Moravec Corner Detection algorithm

This is one of the earliest corner detection algorithms and defines a corner to be a point with low self-similarity. The algorithm tests each pixel in the image to see if a corner is present, by considering how similar a patch centered on the pixel is to nearby, largely overlapping patches. The similarity is measured by taking the sum of squared differences (SSD) between the two patches. A lower number indicates more similarity.

If the pixel is in a region of uniform intensity, then the nearby patches will look similar. If the pixel is on an edge, then nearby patches in a direction perpendicular to the edge will look quite different, but nearby patches in a direction parallel to the edge will result only in a small change. If the pixel is on a feature with variation in all directions, then none of the nearby patches will look similar.

The corner strength is defined as the smallest SSD between the patch and its neighbors (horizontal, vertical and on the two diagonals). If this number is locally maximal, then a feature of interest is present.

As pointed out by Moravec, one of the main problems with this operator is that it is not isotropic: if an edge is present that is not in the direction of the neighbours, then it will not be detected as an interest point.

Denote the image intensity of a pixel at (x, y) by I(x, y).

Input: grayscale image, window size, threshold T
Output: map indicating position of each detected corner

1. For each pixel (x, y) in the image calculate the intensity variation from a shift (u, v) as:

where the shifts (u,v) considered are:
(1,0),(1,1),(0,1),(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)

2. Construct the cornerness map by calculating the cornerness measure C(x, y) for each pixel (x, y):

3. Threshold the interest map by setting all C(x, y) below a threshold T to zero.

4. Perform non-maximal suppression to find local maxima.

All non-zero points remaining in the cornerness map are corners.

Source:http://www.cim.mcgill.ca/~dparks/CornerDetector/mainMoravec.htm

Matlab Code:
% calculate moravec operator of an image
function [corner,ch,cv,cd1,cd2] = cornerMoravec(I,border)


hori = [1 -1];
vert = hori';
diag1 = [1 0; 0 -1];
diag2 = [0 1; -1 0];


average = ones(4,4); % average filter


conv_type='same';


h = conv2(I,hori,conv_type);
v = conv2(I,vert,conv_type);
d1 = conv2(I,diag1,conv_type);
d2 = conv2(I,diag2,conv_type);


c=zeros(size(I));
for i=1:prod(size(I))
c(i) = min([h(i)^2 v(i)^2 d1(i)^2 d2(i)^2]);
end


for i=2:size(I,1)-1
for j=2:size(I,2)-1


hh = sum(sum(abs(h(i-1:i+1,j-1:j+1)))); % 3x3 subimage
vv = sum(sum(abs(v(i-1:i+1,j-1:j+1)))); % 3x3 subimage
dd1 = sum(sum(abs(d1(i-1:i+1,j-1:j+1)))); % 3x3 subimage
dd2 = sum(sum(abs(d2(i-1:i+1,j-1:j+1)))); % 3x3 subimage


c(i,j) = min(hh,min(vv,min(dd1,dd2)));
ch(i,j) = hh;
cv(i,j) = vv;
cd1(i,j) = dd1;
cd2(i,j) = dd2;


end
end


corner=c;
corner=corner(border+1:end-border,border+1:end-border);
ch = ch(border+1:end-border,border+1:end-border);
cv = cv(border+1:end-border,border+1:end-border);
cd1 = cd1(border+1:end-border,border+1:end-border);
cd2 = cd2(border+1:end-border,border+1:end-border);
.