CANNYEDGEPROD_BASE - Base function for CANNYEDGEPROD.

Contents

Syntax

[edgemap, mag, or] = CANNYEDGEPROD_BASE(I, sigma2, sigma1, der, c, reduce );

See also

Ressembles: CANNYEDGEPROD, CANNYEDGE_BASE. Requires: GRDSMOOTH_BASE, CANNYEDGEMAP_BASE.

Function implementation

function [edgemap, mag, or] = cannyedgeprod_base(I, sig2, sig1, der, c, reduce)

[X,Y,C] = size(I);

ensure to combine two distinct scales

if sig1==sig2,  sig2 = sig1 + 0.05;  end;
if sig1>sig2,  tmp = sig1;  sig1 = sig2;  sig2 = tmp;  end

deal with the special case of multispectral images

if C>1
    if islogical(reduce) && ~reduce % process channel by channel
        edgemap = false(size(I));
        mag = zeros(size(I));        or = zeros(size(I));
        for c=1:C
            [edgemap(:,:,c), mag(:,:,c), or(:,:,c)] = ...
                cannyedgeprod_base(I(:,:,c), sig2, sig1, der, c, reduce);
        end
        return;

    elseif islogical(reduce) || ...
            (ischar(reduce) && any(strcmpi(reduce,{'isum','igray','imax'})))

        % at that point, if reduce is logical, it is necessarly true

        if C==3 && strcmpi(reduce,'igray')
            [I,d] = rescale(I,0,1);
            I = rgb2gray(I);

        elseif islogical(reduce) || strcmpi(reduce,'isum')
            if C==3
                I = 0.29*I(:,:,1) + 0.59*I(:,:,2) + 0.11*I(:,:,3);
                [I,d] = rescale(I,0,1);
            else
                [I,d] = rescale(I,0,1);
                I = sum(I, 3);
            end

        elseif strcmpi(reduce,'imax')
            [I,d] = rescale(I,0,1);
            I = max(I, [], 3);
        end

also rescale the adjustment parameter accordingly

        c = c / d;

    end
end

compute the 2D filter responses at finest scale: sig1

[gx1,gy1] = grdsmooth_base(I, sig1, der, [], 'xy');

compute responses at coarsest scale: sig2

[gx2,gy2] = grdsmooth_base(I, sig2, der, [], 'xy');

if C>1 && ischar(reduce) && strcmpi(reduce,'gmax');
    gx2 = max(gx2, [], 3); gy2 = max(gy2, [], 3);
    gx1 = max(gx1, [], 3); gy1 = max(gy1, [], 3);
end

compute the correlation coefficients between the directional filter responses according to Sec.3.5

rhox = corr(gx1(:),gx2(:));
rhoy = corr(gy1(:),gy2(:));

rho = sqrt(2^3 * sig1^3 *sig2^3 / (sig1^2+sig2^2)^3);              %#ok

derive the threshold according to Eq.(3.12) and Sec.3.6

kappax = sqrt(1+2*rhox*rhox) * sig1 * sig2;
kappay = sqrt(1+2*rhoy*rhoy) * sig1 * sig2;
thresp = sqrt(c * (kappax + kappay));

define the scale product responses

gx2 = gx1 .* gx2;
gx2(gx2<0) = 0;
gy2 = gy1 .* gy2;
gy2(gy2 < 0) = 0;

define the combined gradient magnitude according to Eq.(3.13)

mag = sqrt(gx2 + gy2);

threshold to remove noise

magmax = max(mag(:));
if magmax>0
    mag = mag / magmax;   % normalize
    thresp = thresp / magmax;
end
mag(mag<=thresp) = 0;

define the combined gradient orientation according to Eq.(3.13); the orientation information is recovered from the scale product responses and the finest scale sig1 (through the signs of gy1 and gx1)

or = atan2(sign(gy1) .* sqrt(gy2), sign(gx1) .* sqrt(gx2));
%or = atan2(-sqrt(gx1) .* sign(gx1),sqrt(gy2) .* sign(gy1));

finally compute the edge map

edgemap = cannyedgemap_base(gx2, gy2, der, mag, or, [], []);
% ratio = [1/3 0.08];
% hyst = [];

final output, special case

if C>1 && ischar(reduce) && strcmpi(reduce,'eor')
    [edgemap, J] = max(edgemap, [], 3);
    subm = reshape(1:X*Y,[X Y]) + (J-1)*X*Y;
    mag = mag(subm);
    or = or(subm);
end

end % end of cannyedgeprod_base