Extended box filter Gaussian convolution

An improvement of box filtering with continuous selection of sigma. More...

Detailed Description

An improvement of box filtering with continuous selection of sigma.

This code implements the extended box filter approximation of Gaussian convolution proposed by Gwosdek, Grewenig, Bruhn, and Weickert. The extended box filter is the recursive filter

The process to use these functions is the following:

1. ebox_precomp() to precompute coefficients for the convolution
2. ebox_gaussian_conv() or ebox_gaussian_conv_image() to perform the convolution itself (may be called multiple times if desired)

Example

ebox_coeffs c;
num *buffer;

ebox_precomp(&c, sigma, K);
buffer = (num *)malloc(sizeof(num) * N);
ebox_gaussian_conv(c, dest, buffer, src, N, stride);
free(buffer);

Reference

• P. Gwosdek, S. Grewenig, A. Bruhn, J. Weickert, "Theoretical Foundations of Gaussian Convolution by Extended Box Filtering," International Conference on Scale Space and Variational Methods in Computer Vision, pp. 447-458, 2011. http://dx.doi.org/10.1007/978-3-642-24785-9_38

Data Structures
struct	ebox_coeffs_
	Coefficients for extended box filter Gaussian approximation. More...

Typedefs
typedef struct ebox_coeffs_	ebox_coeffs
	Coefficients for extended box filter Gaussian approximation.

Functions
static void	ebox_filter (num *dest, long dest_stride, const num *src, long src_stride, long N, long r, num c_1, num c_2)
	Perform one pass of extended box filtering. More...
void	ebox_precomp (ebox_coeffs *c, double sigma, int K)
	Precompute coefficients for extended box filtering. More...
void	ebox_gaussian_conv (ebox_coeffs c, num *dest, num *buffer, const num *src, long N, long stride)
	Extended box filtering approximation of Gaussian convolution. More...
void	ebox_gaussian_conv_image (ebox_coeffs c, num *dest, num *buffer, const num *src, int width, int height, int num_channels)
	Extended box filtering approximation of 2D Gaussian convolution. More...

Function Documentation

static void ebox_filter ( num *  dest, long  dest_stride, const num *  src, long  src_stride, long  N, long  r, num  c_1, num  c_2  )

static

Perform one pass of extended box filtering.

Parameters

dest	destination array
dest_stride	stride between successive samples of dest
src_stride	src array (must be distinct from dest)
src_stride	stride between successive samples of src
N	number of samples
r	radius of the inner box
c_1	weight of the outer box
c_2	weight of the inner box

This routine performs one pass of extended box filtering with inner box radius r,

Note

The computation is out-of-place, src and dest must be distinct.

Definition at line 69 of file gaussian_conv_ebox.c.

void ebox_gaussian_conv	(	ebox_coeffs	c,
		num *	dest_data,
		num *	buffer_data,
		const num *	src,
		long	N,
		long	stride
	)

Extended box filtering approximation of Gaussian convolution.

Parameters

c	ebox_coeffs created by ebox_precomp()
dest_data	destination array
buffer_data	array with space for at least N samples
src	input, overwritten if src = dest_data
N	number of samples
stride	stride between successive samples

This routine performs the extended box filtering approximation of Gaussian convolution by multiple passes of the extended box filter. The filtering itself is performed by ebox_filter().

Since ebox_filter() requires that the source and destination are distinct, the iteration alternates the roles of two arrays. See box_gaussian_conv() for more detailed discussion.

The convolution can be performed in-place by setting src = dest_data (the source array is overwritten with the result). However, buffer_data must be distinct from dest_data.

Definition at line 117 of file gaussian_conv_ebox.c.

void ebox_gaussian_conv_image	(	ebox_coeffs	c,
		num *	dest,
		num *	buffer,
		const num *	src,
		int	width,
		int	height,
		int	num_channels
	)

Extended box filtering approximation of 2D Gaussian convolution.

Parameters

c	ebox_coeffs created by ebox_precomp()
dest	destination image
buffer	array with at least max(width,height) samples
src	input image, overwritten if src = dest
width	image width
height	image height
num_channels	number of image channels

Similar to ebox_gaussian_conv(), this routine approximates 2D Gaussian convolution with extended box filtering.

The convolution can be performed in-place by setting src = dest (the source array is overwritten with the result). However, buffer must be be distinct from dest.

Definition at line 185 of file gaussian_conv_ebox.c.

void ebox_precomp	(	ebox_coeffs *	c,
		double	sigma,
		int	K
	)

Precompute coefficients for extended box filtering.

Parameters

c	ebox_coeffs pointer to hold precomputed coefficients
sigma	Gaussian standard deviation
K	number of filtering passes

This routine precomputes the coefficients for extended box filtering Gaussian convolution approximation.

Definition at line 35 of file gaussian_conv_ebox.c.