Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Radial basis function interpolation: numerical and analytical developments
Radial basis function interpolation: numerical and analytical developments
3D scattered data interpolation and approximation with multilevel compactly supported RBFs
Graphical Models - Special issue on SMI 2003
RBF-based image restoration utilising auxiliary points
Proceedings of the 2009 Computer Graphics International Conference
Scattered data interpolation in N-dimensional space
SITE'12 Proceedings of the 11th international conference on Telecommunications and Informatics, Proceedings of the 11th international conference on Signal Processing
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Interpolation based on Radial Basis Functions (RBF) is very often used for scattered scalar data interpolation in n-dimensional space in general. RBFs are used for surface reconstruction of 3D objects, reconstruction of corrupted images etc. As there is no explicit order in data sets, computations are quite time consuming that leads to limitation of usability even for static data sets. Generally the complexity of computation of RBF interpolation for N points is of O(N3) or O(k N2), k is a number of iterations if iterative methods are used, which is prohibitive for real applications. The inverse matrix can also be computed by the Strassen algorithm based on matrix block notation with O(N2.807) complexity. Even worst situation occurs when interpolation has to be made over non-constant data sets, as the whole set of equations for determining RBFs has to be recomputed. This situation is typical for applications in which some points are becoming invalid and new points are acquired. In this paper a new technique for incremental RBFs computation with complexity of O(N2) is presented. This technique enables efficient insertion of new points and removal of selected or invalid points. Due to the formulation it is possible to determine an error if one point is removed that leads to a possibility to determine the most important points from the precision of interpolation point of view and insert gradually new points, which will progressively decrease the error of interpolation using RBFs. The Progressive RBF Interpolation enables also fast interpolation on "sliding window" data due to insert/remove operations which will also lead to a faster rendering.