Find Image Extrema

Find local maxima, local minima, saddle points, and flat regions in an image.

Tristan Ursell
Image Extrema Finder
May 2013

[x,y,z,c]=imextrema(im1);
[x,y,z,c]=imextrema(im1,hood);

Estimate extrema in an image at pixel resolution. The input image 'im1'
is a grayscale image of any class. The outputs 'x' and 'y' specify the%pixel positions of the extrema, 'z' specifies the value of the image at
the extrema positions, and 'c' classifies the extrema, with:

c = -1 --> local minimum
c = 0 --> saddle point
c = +1 --> local maximum
c = +2 --> locally flat / extrema undefined

The optional variable 'hood' specifies the topology of the pixel
neighborhood used to find extrema, the options are hood = 4 or hood = 8,
8 is the default.

Some extrema may not be mathematically defined at a single point, i.e. in
the example below the saddle points come in pixel doublets -- this is a
property of image discretization, not an issue with the algorithm.

Image extrema can not occur on the image edge.

If noise is an issue you might consider smoothing the input image with a
Gaussian blur filter or a hmin (matlab: imhmin) transform.

The algorithm will not find ridge lines.

EXAMPLE 1:
dx=500;
Xpos=ones(dx,1)*(1:dx);
Ypos=Xpos';
Im1=cos(4*pi*Xpos/dx).*cos(6*pi*Ypos/dx)+5*((Xpos-dx/2).^2/dx^2+(Ypos-dx/2).^2/dx^2);
Im1(Im1<-0.9)=-0.9;

[x,y,z,c]=imextrema(Im1);

figure
hold on
imagesc(Im1)
plot(x(c==1),y(c==1),'w.')
plot(x(c==-1),y(c==-1),'k.')
plot(x(c==0),y(c==0),'kx')
plot(x(c==2),y(c==2),'wx')
axis equal tight
title(['white dots = maxima, black dots = minima, black x = saddles, white x = flat'])

EXAMPLE 2:
Im1=imread('rice.png');
Im1(Im1<100)=0;

[x,y,z,c]=imextrema(Im1);

figure
hold on
imagesc(Im1)
plot(x(c==1),y(c==1),'rx')
axis equal tight
title(['red x = maxima'])
colormap(gray)