Paper Info
Title
Optimal Knots Selection for Sparse Reduced Data.
Abstract
We discuss an interpolation scheme based on optimization to fit a given ordered sample of reduced data $$Q_m$$ in arbitrary Euclidean space. Here the corresponding knots are not given and need to be first somehow guessed. This is accomplished by solving an appropriate optimization problem, where the missing knots minimize the cost function measuring the total squared norm of acceleration of the interpolant here a natural spline. The initial infinite dimensional optimization set to minimize an acceleration within the class of admissible curves is reduced to the finite dimensional problem, for which the unknown optimal interpolation knots are to be found. The latter introduces a highly non-linear optimization task, both difficult for theoretical analysis and in derivation of computationally feasible optimization scheme in particular handling medium and large number of data points. The experiments to compare the interpolants based either on optimal knots or on the so-called cumulative chords are performed for 2D and 3D data. The problem of interpolating or approximating reduced data is applicable in computer vision image segmentation, in computer graphics curve modeling in computer aided geometrical design or in engineering and physics trajectory modeling.
Year
DOI
Venue
2015
10.1007/978-3-319-30285-0_1
PSIVT Workshops
Keywords
Field
DocType
Reduced sparse data, Interpolation, Knots selection
Spline (mathematics),Infinite-dimensional optimization,Square (algebra),Computer science,Interpolation,Artificial intelligence,Optimization problem,Data point,Mathematical optimization,Pattern recognition,Algorithm,Euclidean space,Knot (unit)
Conference
Volume
ISSN
Citations 
9555
0302-9743
4
PageRank 
References 
Authors
0.47
18
2
Name
Order
Citations
PageRank
Ryszard Kozera116326.54
Lyle Noakes214922.67