Filtering by repeated integration
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Algorithms for Low-Level Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Box splines
Recursive implementation of the Gaussian filter
Signal Processing
Continuous wavelet transform with arbitrary scales and O(N) complexity
Signal Processing
Theoretical Foundations of Anisotropic Diffusion in Image Processing
Proceedings of the 7th TFCV on Theoretical Foundations of Computer Vision
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
Spatially variant convolution with scaled B-splines
IEEE Transactions on Image Processing
Fast detection of cells using a continuously scalable Mexican-hat-like template
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Fast anisotropic Gauss filtering
IEEE Transactions on Image Processing
Recursive Anisotropic 2-D Gaussian Filtering Based on a Triple-Axis Decomposition
IEEE Transactions on Image Processing
Fast detection of cells using a continuously scalable Mexican-hat-like template
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
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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.