A Survey of Gaussian Convolution Algorithms
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Approximation by finite impulse response filtering. More...
Approximation by finite impulse response filtering.
This code approximates Gaussian convolution with finite impulse response (FIR) filtering. By truncating the Gaussian to a finite support, Gaussian convolution is approximated by
The process to use these functions is the following:
Data Structures | |
struct | fir_coeffs_ |
Coefficients for FIR Gaussian approximation. More... | |
Typedefs | |
typedef struct fir_coeffs_ | fir_coeffs |
Coefficients for FIR Gaussian approximation. | |
Functions | |
static num * | make_g_trunc (num sigma, long r) |
Construct truncated Gaussian filter for FIR convolution. More... | |
static void | conv_sym (num *dest, const num *src, long N, long stride, const num *h, long r) |
Convolution with a symmetric filter. More... | |
int | fir_precomp (fir_coeffs *c, double sigma, num tol) |
Precompute filter coefficients for FIR filtering. More... | |
void | fir_gaussian_conv (fir_coeffs c, num *dest, const num *src, long N, long stride) |
FIR Gaussian convolution. More... | |
void | fir_gaussian_conv_image (fir_coeffs c, num *dest, num *buffer, const num *src, int width, int height, int num_channels) |
FIR filtering approximation of 2D Gaussian convolution. More... | |
void | fir_free (fir_coeffs *c) |
Release memory associated with fir_coeffs struct. More... | |
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static |
Convolution with a symmetric filter.
dest | destination (must be distinct from src) |
src | source signal |
N | signal length |
stride | stride between successive src and dest samples |
h | symmetric filter, an array of length r + 1 |
r | radius of filter h |
This routine computes the convolution of src
and h
according to
where src
is extrapolated with half-sample symmetry.
Definition at line 82 of file gaussian_conv_fir.c.
void fir_free | ( | fir_coeffs * | c | ) |
Release memory associated with fir_coeffs struct.
c | fir_coeffs created by fir_precomp() |
Definition at line 197 of file gaussian_conv_fir.c.
void fir_gaussian_conv | ( | fir_coeffs | c, |
num * | dest, | ||
const num * | src, | ||
long | N, | ||
long | stride | ||
) |
FIR Gaussian convolution.
c | fir_coeffs created by fir_precomp() |
dest | output convolved data (must be distinct from src) |
src | data to be convolved |
N | number of samples |
stride | stride between successive samples |
This routine approximates 1D Gaussian convolution with the FIR filter. The computation itself is performed by conv_sym().
src
and dest
must be distinct. Definition at line 137 of file gaussian_conv_fir.c.
void fir_gaussian_conv_image | ( | fir_coeffs | c, |
num * | dest, | ||
num * | buffer, | ||
const num * | src, | ||
int | width, | ||
int | height, | ||
int | num_channels | ||
) |
FIR filtering approximation of 2D Gaussian convolution.
c | fir_coeffs created by fir_precomp() |
dest | destination image |
buffer | array with at least width samples |
src | source image, must be distinct from dest |
width | image width |
height | image height |
num_channels | number of image channels |
Similar to fir_gaussian_conv(), this routine performs 2D FIR-based Gaussian convolution.
Definition at line 158 of file gaussian_conv_fir.c.
int fir_precomp | ( | fir_coeffs * | c, |
double | sigma, | ||
num | tol | ||
) |
Precompute filter coefficients for FIR filtering.
c | fir_coeffs pointer to hold precomputed coefficients |
sigma | Gaussian standard deviation |
tol | filter accuracy (smaller tol implies larger filter) |
This routine calls make_g_trunc() to construct the truncated Gaussian FIR filter. The radius of the filter is determined such that
By Young's inequality, the error between convolution using this truncated FIR filter and exact Gaussian convolution is bounded,
Definition at line 117 of file gaussian_conv_fir.c.
Construct truncated Gaussian filter for FIR convolution.
sigma | Gaussian standard deviation |
r | radius of the filter |
This routine constructs a truncated Gaussian for a specified radius
r
,
The filter should be released by the caller with free()
.
Definition at line 43 of file gaussian_conv_fir.c.