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.
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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.

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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

@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}, }

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