Article

Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection

Authors:

Vladimir Savchenko,

Lothar SchmittAuthors Info & Claims

SMA '01: Proceedings of the sixth ACM symposium on Solid modeling and applications

Pages 39 - 46

https://doi.org/10.1145/376957.376962

Published: 01 May 2001 Publication History

Abstract

In this paper, we present an application of numerical optimization for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data) by employing a specially designed genetic algorithm to solve a problem concerning computer-aided design in dentistry. Using a space mapping technique the surface of a given model tooth is fitted by a shape transformation to extrapolate (or reconstruct) the remaining surface of a patient's tooth with occurring damage such as a “drill hole.” Thereby, the genetic algorithm minimizes the error of the approximation by optimizing a set of control points that determine the coefficients for spline functions, which in turn define a space transformation. The fitness function to be minimized by the genetic algorithm is the error between the transformed occlusal surface of the model tooth and the remaining occlusal surface of the damaged (drilled) tooth. The algorithm, that is used, is based upon a proposal by Mahfoud and Goldberg. It uses a simulated-annealing type selection scheme, which is applied sequentially (pair-wise, or one-by-one) to the members in the parent generation and their respective offspring generated by mutation-crossover. We outline a proof of convergence for this algorithm. The algorithm is parallel in regard to computing the fitness-values of creatures.

References

[1]

E.H.L. Aarts and P.J.M. van Laarhoven, Simulated Annealing: An Introduction, Statistica Neerlandica 43, 1989, 31-52

[2]

H. Akakie, A new look at the statistical model identification, IEEE Transactions Automatic Control, Vol. AC-19, 6, 1974, 716-723

[3]

P. Bentely, Evolutionary Design by Computers, Morgan Kaufman, 1999

Digital Library

[4]

L. Chu and B.A. Barsky, Cylindrical coordinate representations for modeling surfaces of the cornea and contact lenses, Proc. Int. Conf. on Shape Modeling, IEEE Computer Society Press, 1997, 98-113

Digital Library

[5]

F. Duret, J.L. Blouin, and B. Duret, CAD/CAM in dentistry, J. Am. Dent. Assoc., 117(11), 1988, 715-720

[6]

M. Goel, R.L. Thompson, The evolution of the trilobite eye, Computer Simulations of Self-Organization in Biological Systems, part 11, Croom Helm, London & Sydney, 1988, 275-290

Digital Library

[7]

D.E. Goldberg, Genetic Algorithms, in Search, Optimization & Machine Learning, Addison-Wesley, 1989

Digital Library

[8]

M. Halstead, B. Barsky, S. Klein, and R. Mandell, Reconstructing curved surfaces from specular reflection patterns using spline surface fitting of normals. Conf. Proc. SIGGRAPH 96, H. Rushmeier (ed.), Addison Wesley, 1996, 335-342

Digital Library

[9]

T. Hermann, Z. Kovacs, and T. Varady, Special applications in surface fitting, Geometric Modeling: Theory and Practice, W. Strasser, R. Klein and R.Rau (Eds), Springer, 1997, 14-31

[10]

J.H. Holland, K.J. Holyoak, R.E. Nisbett, P.R. Thagard, Induction: Processes of Inference Learning and Discovery, MIT Press, 1986

Digital Library

[11]

D.L. Isaacson and R.W. Madsen, Markov Chains: Theory and Applications, Prentice-Hall, 1961

[12]

J.R. Koza, Genetic Programming, M1T Press, 1992

Digital Library

[13]

J.R. Koza, Genetic Programming 11, MIT Press, 1994

[14]

J. Loos, G. Greiner, and H.-P. Seidel, A variational approach to progressive lens design, Computer-Aided Design, Vol. 30, No. 8, 1998, 595-602

[15]

J. Loos, Ph. Slusailek, and H.-P. Seidel, Using wavefront tracing for the visualization and optimization of progressive lenses, EUROGRAPHICS'98, Computer Graphics Forum, vol. 17, No. 3, 1998, 255-265

[16]

S.W. Mahfoud and D.E. Goldberg, A Genetic Algorithm for Parallel Simulated Annealing, in: R. Manner, B. Manderick (eds.), Parallel Problem Solving from Nature 2, Elsevier, 1992, 301-310

[17]

S.W. Mahfoud and D.E. Goldberg, Parallel recombinative simulated annealing: a genetic algorithm, Parallel Computing 21, 1995, 1-28

Digital Library

[18]

M. Manela, N. Thornhill, and J.A. Campbel, Fitting spline functions to noisy data using a genetic algorithm. Proc. of the Fifth Int. Conf. on Genetic Algorithms, Morgan Kaufmann, 1993, 549-556

Digital Library

[19]

A. Markus, G. Renner, and J. Vancza, Spline interpolation with genetic algorithms, Proc. Int. Conf. on Shape Modeling, IEEE Computer Society Press, 1997, 47-54

Digital Library

[20]

K. Myszkowski, V.V. Savchenko and T.L. Kunii, Computer modeling for the occlusal surface of teeth, Proc. CGI'96 Conf., Pohang, Korea, June 24-28, 1996, 196-198

Digital Library

[21]

A. Pasko, V. Adzhiev, A. Sourin, and V. Savchenko, Function representation in geometric modeling: concepts, implementation and applications, The Visual Computer, 11(6), 1995, 429-446

[22]

V.V. Savchenko, 3-D Geometric Modeller with Haptic Feedback: Engraving Simulation, in proceedings 2 m PHANTOM Users Research Symposium 2000, M. Harders and S. Huber, (eds.), Zurich, Switzerland, July 6-7, 2000, 35- 42

[23]

V.V. Savchenko and A.A. Pasko, Transformation of functionally defined shapes by extended space mappings, The Visual Computer, 1998,257-270

[24]

V.V. Savchenko, A.A. Pasko, Evolutionary optimization of functionally defined shapes: Case study of natural optical objects, Computer Graphics Int. Conf. 1999, The University of Calgary, Canada, IEEE Computer Society, June 7-11, 1999, 20-24

Digital Library

[25]

V.V. Savchenko, A.A. Pasko, T.L. Kunii, and A.V. Savchenko, Feature based sculpting of functionally defined 3-D geometric objects, T.S. Chua et al. (eds), Proc. of the MMM'95, Nov. 1995, 341-348

[26]

V.V. Savchenko, A.A. Pasko, O. Okunev and T.L. Kunii, Function representation of solids reconstructed from scattered surface points and countours, Computer Graphics Forum, 14(4), 1995, 181-188

[27]

V.V. Savchenko, A.A. Pasko, A.I. Surin, T.L. Kunii, Volume Modeling: Representations and advanced operations, Computer Graphics Int. Conf., F. Wolter and N.M. Patrikalakis (eds.), Hannover, Germany, IEEE Computer Society, June 22-26 1998, 4-13

Digital Library

[28]

L.M. Schmitt, Theory of Genetic Algorithms, to appear in Theoretical Computer Science, 2001, 61p. (available as preprint from the author)

Digital Library

[29]

L.M. Schmitt, C.L. Nehaniv, R.H. Fujii, Linear Analysis of Genetic Algorithms, Theoretical Computer Science 200, 1998, 101-134

Digital Library

[30]

E. Seneta, Non-negative Matrices and Markov Chains, Springer Series in Statistics, Springer, 1981

[31]

V. V. Shapiro, Real functions for representation of rigid solids, Computer Aided Geometric Design, 11(2), 1994, 153- 175

Digital Library

[32]

T. Sohmura and J. Takahashi, Improvement of CAD to produce crown by considering occlusion., Dental Materials Journal, 12(2), 1993, 190-195

[33]

V. A. Vasilenko, Spline functions: theory, algorithms and programs, (in Russian), Nauka (Novosibirsk), 1983

[34]

M. D. Vose, The Simple Genetic Algorithm: Foundations and Theory (Complex Adaptive Systems), Bradford Books, 1999

Digital Library

Cited By

Kozhekin NSavchenko VSenin MHagiwara I(2018)An approach to surface retouching and mesh smoothingThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-003-0218-y19:7-8(549-564)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s00371-003-0218-y
Mourato Fdos Santos MBirra FRomão TCorreia NInami MDias EChambel TKato HPrada RTerada T(2011)Automatic level generation for platform videogames using genetic algorithmsProceedings of the 8th International Conference on Advances in Computer Entertainment Technology10.1145/2071423.2071433(1-8)Online publication date: 8-Nov-2011
https://dl.acm.org/doi/10.1145/2071423.2071433
YAMAZAKI DSAVCHENKO V(2008)A Software System for Filling Complex Holes in 3D Meshes by Flexible Interacting ParticlesJournal of Computational Science and Technology10.1299/jcst.2.6552:4(655-668)Online publication date: 2008
https://doi.org/10.1299/jcst.2.655
Show More Cited By

Index Terms

Recommendations

Development of a parallel optimization method based on genetic simulated annealing algorithm

This paper presents a parallel genetic simulated annealing (PGSA) algorithm that has been developed and applied to optimize continuous problems. In PGSA, the entire population is divided into sub-populations, and in each sub-population the algorithm ...
Multi-niche crowding in the development of parallel genetic simulated annealing
GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation

In this paper, a new hybrid of genetic algorithm (GA) and simulated annealing (SA), referred to as GSA, is presented. In this algorithm, SA is incorporated into GA to escape from the local optima. Then, the idea of hierarchical parallel GA is borrowed ...
An Effective Hybrid Genetic Simulated Annealing Algorithm for Process Planning Problem
ICNC '09: Proceedings of the 2009 Fifth International Conference on Natural Computation - Volume 05

Process planning is an essential part for a Computer Aided Process Planning (CAPP) system in the dynamic workshop environment. It is a combinatorial optimization problem to conduct operations selection and operations sequencing simultaneously with ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

SMA '01: Proceedings of the sixth ACM symposium on Solid modeling and applications

May 2001

328 pages

ISBN:1581133669

DOI:10.1145/376957

Editors:
David C. Anderson
Purdue Univ.
,
Kunwoo Lee
Seoul National Univ.

Copyright © 2001 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 2001

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

SM01

Sponsor:

SIGGRAPH

SM01: ACM Solid Modeling Symposium 2001

Michigan, Ann Arbor, USA

Acceptance Rates

Overall Acceptance Rate 86 of 173 submissions, 50%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

13
Total Citations
View Citations
838
Total Downloads

Downloads (Last 12 months)5
Downloads (Last 6 weeks)0

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Kozhekin NSavchenko VSenin MHagiwara I(2018)An approach to surface retouching and mesh smoothingThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-003-0218-y19:7-8(549-564)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s00371-003-0218-y
Mourato Fdos Santos MBirra FRomão TCorreia NInami MDias EChambel TKato HPrada RTerada T(2011)Automatic level generation for platform videogames using genetic algorithmsProceedings of the 8th International Conference on Advances in Computer Entertainment Technology10.1145/2071423.2071433(1-8)Online publication date: 8-Nov-2011
https://dl.acm.org/doi/10.1145/2071423.2071433
YAMAZAKI DSAVCHENKO V(2008)A Software System for Filling Complex Holes in 3D Meshes by Flexible Interacting ParticlesJournal of Computational Science and Technology10.1299/jcst.2.6552:4(655-668)Online publication date: 2008
https://doi.org/10.1299/jcst.2.655
Yoo KHa JYoo J(2007)Modeling Inlay/Onlay Prostheses with Mesh Deformation TechniquesProceedings of the 7th international conference on Computational Science, Part II10.1007/978-3-540-72586-2_21(154-157)Online publication date: 27-May-2007
https://dl.acm.org/doi/10.1007/978-3-540-72586-2_21
Han SLee IHan C(2007)A Hybrid Genetic Algorithm with Simulated Annealing for Nonlinear Blind Equalization Using RBF NetworksProceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I10.1007/978-3-540-71618-1_29(257-265)Online publication date: 11-Apr-2007
https://dl.acm.org/doi/10.1007/978-3-540-71618-1_29
Yin LSong XSong YHuang TLi J(2006)An overview of in vitro abrasive finishing & CAD/CAM of bioceramics in restorative dentistryInternational Journal of Machine Tools and Manufacture10.1016/j.ijmachtools.2005.07.04546:9(1013-1026)Online publication date: Jul-2006
https://doi.org/10.1016/j.ijmachtools.2005.07.045
Song YLi JYin LHuang TGao P(2006)The feature-based posterior crown design in a dental CAD/CAM systemThe International Journal of Advanced Manufacturing Technology10.1007/s00170-005-0289-131:11-12(1058-1065)Online publication date: 21-Jan-2006
https://doi.org/10.1007/s00170-005-0289-1
Yoo kHa J(2005)An External Surfaces Modeling of Inlay/onlay Using Geometric TechniquesThe KIPS Transactions:PartA10.3745/KIPSTA.2005.12A.6.51512A:6(515-522)Online publication date: 1-Dec-2005
https://doi.org/10.3745/KIPSTA.2005.12A.6.515
SAVCHENKO V(2005)Trends and Solutions in CAD/CGJSME International Journal Series C10.1299/jsmec.48.18448:2(184-196)Online publication date: 2005
https://doi.org/10.1299/jsmec.48.184
Kojekine NSavchenko VHagiwara I(2004)Surface reconstruction based on compactly supported radial basis functionsGeometric modeling10.5555/985821.985834(218-231)Online publication date: 1-Jan-2004
https://dl.acm.org/doi/10.5555/985821.985834
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents