## Abstract

This paper introduces a new nonparametric estimation approach inspired from quantum mechanics. Kernel density estimation associates a function to each data sample. In classical kernel estimation theory the probability density function is calculated by summing up all the kernels. The proposed approach assumes that each data sample is associated with a quantum physics particle that has a radial activation field around it. Schrodinger differential equation is used in quantum mechanics to define locations of particles given their observed energy level. In our approach, we consider the known location of each data sample and we model their corresponding probability density function using the analogy with the quantum potential function. The kernel scale is estimated from distributions of K-nearest neighbours statistics. In order to apply the proposed algorithm to pattern classification we use the local Hessian for detecting the modes in the quantum potential hypersurface. Each mode is assimilated with a nonparametric class which is defined by means of a region growing algorithm. We apply the proposed algorithm on artificial data and for the topography segmentation from radar images of terrain. (c) 2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Original language | English |
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Pages (from-to) | 875-889 |

Number of pages | 15 |

Journal | Pattern recognition |

Volume | 40 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2007 |

## Keywords

- kernel density estimation
- nonparametric modelling
- quantum mechanics
- vector field segmentation
- DENSITY-FUNCTION
- MEAN SHIFT
- GRADIENT
- SPACE
- MODE