Fast Gauss Bilateral Filtering

Fast Anisotropi Gauss Filtering

Fast Anisotropic Gauss Filtering

We derive the decomposition of the anisotropic Gaussian in a one-dimensional (1-D) Gauss filter in the x-direction followed by a 1-D filter in a nonorthogonal direction phi. So also the anisotropic Gaussian can be decomposed by dimension. This appears to be extremely efficient from a computing perspective. An implementation scheme for normal convolution and for recursive filtering is proposed. ...

Fast O(1) bilateral filtering using trigonometric range kernels

It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithms in the image-processing literature. Along with the spatial filter, the edge-preserving bilateral filter involves an additional range kernel...

The Fast Gauss Transform

Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like NM as N and M increase; this makes it very expensive to carry out such calculations on a large scale. In this paper, an algorithm is presented which evaluates the sum of N Gaussians at M arbitrarily distributed points in C. (N + M) work, ...

The Fast Generalized Gauss Transform

The fast Gauss transform allows for the calculation of the sum of N Gaussians at M points in O(N + M) time. Here, we extend the algorithm to a wider class of kernels, motivated by quadrature issues that arise in using integral equation methods for solving the heat equation on moving domains. In particular, robust high-order product integration methods require convolution with O(q) distinct Gaus...