Determination of Stationary Points and Their Bindings in Dataset Using RBF Methods
Stationary points of multivariable function which represents some surface have an important role in many application such as computer vision, chemical physics, etc. Nevertheless, the dataset describing the surface for which a sampling function is not known is often given. Therefore, it is necessary to propose an approach for finding the stationary points without knowledge of the sampling function.
In this paper, an algorithm for determining a set of stationary points of given sampled surface and detecting the bindings between these stationary points (such as stationary points lie on line segment, circle, etc.) is presented. Our approach is based on the piecewise RBF interpolation of the given dataset.
KeywordsStationary points RBF interpolation Shape parameter Shape detection Nearest neighbor
The authors would like to thank their colleagues at the University of West Bohemia, Plzeň, for their discussions and suggestions, and the anonymous reviewers for their valuable comments. Special thanks belong to Jan Dvorak, Lukas Hruda and Martin Červenka for their independent experiments and valuable comments. The research was supported by the Czech Science Foundation GAČR project GA17-05534S and partially supported by the SGS 2016-013 project.
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