Low-level feature extraction (including edge detection) - Feature Extraction and Image Processing - page 140

%Gradient Corner Detector
%op=T tangent direction
%op=TI tangent inverse
%op=N normal direction
%op=NI normal inverse

function outputimage = GradCorner(inputimage,op)

[rows,columns]=size(inputimage); %Image size
outputimage=zeros(rows,columns); %Result image
[Mx,My]=Gradient(inputimage);

%Gradient images

[M,A]=Edges(inputimage); %Edge Suppression

M=MaxSupr(M,A);
[Mxx,Mxy]=Gradient(Mx); %Derivatives of the gradient image

[Myx,Myy]=Gradient(My);

%compute curvature
for x=l:columns
for y=l:rows
if(M(y,x)~=0)
My2=My(y,x)^2; Mx2=Mx(y,x)^2; MxMy=Mx(y,x)*My(y,x);
if((Mx2+My2)~=0)
if(op== ′ Tl ′ )
outputimage(y,x)=(1/(Mx2+My2)^1.5)*(My2*Mxx(y,x)-
MxMy*Myx(y,x)-Mx2*Myy(y,x)+MxMy*Mxy(y,x));
elseif (op== ′ N ′ )
outputimage(y,x)=(1/(Mx2+My2)^1.5)*(Mx2*Myx(y,x)-
MxMy*Mxx(y,x)-MxMy*Myy(y,x)+My2*Mxy(y,x));
elseif (op=='NI')
outputimage(y,x)=(1/(Mx2+My2)^1.5)*(-Mx2*Myx(y,x)
+MxMy*Mxx(y,x)-MxMy*Myy(y,x)+My2*Mxy(y,x));
else % tangential as default
outputimage(y,x)=(1/(Mx2+My2)^1.5)*(My2*Mxx(y,x)-
MxMy*Myx(y,x)+Mx2*Myy(y,x)-MxMy*Mxy(y,x));
end
end
end
end
end

Code 4.18 Curvature by measuring changes in intensity

an image is not a totally reliable way of determining curvature, and hence corner information.
This is in part due to the higher order of the differentiation process. (Also, scale has not
been included within the analysis.)

4.6.4 Autocorrelation as a measure of curvature

In the previous section, we measured curvature as the derivative of the function ϕ ( x , y )
along a particular direction. Alternatively, a measure of curvature can be obtained by