# SIMPLIFIED REPRESENTATION OF LARGE RANGE DATASET

### Hongchuan Yu, Mohammed Bennamoun

#### Abstract

In this paper, we consider two approaches of simplifying medium- and large-sized range datasets to a compact data point set, based on the Radial Basis Functions (RBF) approximation. The first algorithm uses a Pseudo-Inverse Approach for the case of given basis functions, and the second one uses an SVD-Based Approach for the case of unknown basis functions. The novelty of this paper consists in a novel partition-based SVD algorithm for a symmetric square matrix, which can effectively reduce the dimension of a matrix in a given partition case. Furthermore, this algorithm is combined with a standard clustering algorithm to form our SVD-Based Approach, which can then seek an appropriate partition automatically for dataset simplification. Experimental results indicate that the presented Pseudo-Inverse Approach requires a uniform sampled control point set, and can obtain an optimal least square solution in the given control point set case. While in the unknown control point case, the presented SVD-Based Approach can seek an appropriate control point set automatically, and the resulting surface preserves more of the essential details and is prone to less distortions.

#### References

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#### Paper Citation

#### in Harvard Style

Yu H. and Bennamoun M. (2006). **SIMPLIFIED REPRESENTATION OF LARGE RANGE DATASET** . In *Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,* ISBN 972-8865-40-6, pages 172-179. DOI: 10.5220/0001374201720179

#### in Bibtex Style

@conference{visapp06,

author={Hongchuan Yu and Mohammed Bennamoun},

title={SIMPLIFIED REPRESENTATION OF LARGE RANGE DATASET},

booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,},

year={2006},

pages={172-179},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001374201720179},

isbn={972-8865-40-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,

TI - SIMPLIFIED REPRESENTATION OF LARGE RANGE DATASET

SN - 972-8865-40-6

AU - Yu H.

AU - Bennamoun M.

PY - 2006

SP - 172

EP - 179

DO - 10.5220/0001374201720179