IEEE Trans Image Process - New families of Fourier eigenfunctions for steerable filtering.

Tópicos

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Resumo

A new diadic family of eigenfunctions of the 2-D Fourier transform has been discovered. Specifically, new wavelets are derived by steering the elongated Hermite-Gauss filters with respect to rotations, thus obtaining a natural generalization of the Laguerre-Gauss harmonics. Interestingly, these functions are also proportional to their 2-D Fourier transform. Their analytical expression is provided in a compact and treatable form, by means of a new ad hoc matrix notation in which the cases of even and odd orders of the Hermite polynomials are unified. Moreover, these functions can be efficiently implemented by means of a recursive formula that is derived in this paper. The proposed filters are applied to the problem of gradient estimation to improve the theoretical Canny tradeoff of position accuracy versus noise rejection that occurs in edge detection. Experimental results show considerable improvements in using the new wavelets over both isotropic Gaussian derivatives and other elongated steerable filters more recently introduced. Finally, being the proposed wavelets a set of Fourier eigenfunctions, they can be of interest in other fields of science, such as optics and quantum mechanics.

Resumo Limpo

new diadic famili eigenfunct d fourier transform discov specif new wavelet deriv steer elong hermitegauss filter respect rotat thus obtain natur general laguerregauss harmon interest function also proport d fourier transform analyt express provid compact treatabl form mean new ad hoc matrix notat case even odd order hermit polynomi unifi moreov function can effici implement mean recurs formula deriv paper propos filter appli problem gradient estim improv theoret canni tradeoff posit accuraci versus nois reject occur edg detect experiment result show consider improv use new wavelet isotrop gaussian deriv elong steerabl filter recent introduc final propos wavelet set fourier eigenfunct can interest field scienc optic quantum mechan

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