# Approximation of Geometric Structures with Growing Cell Structures and Growing Neural Gas - A Performance Comparison

### Hendrik Annuth, Christian-A. Bohn

#### Abstract

We compare Growing Cell Structures and Growing Neural Gas, which were introduced by Bernd Fritzke and which are famous for their facilities in classification, clustering, dimensionality reduction, data visualization, and approximation tasks. We practically test and analyze their capabilities in geometric approximation and focusing on the application of surface reconstruction from 3D point-data. Our focus is to work out the differences of the algorithms that are especially relevant concerning approximation purposes. We address the issue of suitable input data, their applied graphs, their topological properties, their run time complexities and we present a summary of suggested alternations to both approaches and evaluate our results.

#### References

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#### Paper Citation

#### in Harvard Style

Annuth H. and Bohn C. (2012). **Approximation of Geometric Structures with Growing Cell Structures and Growing Neural Gas - A Performance Comparison** . In *Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)* ISBN 978-989-8565-33-4, pages 552-557. DOI: 10.5220/0004157405520557

#### in Bibtex Style

@conference{ncta12,

author={Hendrik Annuth and Christian-A. Bohn},

title={Approximation of Geometric Structures with Growing Cell Structures and Growing Neural Gas - A Performance Comparison},

booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)},

year={2012},

pages={552-557},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004157405520557},

isbn={978-989-8565-33-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)

TI - Approximation of Geometric Structures with Growing Cell Structures and Growing Neural Gas - A Performance Comparison

SN - 978-989-8565-33-4

AU - Annuth H.

AU - Bohn C.

PY - 2012

SP - 552

EP - 557

DO - 10.5220/0004157405520557