New Generation Computing

, Volume 22, Issue 3, pp 271–293 | Cite as

Procedural texture evolution using multi-objective optimization

  • Brian J. Ross
  • Han Zhu
Regular Papers


This paper investigates the application of evolutionary multi-objective optimization to two-dimensional procedural texture synthesis. Genetic programming is used to evolve procedural texture formulae. Earlier work used multiple feature tests during fitness evaluation to rate how closely a candidate texture matches visual characteristics of a target texture image. These feature test scores were combined into an overall fitness score using a weighted sum. This paper improves this research by replacing the weighted sum with a Pareto ranking scheme, which preserves the independence of feature tests during fitness evaluation. Three experiments were performed: a pure Pareto ranking scheme, and two Pareto experiments enhanced with parameterless population divergence strategies. One divergence strategy is similar to that used by the NSGA-II system, and scores individuals using their nearest-neighbour distance in feature-space. The other strategy uses a normalized, ranked abstraction of nearest neighbour distance. A result of this work is that acceptable textures can be evolved much more efficiently and with less user intervention with MOP evolution than compared to the weighted sum approach. Although the final acceptability of a texture is ultimately a subjective decision of the user, the proposed use of multi-objective evolution is useful for generating for the user a diverse assortment of possibilities that reflect the important features of interest.


Procedural Textures Multi-objective Optimization Genetic Programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    Coello, C. A. C., Van Veldhuizen, D. A. and Lamont, G. B.,Evolutionary Algorithms for Solving Multi-Objective Problems, Kluwer Academic Publishers, 2002.Google Scholar
  2. 2).
    Deb, K., Agrawa, S., Pratap, A. and Meyarivan, T., “A Fast Elitist Nondominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II,” inProc. PPSN VI, pp. 849–858, Springer-Verlag, 2000.Google Scholar
  3. 3).
    Ebert, D. S., Musgrave, F. K., Peachey, D., Perlin, K. and Worley, S.,Texturing and Modeling: a Procedural Approach, 2 ed., Academic Press, 1998.Google Scholar
  4. 4).
    Fonseca, C. M. and Fleming, P. J., “An Overview of Evolutionary Algorithms in Multiobjective Optimization,”Evolutionary Computation, 3, 1, pp. 1–16, 1995.CrossRefGoogle Scholar
  5. 5).
    Goldberg, D. E.,Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, 1989.Google Scholar
  6. 6).
    Holland, J. H.,Adaptation in Notural and Artificial Systems, MIT Press, 1992.Google Scholar
  7. 7).
    Horn, J., Nafpliotis, N. and Goldberg, D. E., “A Niched Pareto Genetic Algorithm for Multiobjective Optimization,” inProc. ICEC’94, pp. 82–87, 1994.Google Scholar
  8. 8).
    Ibrahim, A. E. M., “GenShade: an Evolutionary Approach to Automatic and Interactive Procedural Texture Generation,” Ph.D. thesis, Texas A & M University, Dec. 1998.Google Scholar
  9. 9).
    Koza, J. R.,Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, 1992.Google Scholar
  10. 10).
    Laumanss, M., Zitzler, E. and Thiele, L., “On the Effects of Archiving, Elitism, and Density Based Selection in Evolutionary Multi-objective Optimization,” inProc. 1st Int. Conf. on Evolutionary Multi-Criterion Optimization, pp. 181–196, Springer-Verlag, 2001.Google Scholar
  11. 11).
    Lu, H. and Yen, G. G., “Rank-Density Based Multiobjective Genetic Algorithm,” inProc. CEC 2002, pp. 941–949, 2002.Google Scholar
  12. 12).
    Purshouse, R. C. and Fleming, P. J., “Elitism, Sharing, and Ranking Choices in Evolutionary Multi-Criterion Optimisation,”Technical Report 815, Dept. of Automatic Control and Systems Engineering, University of Sheffield, Jan. 2002.Google Scholar
  13. 13).
    Rooke, S., “Eons of Genetically Evolved Algorithmic Images,” in Bentley, P. J. and Corne, D. W. (eds.),Creative Evolutionary Systems, Morgan Kaufmann, pp. 330–365, 2002.Google Scholar
  14. 14).
    Rowe, J., Vinsen, K. and Marvin, N., “Parallel GAs for Multiobjective Functions,” inProc. of the 2nd Nordic Workshop on Genetic Algorithms and their Applications (2NWGA), pp. 61–70, University of Vaasa, Finland, 1996.Google Scholar
  15. 15).
    Sims, K., “Interactive Evolution of Equations for Procedural Models,”The Visual Computer, 9, pp. 466–476, 1993.CrossRefGoogle Scholar
  16. 16).
    Smith, J. R., “Integrated Spatial and Feature Image Systems: Retrieval, Analysis and Compression,” Ph.D. thesis, Center for Telecommunications Research, Graduate School of Arts and Sciences, Columbia University, 1997.Google Scholar
  17. 17).
    Stollnitz, E., Derose, T. and Salesin, D.,Wavelets for Computer Graphics: Theory and Application, Morgan Kaufmann, 1996.Google Scholar
  18. 18).
    Upstill, S.,The Renderman Companion: A Programmer’s Guide to Realistic Computer Graphics, Addison-Wesley, 1989.Google Scholar
  19. 19).
    Veldhuizen, D. A. van and Lamont, G. B., “Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art,”Evolutionary Computation, 8, 2, pp. 125–147, 2000,CrossRefGoogle Scholar
  20. 20).
    Watt, A. and Watt, M.,Advanced Animation and Rendering Techniques: Theory and Practice, ACM Press, 1992.Google Scholar
  21. 21).
    Wiens, A. L. and Ross, B. J., “Gentropy: Evolutionary 2D Texture Generation,”Computers and Graphics Journal, 26, 1, pp. 75–88, Feb. 2002.CrossRefGoogle Scholar
  22. 22).
    Zongker, D. and Punch, B.,lil-gp 1.0. User’s Manual, Dept. of Computer Science, Michigan State University, 1995.Google Scholar

Copyright information

© Ohmsha, Ltd. and Springer 2004

Authors and Affiliations

  • Brian J. Ross
    • 1
  • Han Zhu
    • 1
  1. 1.Dept. of Computer ScienceBrock UniversitySt. CatharinesCanada

Personalised recommendations