Alvarez-Mazorra Gaussian convolution

A first-order recursive filter approximation, computed in-place. More...

Detailed Description

A first-order recursive filter approximation, computed in-place.

This code implements Alvarez and Mazorra's recursive filter approximation of Gaussian convolution. The Gaussian is approximated by a cascade of first-order recursive filters,

References

• Alvarez, Mazorra, "Signal and Image Restoration using Shock Filters and Anisotropic Diffusion," SIAM J. on Numerical Analysis, vol. 31, no. 2, pp. 590-605, 1994. http://www.jstor.org/stable/2158018

Functions
void	am_gaussian_conv (num *dest, const num *src, long N, long stride, double sigma, int K, num tol, int use_adjusted_q)
	Gaussian convolution with Alvarez-Mazorra. More...
void	am_gaussian_conv_image (num *dest, const num *src, int width, int height, int num_channels, num sigma, int K, num tol, int use_adjusted_q)
	2D Gaussian convolution with Alvarez-Mazorra More...

Function Documentation

void am_gaussian_conv	(	num *	dest,
		const num *	src,
		long	N,
		long	stride,
		double	sigma,
		int	K,
		num	tol,
		int	use_adjusted_q
	)

Gaussian convolution with Alvarez-Mazorra.

Parameters

dest	output convolved data
src	input data, modified in-place if src = dest
N	number of elements
stride	stride between successive samples
sigma	standard deviation of the Gaussian in pixels
K	number of passes (larger implies better accuracy)
tol	accuracy in evaluating left boundary sum
use_adjusted_q	if nonzero, use proposed regression for q

Implements the fast approximate Gaussian convolution algorithm of Alvarez and Mazorra, where the Gaussian is approximated by K passes of a first- order causal filter and a first-order anticausal filter,

Boundaries are handled with half-sample symmetric extension, and tol specifies the accuracy for approximating an infinite sum on the left boundary.

Gaussian convolution is approached as approximating the heat equation and each timestep is performed with an efficient recursive computation. Using more steps yields a more accurate approximation of the Gaussian. Reasonable values for the parameters are K = 4, tol = 1e-3.

The convolution can be performed in-place by setting src = dest (the source array is overwritten with the result).

Definition at line 81 of file gaussian_conv_am.c.

void am_gaussian_conv_image	(	num *	dest,
		const num *	src,
		int	width,
		int	height,
		int	num_channels,
		num	sigma,
		int	K,
		num	tol,
		int	use_adjusted_q
	)

2D Gaussian convolution with Alvarez-Mazorra

Parameters

dest	output convolved data
src	input, modified in-place if src = dest
width,height,num_channels	the image dimensions
sigma	Gaussian standard deviation
K	number of passes
tol	accuracy for left boundary sum
use_adjusted_q	if nonzero, use proposed q

Similar to am_gaussian_conv(), this routine approximates 2D Gaussian convolution with Alvarez-Mazorra recursive filtering.

The convolution can be performed in-place by setting src = dest (the source array is overwritten with the result).

Definition at line 159 of file gaussian_conv_am.c.