表示します

ダウンロード実績データは、公開の翌日以降に作成されます。

引用文献

M. M. France, A. Hénault, and J. Mandelbrojt, “Art, therefore entropy,” Leonardo 27, 219–221 (1994).

P. Machado, J. Romero, M. Nadal, A. Santos, J. Correia, and A. Carballal, “Computerized measures of visual complexity,” Acta Psychol. 160, 43–57 (2015).

S. Martiniani, P. M. Chaikin, and D. Levine, “Quantifying hidden order out of equilibrium,” Phys. Rev. X 9, 011031 (2019).

S. Lakhal, A. Darmon, J. P. Bouchaud, and M. Benzaquen, “Beauty and structural complexity,” Phys. Rev. Res. 2, 022058 (2020).

K. G. Larkin, “Reflections on shannon information: In search of a natural information-entropy for images,” arXiv preprint arXiv:1609.01117 (2016).

T. M. Khan, S. S. Naqvi, and E. Meijering, “Leveraging image complexity in macro-level neural network design for medical image segmentation,” Sci. Rep. 12, 22286 (2022).

H. V. Ribeiro, L. Zunino, E. K. Lenzi, P. A. Santoro, and R. S. Mendes, “Complexity-entropy causality plane as a complexity measure for two-dimensional patterns,” PLoS One 7, 1–9 (2012).

H. Y. D. Sigaki, M. Perc, and H. V. Ribeiro, “History of art paintings through the lens of entropy and complexity,” Proc. Natl. Acad. Sci. U. S. A. 115, E8585–E8594 (2018).

C. Bandt and K. Wittfeld, “Two new parameters for the ordinal analysis of images,” Chaos 33 (2023).

A. A. Bagrov, I. A. Iakovlev, A. A. Iliasov, M. I. Katsnelson, and V. V. Mazurenko, “Multiscale structural complexity of natural patterns,” Proc. Natl. Acad. Sci. U. S. A. 117, 30241–30251 (2020).

V. V. Mazurenko, I. A. Iakovlev, O. M. Sotnikov, and M. I. Katsnelson, “Estimating patterns of classical and quantum skyrmion states,” J. Phys. Soc. Jpn. 92, 081004 (2023).

J. Rigau, M. Feixas, and M. Sbert, “Informational aesthetics measures,” IEEE Comput. Graph. Appl. 28, 24–34 (2008).

S. J. Wan, P. Prusinkiewicz, and S. K. M. Wong, “Variance-based color image quantization for frame buffer display,” Color Res. Appl. 15, 52–58 (1990).

J. R. Bentley, “The origin of man’yōgana,” Bull. Sch. Orient. Afr. Stud. 64, 59–73 (2001).

K. Heffernan, “The role of phonemic contrast in the formation of Sino-Japanese,” J. East Asian Linguist. 16, 61–86 (2007).

G. T. Fechner, Elemente der psychophysik, Vol. 2 (Breitkopf u. Härtel, 1860).

D. Algom, “The Weber–Fechner law: A misnomer that persists but that should go away.” Psychol. Rev. 128, 757 (2021).

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust., Speech, Signal Process 29, 1153–1160 (1981).

G. Kylberg and I. M. Sintorn, “On the influence of interpolation method on rotation invariance in texture recognition,” EURASIP J. Image Video Process. 2016, 1–12 (2016).

R. B. Potts, “Some generalized order-disorder transformations,” Math. Proc. Camb. Philos. Soc. 48, 106–109 (1952).

J. Ashkin and E. Teller, “Statistics of two-dimensional lattices with four components,” Phys. Rev. 64, 178 (1943).

E. Ising, Beitrag zur theorie des ferro-und paramagnetismus, Ph.D. thesis, Grefe & Tiedemann Hamburg, Germany (1924).

R. J. Glauber, “Time-dependent statistics of the Ising model,” J. Math. Phys. 4, 294–307 (1963).

K. Kawasaki, “Diffusion constants near the critical point for time-dependent Ising models. I,” Phys. Rev. 145, 224 (1966).

K. Kawasaki, “Diffusion constants near the critical point for time-dependent Ising models. II,” Phys. Rev. 148, 375 (1966).

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).

W. K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika 57, 97–109 (1970).

K. Binder, “Static and dynamic critical phenomena of the two-dimensional q-state Potts model,” J. Stat. Phys. 24, 69–86 (1981).

G. Wahba, “Smoothing noisy data with spline functions,” Numer. Math. 24, 383–393 (1975).

M. E. J. Newman and G. T. Barkema, Monte Carlo methods in statistical physics (Oxford University Press, USA, 1999).

J. P. Sethna, Statistical mechanics: entropy, order parameters, and complexity, Vol. 14 (Oxford University Press, USA, 2021).

V. L. Berezinskii, “Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. classical systems,” Sov. Phys. JETP 32, 493–500 (1971).

J. M. Kosterlitz and D. J. Thouless, “Ordering, metastability and phase transitions in two-dimensional systems,” J. Phys. C: Solid State Phys. 6, 1181 (1973).

J. M. Kosterlitz, “The critical properties of the two-dimensional xy model,” J. Phys. C: Solid State Phys. 7, 1046 (1974).

J. Tobochnik and G. V. Chester, “Monte Carlo study of the planar spin model,” Phys. Rev. B 20, 3761 (1979).

R. Gupta and C. F. Baillie, “Critical behavior of the two-dimensional XY model,” Phys. Rev. B 45, 2883 (1992).

J. Xu and H. R. Ma, “Density of states of a two-dimensional XY model from the Wang-Landau algorithm,” Phys. Rev. E 75, 041115 (2007).

J. F. Yu, Z. Y. Xie, Y. Meurice, Y. Liu, A. Denbleyker, H. Zou, M. P. Qin, J. Chen, and T. Xiang, “Tensor renormalization group study of classical XY model on the square lattice,” Phys. Rev. E 89, 013308 (2014).

P. Jakubczyk and A. Eberlein, “Thermodynamics of the two-dimensional XY model from functional renormalization,” Phys. Rev. E 93, 062145 (2016).

Y. D. Hsieh, Y. J. Kao, and A. W. Sandvik, “Finite-size scaling method for the Berezinskii–Kosterlitz–Thouless transition,” J. Stat. Mech.: Theory Exp. 2013, P09001 (2013).

W. Zhang, J. Liu, and T. C. Wei, “Machine learning of phase transitions in the percolation and XY models,” Phys. Rev. E 99, 032142 (2019).

X. Leoncini, A. D. Verga, and S. Ruffo, “Hamiltonian dynamics and the phase transition of the XY model,” Phys. Rev. E 57, 6377 (1998).

J. N. Onuchic, Z. Luthey-Schulten, and P. G. Wolynes, “Theory of protein folding: the energy landscape perspective,” Annu. Rev. Phys. Chem. 48, 545–600 (1997).

P. G. Debenedetti and F. H. Stillinger, “Supercooled liquids and the glass transition,” Nature 410, 259–267 (2001).

D. J. Wales, “Exploring energy landscapes,” Annu. Rev. Phys. Chem. 69, 401–425 (2018).

C. Wiegand, “The meaning of Mondrian,” J. Aesthet. Art Crit. 2, 62–70 (1943).

A. Chandler, The Aesthetics of Piet Mondrian (MSS Information Corporation New York, 1972).

I. C. McManus, B. Cheema, and J. Stoker, “The aesthetics of composition: A study of Mondrian,” Empirical Studies of the Arts 11, 83–94 (1993).

A. Fallahzadeh and G. Gamache, “Equilibrium and rhythm in Piet Mondrian’s Neo-Plastic compositions,” Cogent Arts Humanit. 5, 1525858 (2018).

H. Bacher and S. Suryavanshi, Vision: Color and Composition for Film (Laurence King Publishing, 2018).

J. A. Parker, R. V. Kenyon, and D. E. Troxel, “Comparison of interpolating methods for image resampling,” IEEE Trans. Med. Imaging 2, 31–39 (1983).

L. M. Martyushev and V. D. Seleznev, “Maximum entropy production principle in physics, chemistry and biology,” Phys. Rep. 426, 1–45 (2006).

G. Paschos, “Perceptually uniform color spaces for color texture analysis: an empirical evaluation,” IEEE Trans. Image Process. 10, 932–937 (2001).

K. T. Litherland and A. I. Mørch, “Instruction vs. emergence on r/place: Understanding the growth and control of evolving artifacts in mass collaboration,” Comput. Human Behav. 122, 106845 (2021).

A. M. Adams, J. Fernandez, and O. Witkowski, “Two ways of understanding social dynamics: Analyzing the predictability of emergent of objects in Reddit r/place dependent on locality in space and time,” arXiv preprint arXiv:2206.03563 (2022).

C. Castellano, S. Fortunato, and V. Loreto, “Statistical physics of social dynamics,” Rev. Mod. Phys. 81, 591 (2009).

A. J. Koch and H. Meinhardt, “Biological pattern formation: from basic mechanisms to complex structures,” Rev. Mod. Phys. 66, 1481 (1994).

A. Nakamasu, G. Takahashi, A. Kanbe, and S. Kondo, “Interactions between zebrafish pigment cells responsible for the generation of Turing patterns,” Proc. Natl. Acad. Sci. U. S. A. 106, 8429–8434 (2009).

S. Kondo and T. Miura, “Reaction-diffusion model as a framework for understanding biological pattern formation,” Science 329, 1616–1620 (2010).

B. M. Alessio and A. Gupta, “Diffusiophoresis-enhanced Turing patterns,” Sci. Adv. 9, eadj2457 (2023).

K. B. Singh and M. S. Tirumkudulu, “Cracking in drying colloidal films,” Phys. Rev. Lett. 98, 218302 (2007).

A. F. Routh, “Drying of thin colloidal films,” Rep. Prog. Phys. 76, 046603 (2013).

M. Leang, F. Giorgiutti-Dauphine, L. T. Lee, and L. Pauchard, “Crack opening: from colloidal systems to paintings,” Soft Matter 13, 5802–5808 (2017).

J. P. Gollub and J. S. Langer, “Pattern formation in nonequilibrium physics,” Rev. Mod. Phys. 71, S396 (1999).

F. Gallaire and P. T. Brun, “Fluid dynamic instabilities: theory and application to pattern forming in complex media,” Philos. Trans. R. Soc. A 375, 20160155 (2017).

S. Zetina, F. A. Godı́nez, and R. Zenit, “A hydrodynamic instability is used to create aesthetically appealing patterns in painting,” PLoS One 10, e0126135 (2015).

B. Palacios, A. Rosario, M. M. Wilhelmus, S. Zetina, and R. Zenit, “Pollock avoided hydrodynamic instabilities to paint with his dripping technique,” PLoS One 14, e0223706 (2019).

R. Zenit, “Some fluid mechanical aspects of artistic painting,” Phys. Rev. Fluids 4, 110507 (2019).

A. J. Reagan, L. Mitchell, D. Kiley, C. M. Danforth, and P. S. Dodds, “The emotional arcs of stories are dominated by six basic shapes,” EPJ Data Sci. 5, 1–12 (2016).

M. Perc, “Beauty in artistic expressions through the eyes of networks and physics,” J. R. Soc. Interface 17, 20190686 (2020).

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1254–1259 (1998).

L. Itti and C. Koch, “Computational modelling of visual attention,” Nat. Rev. Neurosci. 2, 194–203 (2001).

J. Harel, C. Koch, and P. Perona, “Graph-based visual saliency,” in Advances in Neural Information Processing Systems, Vol. 19, edited by B. Schölkopf, J. Platt, and T. Hoffman (MIT Press, 2006).

D. Kim, S. W. Son, and H. Jeong, “Large-scale quantitative analysis of painting arts,” Sci. Rep. 4, 7370 (2014).

B. Lee, D. Kim, S. Sun, H. Jeong, and J. Park, “Heterogeneity in chromatic distance in images and characterization of massive painting data set,” PLoS One 13, e0204430 (2018).

B. Lee, M. K. Seo, D. Kim, I. Shin, M. Schich, H. Jeong, and S. K. Han, “Dissecting landscape art history with information theory,” Proc. Natl. Acad. Sci. U. S. A. 117, 26580–26590 (2020).

A. Karjus, M. Canet Solà, T. Ohm, S. E. Ahnert, and M. Schich, “Compression ensembles quantify aesthetic complexity and the evolution of visual art,” EPJ Data Sci. 12, 21 (2023).

H. H. Jiang, L. Brown, J. Cheng, M. Khan, A. Gupta, D. Workman, A. Hanna, J. Flowers, and T. Gebru, “AI art and its impact on artists,” in Proceedings of the 2023 AAAI/ACM Conference on AI, Ethics, and Society (2023) pp. 363–374.

A. Y. J. Ha, J. Passananti, R. Bhaskar, S. Shan, R. Southen, H. Zheng, and B. Y. Zhao, “Organic or diffused: Can we distinguish human art from AI-generated images?” arXiv preprint arXiv:2402.03214 (2024).