SDGDEDGE_BASE - Base function for SDGDEDGE.

Contents

Syntax

   edgemap = SDGDEDGE_BASE(I, plus, sigma, mu, thres, hsize);

Acknowledgment:

Sergei Koptenko, Resonant Medical, Montreal (Qc., Canada), www.resonantmedical.com.

See also

Ressembles: SDGDEDGE, EDGECORNER_BASE, CANNYEDGE_BASE, CANNYEDGEMAP_BASE, ROTHWELLEDGE_BASE, CONGRUENCYEDGE_BASE, COMPASSEDGE_BASE, ANISOEDGE_BASE, ELDERZUCKEREDGE_BASE, KOETHEDGE_BASE, PETROUEDGE_BASE. Requires: CONV2.

Function implementation

function edgemap = sdgdedge_base(I, plus, sigma, mu, thres, hsize)

internal parameters

C = size(I,3);
if isempty(hsize),    hsize = ceil(3 * sigma);  end;
x = 2*hsize + 1;

dealing with multispectral images

if C>1
    edgemap = false(size(I));
    for c=1:C
        edgemap(:,:,c) = sdgdedge_base(I(:,:,c), plus, sigma, mu, thres, hsize);
     end
    return;
end

compute the derivarives kernels

dGx = GaussDx2(x, mu, sigma, hsize); % first derivative dGx
dGy = dGx';                             % first derivative dGy
dGxx = conv2(dGx, dGx, 'same');         % second Derivative dGxx
dGyy = dGxx';                           % second Derivative dGyy
dGxy = conv2(dGx, dGy, 'same');         % second Derivative dGxy

estimate the derivatives

a_x = conv2(I, dGx, 'same');
a_y = conv2(I, dGy, 'same');
a_xx = conv2(I, dGxx, 'same');
a_yy = conv2(I, dGyy, 'same');
a_xy = conv2(I, dGxy, 'same');
% warning off MATLAB:divideByZero
% Warning: derivatives a_x and a_y for some pixels may be zero; this produce
% an error "divideByZero" and such pixels gets value =NaN. It is recomended
% to check for NaNs after filtering and replacing it with any value of
% convenience: zero, global minimum, etc...
% warning on MATLAB:divideByZero

output of the filter

edgemap = (a_xx .* a_x.^2 + 2* a_xy .* a_x .* a_y + a_yy .* a_y .^2 );
edgemap = edgemap ./ (a_x .^2 + a_y .^2);

if plus,      edgemap =  edgemap + a_xxm + a_yy;   end

final binary map

mm = max(edgemap(:));
edgemap = edgemap / mm > thres;

end % end of sdgdedge_base

Subfunction

GAUSSDX2 - Compute a 2D Gaussian Derivative.

Inputs: gdsize : size of Gaussian kernel.

|mu| : mean of the Gaussian.

|sigma| : standard deviation of a Gaussian function.

|sigma_width| : defines where to cut the Gaussian kernel tail (or width
   of the kernel in sigma); default: |sigma_width=3| or 98% of Gaussian.

Output: gausskernel_2d : derivative kernel.

%--------------------------------------------------------------------------
function GaussKernel_2D = GaussDx2(GDsize, mu, sigma, sigma_width)

x = linspace(-sigma_width, sigma_width, GDsize);

Gaussian = exp(- 0.5*(((x - mu)/ sigma) .^2)) /(sigma * realsqrt(2 * pi));
Gaussian = Gaussian / sum(Gaussian); % normalize the sum of samples to 1

GaussKernel_1D = (mu - x) .* Gaussian / sigma^2;
% normalize kernel
GaussKernel_1D  = GaussKernel_1D  /sum(GaussKernel_1D .* (mu-x));
GaussKernel_2D = conv2(GaussKernel_1D, Gaussian', 'full');
end % end of GaussDx2