Signal Processing for Computer Vision
Signal Processing for Computer Vision
Numerical Methods for Special Functions
Numerical Methods for Special Functions
Loglets: generalized quadrature and phase for local spatio-temporal structure estimation
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
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Convolution kernels are a commonly used tool in computer vision. These kernels are often specified by an ideal frequency response and the actual filter coefficients are obtained by minimizing some weighted distance with respect to the ideal filter. State-of-the-art approaches usually replace the continuous frequency response by a discrete Fourier spectrum with a multitude of samples compared to the kernel size, depending on the smoothness of the ideal filter and the weight function. The number of samples in the Fourier domain grows exponentially with the dimensionality and becomes a bottleneck concerning memory requirements. In this paper we propose a method that avoids the discretization of the frequency space and makes filter optimization feasible in higher dimensions than the standard approach. The result is no longer depending on the choice of the sampling grid and it remains exact even if the weighting function is singular in the origin. The resulting improper integrals are efficiently computed using Gauss-Jacobi quadrature.