Naslov
Convolution on the n-sphere with application to pdf modeling

Autori
Dokmanić, Ivan ; Petrinović, Davor

Izvornik
IEEE transactions on signal processing (1053-587X) 58 (2010), 3; 1157-1170

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
n-sphere; hypersphere; spherical harmonics; hyperspherical harmonics; rotations; convolution; density estimation

Sažetak
In this paper we derive an explicit form of the convolution theorem for functions on an $n$- sphere. Our motivation comes from the design of a probability density estimator for $n$-dimensional random vectors. We propose a pdf estimation method that uses the derived convolution result on $S^n$. Random samples are mapped onto the $n$-sphere and estimation is performed in the new domain by convolving the samples with the smoothing kernel density. The convolution is carried out in the spectral domain. Samples are mapped between the $n$-sphere and the $n$-dimensional Euclidean space by the generalized stereographic projection. We apply the proposed model to several synthetic and real world datasets and discuss the results.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Elektrotehnika, Računarstvo

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