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

C. Lampert, O. Wirjadi, IEEE Transactions on Image Processing (TIP) 15 (2006) 3501–3513.


Journal Article | Published
Author
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.
Publishing Year
Date Published
2006-11-01
Journal Title
IEEE Transactions on Image Processing (TIP)
Volume
15
Issue
11
Page
3501 - 3513
IST-REx-ID

Cite this

Lampert C, Wirjadi O. An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter. IEEE Transactions on Image Processing (TIP). 2006;15(11):3501-3513. doi: 10.1109/TIP.2006.877501
Lampert, C., & Wirjadi, O. (2006). An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter. IEEE Transactions on Image Processing (TIP), 15(11), 3501–3513. https://doi.org/ 10.1109/TIP.2006.877501
Lampert, Christoph, and Oliver Wirjadi. “An Optimal Non-Orthogonal Separation of the Anisotropic Gaussian Convolution Filter.” IEEE Transactions on Image Processing (TIP) 15, no. 11 (2006): 3501–13. https://doi.org/ 10.1109/TIP.2006.877501 .
C. Lampert and O. Wirjadi, “An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter,” IEEE Transactions on Image Processing (TIP), vol. 15, no. 11, pp. 3501–3513, 2006.
Lampert C, Wirjadi O. 2006. An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter. IEEE Transactions on Image Processing (TIP). 15(11), 3501–3513.
Lampert, Christoph, and Oliver Wirjadi. “An Optimal Non-Orthogonal Separation of the Anisotropic Gaussian Convolution Filter.” IEEE Transactions on Image Processing (TIP), vol. 15, no. 11, IEEE, 2006, pp. 3501–13, doi: 10.1109/TIP.2006.877501 .

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