@inproceedings{Banks:gecco06lbp,
  abstract = {Bi-Directional Reflectance Distribution Functions are
                 used in many fields including computer animation
                 modelling, military defence (radar, lidar, etc.), and
                 others. This paper explores a variety of approaches to
                 modelling BRDFs using different evolutionary computing
                 (EC) techniques. We concentrate on genetic programming
                 (GP) and in hybrid GP approaches, obtaining very close
                 correspondence between models and data. The problem of
                 obtaining parameters that make particular BRDF models
                 fit to laboratory-measured reflectance data is a
                 classic symbolic regression problem. The goal of this
                 approach is to discover the equations that model
                 laboratory-measured data according to several criteria
                 of fitness. These criteria involve closeness of fit,
                 simplicity or complexity of the model (parsimony), form
                 of the result, and speed of discovery. As expected,
                 free form, unconstrained GP gave the best results in
                 terms of minimising measurement errors. However, it
                 also yielded the most complex model forms. Certain
                 constrained approaches proved to be far superior in
                 terms of speed of discovery. Furthermore, application
                 of mild parsimony pressure resulted in not only simpler
                 expressions, but also improved results by yielding
                 small differences between the models and the
                 corresponding laboratory measurements.},
  added-at = {2008-06-19T17:35:00.000+0200},
  address = {Seattle, WA, USA},
  author = {Banks, Edwin Roger and Nunez, Edwin and Agarwal, Paul and McBride, Marshall and Liedel, Ronald and Owens, Claudette},
  biburl = {https://www.bibsonomy.org/bibtex/2ea0f1b7593ff36305acd4e5cae764817/brazovayeye},
  booktitle = {Late breaking paper at Genetic and Evolutionary
                 Computation Conference {(GECCO'2006)}},
  editor = {Grahl, J{\"{o}}rn},
  interhash = {296634c9cfd2bdab8e5cd5f7e6670365},
  intrahash = {ea0f1b7593ff36305acd4e5cae764817},
  keywords = {genetic algorithms, programming},
  month = {8-12 July},
  notes = {Distributed on CD-ROM at GECCO-2006},
  timestamp = {2008-06-19T17:36:11.000+0200},
  title = {A Comparison of Evolutionary Computing Techniques Used
                 to Model Bi-Directional Reflectance Distribution
                 Functions},
  url = {http://www.cs.bham.ac.uk/~wbl/biblio/gecco2006etc/papers/lbp128.pdf},
  year = 2006
}

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The goal of this approach is to discover the equations that model laboratory-measured data according to several criteria of fitness. These criteria involve closeness of fit, simplicity or complexity of the model (parsimony), form of the result, and speed of discovery. As expected, free form, unconstrained GP gave the best results in terms of minimising measurement errors. However, it also yielded the most complex model forms. Certain constrained approaches proved to be far superior in terms of speed of discovery. 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This paper explores a variety of approaches to\n modelling BRDFs using different evolutionary computing\n (EC) techniques. We concentrate on genetic programming\n (GP) and in hybrid GP approaches, obtaining very close\n correspondence between models and data. The problem of\n obtaining parameters that make particular BRDF models\n fit to laboratory-measured reflectance data is a\n classic symbolic regression problem. The goal of this\n approach is to discover the equations that model\n laboratory-measured data according to several criteria\n of fitness. These criteria involve closeness of fit,\n simplicity or complexity of the model (parsimony), form\n of the result, and speed of discovery. As expected,\n free form, unconstrained GP gave the best results in\n terms of minimising measurement errors. However, it\n also yielded the most complex model forms. Certain\n constrained approaches proved to be far superior in\n terms of speed of discovery. Furthermore, application\n of mild parsimony pressure resulted in not only simpler\n expressions, but also improved results by yielding\n small differences between the models and the\n corresponding laboratory measurements.},\n added-at = {2008-06-19T17:35:00.000+0200},\n address = {Seattle, WA, USA},\n author = {Banks, Edwin Roger and Nunez, Edwin and Agarwal, Paul and McBride, Marshall and Liedel, Ronald and Owens, Claudette},\n biburl = {https://www.bibsonomy.org/bibtex/2ea0f1b7593ff36305acd4e5cae764817/brazovayeye},\n booktitle = {Late breaking paper at Genetic and Evolutionary\n Computation Conference {(GECCO'2006)}},\n editor = {Grahl, J{\\\"{o}}rn},\n interhash = {296634c9cfd2bdab8e5cd5f7e6670365},\n intrahash = {ea0f1b7593ff36305acd4e5cae764817},\n keywords = {genetic algorithms, programming},\n month = {8-12 July},\n notes = {Distributed on CD-ROM at GECCO-2006},\n timestamp = {2008-06-19T17:36:11.000+0200},\n title = {A Comparison of Evolutionary Computing Techniques Used\n to Model Bi-Directional Reflectance Distribution\n Functions},\n url = {http://www.cs.bham.ac.uk/~wbl/biblio/gecco2006etc/papers/lbp128.pdf},\n year = 2006\n}\n\n","author_short":["Banks, E. 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