An Optimal Non-Orthogonal Separation of the Anisotropic Gaussian Convolution Filter

Abstract

We give an analytical and geometrical treatment of what it means to sepa rate a Gaussian kernel along arbitrary axes in Rn, and we present a separation scheme that allows to efficiently implement anisotropic Gaussian convolution filters in arbitrary dimension. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and nterpolation operations needed. Our method relies on non-orthogonal convolution axes and works com- pletely in image space. Thus, it avoids the need for an FFT-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (FIR, IIR) can be integrated. The algorithm is also feasible for hardware that does not contain a floating-point unit. Special emphasis is laid on analyzing the performance and accuracy of our method. In particular, we show that withot any special optimization of the source code, our method can perform anisotropic Gaussian filtering faster than methods relyin on the Fast Fourier Transform