How to find critical points - maxima,minima and saddle points in an image?

Hi Matlab community, I am new to Matlab and sorry if my question is lame. I would like to find the critical points in an image (maxima,minima,saddle points). I am able to find out the maxima and minima using the 'imregionalmax,imregionalmin'function. But i dunno how to find out the saddle points in an image. I really need help, please help me out.

Answer 1

[Matt J]

How about,

    Cx=diff(Image,2,1); Cx(end+2,:)=nan;
    Cy=diff(Image,2,2); Cy(:,end+2)=nan;

    [i,j]=find( Cx.*Cy<=0);

[Matt J]

If you also need obliquely oriented saddle points you could do something very similar to the above, but use conv2 with oblique differencing kernels like,

    kernel = diag([1 -2 1])

[Lalith kumar]

Hi Matt,

Thank you so much for your fast reply. When i tried the code which you suggested, i faced a few hiccups.

[i,j]=find( Cx.*Cy<=0); --> Matrix dimensions must agree.

I think this is due to the cx(end+1,:)=nan and cy(:,end+1)=nan part.

I tried to implement the second order derivative test(hessian matrix). But i am not sure on how to implement that on an image, because for a function, the test is fairly simple and straight forward.

I tried calculating the second order derivative by using this snippet of code :

im=double(dicomread'MR_017.dcm'); %calculating the partial derivatives of the image. [imx,imy]=gradient(im); [imxx,imxy]=gradient(imx); [imyx,imyy]=gradient(imy);

I am not sure on how to proceed after this, because i have never done a test of this sort on an image.

[Matt J]

I think this is due to the cx(end+1,:)=nan and cy(:,end+1)=nan part.

Whoops. Should be end+2 everywhere...