Box filter Gaussian convolution

A fast low-accuracy approximation of Gaussian convolution. More...

Detailed Description

A fast low-accuracy approximation of Gaussian convolution.

This code implements the basic iterated box filter approximation of Gaussian convolution as developed by Wells. This approach is based on the efficient recursive implementation of the box filter as

where r is the box radius.

While box filtering is very efficient, it has the limitation that only a quantized set of values can be approximated because the box radius r is integer. Extended box filter Gaussian convolution and Stacked integral images Gaussian convolution are extensions of box filtering that allow to vary continuously.

Example

num *buffer;

buffer = (num *)malloc(sizeof(num) * N);
box_gaussian_conv(dest, buffer, src, N, stride, sigma, K);
free(buffer);

Reference

• W.M. Wells, "Efficient synthesis of Gaussian filters by cascaded uniform filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 2, pp. 234-239, 1986. http://dx.doi.org/10.1109/TPAMI.1986.4767776

Functions
static void	box_filter (num *dest, long dest_stride, const num *src, long src_stride, long N, long r)
	Perform one pass of box filtering. More...
void	box_gaussian_conv (num *dest, num *buffer, const num *src, long N, long stride, num sigma, int K)
	Box filtering approximation of Gaussian convolution. More...
void	box_gaussian_conv_image (num *dest, num *buffer, const num *src, int width, int height, int num_channels, num sigma, int K)
	Box filtering approximation of 2D Gaussian convolution. More...

Function Documentation

static void box_filter ( num *  dest, long  dest_stride, const num *  src, long  src_stride, long  N, long  r  )

static

Perform one pass of 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 box filter

Performs one pass of box filtering with radius r (diameter 2r+1) according to the recursive filter

Note

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

Definition at line 43 of file gaussian_conv_box.c.

void box_gaussian_conv	(	num *	dest_data,
		num *	buffer_data,
		const num *	src,
		long	N,
		long	stride,
		num	sigma,
		int	K
	)

Box filtering approximation of Gaussian convolution.

Parameters

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
sigma	Gaussian standard deviation in pixels
K	number of box filter passes

Note

This routine can only approximate Gaussian convolution for a quantized set of values. The input argument sigma is rounded to the closest supported value.

This routine performs iterated box filtering approximation of Gaussian convolution. Well's approximation is used to select the box filter radius.

The filtering itself is performed by calling the box_filter() function K times. Since box_filter() requires that the source and destination arrays are distinct, the iteration alternates the roles of the dest and buffer arrays. For example the iteration pseudocode for K = 4 is

    buffer <- box_filter(src)
    dest   <- box_filter(buffer)
    buffer <- box_filter(dest)
    dest   <- box_filter(buffer)
    dest   <- dest * scale

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

Definition at line 105 of file gaussian_conv_box.c.

void box_gaussian_conv_image	(	num *	dest,
		num *	buffer,
		const num *	src,
		int	width,
		int	height,
		int	num_channels,
		num	sigma,
		int	K
	)

Box filtering approximation of 2D Gaussian convolution.

Parameters

dest	destination image
buffer	array with at least max(width,height) samples
src	input, overwritten if src = dest
width	image width
height	image height
num_channels	number of image channels
sigma	Gaussian standard deviation in pixels
K	number of box filter passes

Similar to box_gaussian_conv(), this routine approximates 2D Gaussian convolution with 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 distinct from dest.

Definition at line 195 of file gaussian_conv_box.c.