Corner features in pictures using Harris detector

Hello everyone,

I'm trying to implement an operator that is able to find suitable
corner features for tracking purposes in image sequences. I use the
Harris detector - let me remind what the theory tells :

Let E(x,y) be the change produced by a shift (x,y) at a given position
in the image. Locally we write E as :
E = A x*x + B y*y + 2 C x*y
where :
A = (x*x) * w
B = (y*y) * w
C = (x*y) * w
and w is the gaussian filter.

In matricial form :
E = (x,y) M transp(x,y)

Let a and b be the eigenvalues of M : a and b are the main curvatures
of the image at the position under consideration. Thus, if both a and
b are big, it means that we are at a corner.

The Harris detector is : R = det(M) - lambda*tr(M)^2.
According to the litterature, it is supposed to be positive for
corners, negative along edges and null for flat regions of the
picture.

However, I cannot understand this last statement : since det(M) is
equal to a*b, what happens if both a and b are big, but with opposite
signs ? The Harris detector will be < 0 so there is a risk to miss a
corner.

Or is there something I don't understand ?

.

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