An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter Journal Article


Author(s): Lampert, Christoph; Wirjadi, Oliver
Article Title: An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter
Affiliation
Abstract: We give an analytical and geometrical treatment of what it means to separate a Gaussian kernel along arbitrary axes in Ropfn, and we present a separation scheme that allows us to efficiently implement anisotropic Gaussian convolution filters for data of arbitrary dimensionality. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed. The proposed method relies on nonorthogonal convolution axes and works completely in image space. Thus, it avoids the need for a fast Fourier transform (FFT)-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (finite impulse response and infinite impulse response) can be integrated. Special emphasis is put on analyzing the performance and accuracy of the new method. In particular, we show that without any special optimization of the source code, it can perform anisotropic Gaussian filtering faster than methods relying on the FFT.
Keywords: Anisotropic Gaussian filter; linear filtering; nD image processing; orientation space; separable filters
Journal Title: IEEE Transactions on Image Processing (TIP)
Volume: 15
Issue 11
ISSN: 1057-7149
Publisher: IEEE  
Date Published: 2006-11-01
Start Page: 3501
End Page: 3513
URL:
DOI: 10.1109/TIP.2006.877501
Open access: yes (repository)
IST Austria Authors
  1. Christoph Lampert
    87 Lampert
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