GAUSSKERNEL - Gaussian filter.

Contents

Description

Compute a 1D or 2D Gaussian filter.

Syntax

    f = GAUSSKERNEL(n,s,N);

Inputs

n : size of the filter, odd for no phase in the filter (if too small it will alterate the filter); for a 2D filter, should be n=[n1,n2].

s : standard deviation of the filter.

N : size of the big signal/image (supposed to lie in $[0,1] \times [0,1]$ or $[0,1]$); for a 2D filter, should be N=[N1,N2].

Output

f : Gaussian kernel, normalized so that it sums to 1.

Remark

The equation (in 1D) is: $$ f_s[k] = \exp( -(\frac{x(k)^2} {2 s^2}) ) $$ where $x$ spans the interval $[-1/2,1/2]$.

See also

Ressembles: DIRGAUSSKERNEL, HOURGLASSKERNEL, EUCLIDKERNEL, CONVOLUTION. Requires: MESHGRID.

Function implementation

function f = gausskernel(n, s, N)

parsing parameters

error(nargchk(3, 3, nargin, 'struct'));
error(nargoutchk(1, 1, nargout, 'struct'));

calculation

nd = 1;
if length(n)>1 && (n(2)>1 || isequal(s,0))
    nd = 2;
end

if nd==2 && length(s)==1
    s = [s s];
end
if nd==2 && length(N)==1
    N = [N N];
end

if nd==1
    f = gausskernel_1d(n,s,N);
else
    f = gausskernel_2d(n,s,N);
end

end % end of gausskernel

Subfunctions

GAUSSKERNEL_2D - Compute a 2D Gaussian filter.

%--------------------------------------------------------------------------
function f = gausskernel_2d(n,s,N)

if nargin<3,  N = n;   end

if length(N)==1 || N(1)==1
    N = N(:); N = [N N];
end
if length(s)==1 || s(1)==1
    s = s(:); s = [s s];
end

if s<=0
    f = zeros(n);
    f(round(n/2),round(n/2)) = 1;
    return;
end

x = ( (0:n(1)-1)-(n(1)-1)/2 )/N(1);
y = ( (0:n(2)-1)-(n(2)-1)/2 )/N(2);
[Y,X] = meshgrid(y,x);
f = exp( -(X.^2/ (2*s(1)^2)) - (Y.^2/ (2*s(2)^2)) );
f = f / sum(f(:));
end

GAUSSKERNEL_1D - Compute a 1D Gaussian filter.

%--------------------------------------------------------------------------
function f = gausskernel_1d(n,s,N)

if nargin<3,    N = n;  end;

if s<=0
    f = zeros(n,1);
    f(round(n/2)) = 1;
    return;
end

x = ( (0:n-1)-(n-1)/2 )/(N-1);
f = exp( -x.^2/(2*s^2) );
f = f / sum(f(:));
end