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Aesthetic 3D model evolution

Genetic Programming and Evolvable Machines volume 14, pages 339–367 (2013)Cite this article

Abstract

A new research frontier for evolutionary 2D image generation is the use of mathematical models of aesthetics, with the goal of automatically evolving aesthetically pleasing images. This paper investigates the application of similar models of aesthetics towards the evolution of 3-dimensional structures. We extend existing models of aesthetics used for image evaluation to the 3D realm, by considering quantifiable properties of surface geometry. Analyses used include entropy, complexity, deviation from normality, 1/f noise, and symmetry. A new 3D L-system implementation promotes accurate analyses of surface features, as well as productive rule sets when used with genetic programming. Multi-objective evaluation reconciles multiple aesthetic criteria. Experiments resulted in the generation of many models that satisfied multiple criteria. A human survey was conducted, and survey takers showed a statistically significant preference for high-fitness highly-evolved models over low-fitness unevolved ones. This research shows that aesthetic evolution of 3D structures is a promising new research area for evolutionary design.

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References

  1. A3D, Archive 3D. In: http://archive3d.net/ (2012)

  2. P. Bentley, D. Corne, Creative Evolutionary Systems. (Morgan Kaufmann, USA, 2002)

    Google Scholar 

  3. P. Bentley, J. Wakefield, in Soft Computing in Engineering Design and Manufacturing. Finding acceptable solutions in the pareto-optimal range using multiobjective genetic algorithms (Springer, Berlin, 1997)

  4. S. Bergen, Automatic structure Generation using genetic programming and fractal geometry. Master’s thesis, (Department of Computer Science, Brock University, 2011)

  5. S. Bergen, Aesthetic 3D model evolution gallery. http://www.cosc.brocku.ca/~bross/Aesth3Dmodels/ (2012)

  6. S. Bergen, B. Ross, in Genetic Programming—Theory and Practice VIII. Evolutionary art using summed multi-objective ranks. (Springer, Berlin, 2010), pp. 227–244

  7. G.D. Birkhoff, Aesthetic Measure. (Harvard University Press, Cambridge, 1933)

    MATH  Google Scholar 

  8. Blender, http://www.blender.org/. Last Accessed 4 Dec 2011

  9. C.C. Coello, G. Lamont, D.V. Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems. 2nd edn. (Kluwer, Dordrecht, 2007)

    MATH  Google Scholar 

  10. C. Coia, B. Ross, in Proceedings of the CEC 2011, IEEE. Automatic evolution of conceptual building architectures (2011)

  11. J. Conway, H. Burgiel, C. Goodman-Strauss, The Symmetries of Things. (CRC Press, Boca Raton, 2008)

    MATH  Google Scholar 

  12. D. Corne, J. Knowles, in Proceedings of the GECCO 2007. Techniques for highly multiobjective optimisation: some nondominated points are better than others. (ACM Press, New York, 2007), pp. 773–780

  13. M. Field, M. Golubitsky, Symmetry in chaos. (SIAM, Philadelphia, 2009)

    MATH  Google Scholar 

  14. R. Flack, Evolution of architectural floor plans. Master’s thesis, (Department of Computer Science, Brock University, Canada, 2010)

  15. D. Graham, C. Redies, Statistical regularities in art: relations with visual coding and perception. Vision. Res. 50, 1503–1509 (2010)

    Article  Google Scholar 

  16. G. Greenfield, in Proceedings of the CEC 2003. Evolving aesthetic images using multiobjective optimization (2003), pp. 1903–1909

  17. G. Gunlu, H. Bilge, in ICSCCW. Symmetry analysis for 2D images by using DCT coefficients (2009), pp. 1–4

  18. E. den Heijer, A. Eiben, in Proceedings of the EvoMusArt, LNCS 6025. Comparing aesthetic measures for evolutionary art, vol. 2. (Springer, Berlin, 2010), pp. 311–320

  19. M. Hemberg, U.M. O’Reilly, in GECCO 2002: Proceedings of the Bird of a Feather Workshops, ed. by A. Barry. GENR8—using grammatical evolution in a surface design tool. (AAAI, New York, 2002), pp. 120–123

  20. M. Hemberg, U.M. O’Reilly, A. Menges, K. Jones, M. da Costa Goncalves, S.R. Fuchs, in The Art of Artificial Evolution. Genr8: architects’ experience with an emergent design tool. (Springer, Berlin, 2008)

  21. C. Jacob, Illustrating Evolutionary Computation with Mathematica. (Morgan Kaufmann, USA, 2001)

    Google Scholar 

  22. C. Jacob, A. Lindenmayer, G. Rozenberg, in Parallel Problem Solving from Nature III, Lecture Notes in Computer Science Genetic l-system Programming. Genetic l-system programming. (Springer, Berlin, 1994), pp. 334–343

  23. H. Kawabata, S. Zeki, Neural correlates of beauty. Neurophysiology 91, 1699–1705 (2004)

    Article  Google Scholar 

  24. M. Kazhdan, B. Chazelle, D. Dobkin, T. Funkhouser, S. Rusinkiewicz, A reflective symmetry descriptor for 3D models. Algorithmica 38(1), 201–225 (2004)

    Google Scholar 

  25. J. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection. (MIT Press, Cambridge, 1992)

    MATH  Google Scholar 

  26. M. Li, P. Vitanyi, An Introduction to Kolmogorov Complexity and its Applications: Preface to the First Edition. (Springer, New York, 1997)

  27. H. Lipson, W. Cochran, The Determination of Crystal Structures—3rd Revised and Enlarged ed. (Cornell University Press, Ithaca, 1966)

    Google Scholar 

  28. M. Livingstone, Vision and Art: The Biology of Seeing. (Abrams, New York, 2002)

    Google Scholar 

  29. W.E. Lorensen, H.E. Cline, Marching cubes: A high resolution 3D surface construction algorithm. SIGGRAPH 87 21, 163–169 (1987)

    Article  Google Scholar 

  30. S. Luke, Ecj. http://cs.gmu.edu/eclab/projects/ecj/. Last Accessed 3 Dec 2011

  31. P. Machado, A. Cardoso, in Proceedings of the XIVth Brazilian Symposium on AI. Computing aesthetics. (Springer, Berlin, 1998), pp. 239–249

  32. J. McCormack, in Complex Systems: From Biology to Computation. Interactive evolution of l-system grammars for computer graphics modelling. (ISO Press, Amsterdam, 1993), pp. 118–130

  33. E. Milotti, 1/f noise: a pedagogical review. Arxiv preprint, physics/0204033 http://arxiv.org/abs/physics/0204033 (2002)

  34. C. Neufeld, B. Ross, W. Ralph, The evolution of artistic filters. In: J. Romero, P. Machado (eds) The Art of Artificial Evolution, (Springer, Berlin, 2008)

    Google Scholar 

  35. M. O’Neill, A. Brabazon, in Evolutionary Computation. Evolving a logo design using lindenmayer systems. (2008), pp. 3788–3794

  36. M. O’Neill, J. McDermott, J. Swafford, J. Byrne, E. Hemberg, A. Brabazon, Evolutionary design using grammatical evolution and shape grammars: designing a shelter. Intl. J. Des. Eng. 3, 4–24 (2010)

    Google Scholar 

  37. M. O’Neill, J. Swafford, J. McDermott, J. Byrne, A. Brabazon, E. Shotton, C. McNally, M. Hemberg, in Proceedings of the GECCO ’09. Shape grammars and grammatical evolution for evolutionary design. (ACM, New York, 2009), pp. 1035–1042

  38. W. Pang, K. Hui, Interactive evolutionary 3D fractal modeling. Vis. Comput. 26, 1467–1483 (2010)

    Article  Google Scholar 

  39. W. Ralph, Painting the bell curve: the occurrence of the normal distribution in fine art. (2006, in preparation)

  40. J. Rigau, M. Feixas, M. Sbert, in Proceedings of the Eurographics Workshop Computational Aesthetics in Graphics, Visualization and Imaging. Conceptualizing Birkhoff’s aesthetic measure using Shannon entropy and kolmogorov complexity. (2007), pp. 105–112

  41. J. Rosen, Symmetry Discovered: Concepts and Applications in Nature and Science. (Dover, New York, 1998)

    MATH  Google Scholar 

  42. B. Ross, W. Ralph, H. Zong, in CEC 2006. Evolutionary image synthesis using a model of aesthetics (2006)

  43. K. Sims, Evolving Virtual Creatures. In: SIGGRAPH 94, pp. 15–22 (1994)

  44. B. Spehar, C. Clifford, B. Newell, R. Taylor, Universal aesthetic of fractals. Comput. Graph. 27, 813–820 (2003)

    Article  Google Scholar 

  45. G. Stiny, Introduction to shape and shape grammars. Environ. Plan. B 7, 343–351 (1980)

    Article  Google Scholar 

  46. N. Svangard, P. Nordin, in EvoWorkshops 2004, LNCS 3005. Automated aesthetic selection of evolutionary art by distance based classification of genomes and phenomes using the Universal similarity metric. (Springer, Berlin, 2004), pp. 447–456

  47. S. Todd, W. Latham, Evolutionary Art and Computers. (Academic Press, London, 1992)

    MATH  Google Scholar 

  48. M. Triola, Essentials of Statistics. (Pearson Education, New Jersey, 2010)

    Google Scholar 

  49. R. Voss, J. Clarke, 1/f noise in music: music from 1/f noise. J. Acoust. Soc. Am. 63(1), 258–263 (1978)

    Article  Google Scholar 

  50. von P. Buelow, Genetically Engineered Architecture—Design Exploration with Evolutionary Computation. (VDM, Saarbrücken, 2007)

    Google Scholar 

  51. D.D. Wackerly, W.M. III, R.L. Scheaffer, Mathematical Statistics with Applications, 6th edn. (Duxbury Advanced Series, CA, 2002)

  52. P. Walsh, P. Gade, in IEEE Congress on Evolutionary Computation. The use of an aesthetic measure for the evolution of fractal landscapes. (IEEE, New York, 2011), pp. 1613–1619

  53. A. Watt, F. Policarpo, The Computer Image. (Addison-Wesley, Reading, MA, 1998)

    Google Scholar 

  54. Wikipedia: golden ratio. http://en.wikipedia.org/wiki/Golden_ratio (2012). Last Accessed 22 Nov 2012

  55. Wikipedia: psychology of art. http://en.wikipedia.org/wiki/Psychology_of_art (2012). Last Accessed 22 Nov 2012

  56. Wikipedia: rule of thirds. http://en.wikipedia.org/wiki/Rule_of_thirds (2012). Last Accessed 22 Nov 2012

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Acknowledgments

Thanks to Beatrice Ombuki-Berman, Sheridan Houghten, Bill Ralph, and Cale Fairchild for their advice and assistance, as well as anonymous referees for their constructive comments. This research is supported by an OGSST award and NSERC Discovery Grant 138467.

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Authors and Affiliations

  1. Department of Computer Science, Brock University, 500 Glenridge Ave., St. Catharines, ON, L2S 3A1, Canada

    Steve Bergen & Brian J. Ross

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  1. Steve Bergen
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Correspondence to Brian J. Ross.

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Bergen, S., Ross, B.J. Aesthetic 3D model evolution. Genet Program Evolvable Mach 14, 339–367 (2013). https://doi.org/10.1007/s10710-013-9187-8

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  • DOI: https://doi.org/10.1007/s10710-013-9187-8

Keywords

  • Aesthetics
  • L-systems
  • 3D models
  • Genetic programming
  • Multi-objective evaluation