IEEE Trans Image Process - Fast space-variant elliptical filtering using box splines.

Tópicos

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Resumo

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based upon a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using preintegration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based upon the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.

Resumo Limpo

effici realiz linear spacevari nonconvolut filter challeng comput problem imag process paper demonstr possibl filter imag gaussianlik ellipt window vari size elong orient use fix number comput per pixel associ algorithm base upon famili smooth compact support piecewis polynomi radiallyuniform box spline realiz use preintegr local finitediffer radiallyuniform box spline construct repeat convolut fix number box distribut suitabl scale distribut radial uniform fashion attract featur box spline asymptot behavior simpl covari structur quasisepar converg gaussian increas order use approxim anisotrop gaussian vari covari simpli control scale constitu box distribut base upon second featur develop techniqu continu control size elong orient gaussianlik function final quasisepar structur along certain scale properti box distribut use effici realiz associ spacevari ellipt filter requir o comput per pixel irrespect shape size filter

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