DIRGAUSSKERNEL - Oriented Gaussian kernel.

Contents

Description

Compute an oriented Gaussian kernel using the approach of [GSW03] and possibly using the code of [ANIGAUSS].

Syntax

     H = DIRGAUSSKERNEL(s1, s2, theta, m, method);

Inputs

s1 : vector of size (1,n) (or (n,1)) of standard deviation(s) along the first (short) axis.

s2 : vector of standard deviation(s) along the (long) second axis, with same dimension as s1.

theta : vector of orientation(s) of the kernel, with same dimension as s1 (in radians).

m : maxium size of the kernel (typ. m=128).

method : string setting the implementation used for computing the anisotropic filters; it is:

Output

h : (array of) matrix(ces) (all with maximum size (m,m)) storing the n oriented Gaussian filters.

References

[GSW03] J.M. Geusebroek, A.W.M. Smeulders, and J. Van de Weijer: "Fast anisotropic gauss filtering", IEEE Trans. on Image Processing, 12(8):938-943, 2003. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1217270&tag=1

[ANIGAUSS] Source code and documentation available at http://staff.science.uva.nl/~mark/downloads.html

See also

Ressembles: GAUSSKERNEL, HOURGLASSKERNEL, EUCLIDKERNEL, CONVOLUTION. Requires: ANIGAUSS.

Function implementation

function H = dirgausskernel(sigma1, sigma2, theta, m, method)

parsing/checking parameters

error(nargchk(3, 5, nargin, 'struct'));
error(nargoutchk(1, 1, nargout, 'struct'));

if ~all(size(sigma1)==size(sigma2)) || ~all(size(sigma1)==size(theta))
    error('dirgausskernel:inputerror', ...
        'input sigmas and theta must have same dimension');

elseif strcmp(method,'geu') && ~exist('anigauss','file')
    error('dirgausskernel:unknownfunction','anigauss toolbox needs to be loaded');
end

main calculation

n = length(sigma1(:));

% size of the kernel
s = max([sigma1(:);sigma2(:)]);
m = min( s*3, m);
m = round(m/2)*2 + 1;

if strcmp(method,'geu'),
    h = zeros(m,m);
    c = (m + 1)/2;
    h(c,c) = 1;
end

% create the output filters
H = zeros( m, m, n);

for i=1:n

    s1 = sigma1(i);
    s2 = sigma2(i);
    t = theta(i);

    switch method

        case 'geu'
            angle =  t / pi *180;
            % trick of ANIGAUSS: note the order of (s1,s2)... only way to
            % respect the orientation
            if s1<s2
                tmp = s1;
                s1 = s2;
                s2 = tmp;
            end
            H(:,:,i) = anigauss(h, s1, s2, angle, 0, 0);

        case '2d'
            s1 = s1*s1;
            s2 = s2*s2;
            x = linspace(-m/2,m/2,m);
            [Y,X] = meshgrid(x,x);
            % rotate
            X1 = cos(t)*X + sin(t)*Y;
            Y1 = - sin(t)*X + cos(t)*Y;
            X1 = X1 / s1;
            Y1 = Y1 / s2;
            h = exp( -(X1.^2 + Y1.^2) );
            h = h/sum(h(:));
            H(:,:,i) = h;
            return

    end

end

end % end of dirgausskernel