Since you'd expect a ridge/peak detection filter to have a positive response to a positive ridge/peak, you'd use the negated second derivative, and add that.
Look at these pictures:
- the
[-1 5 -1]
kernel, i.e. identity - laplacian = identity filter - the picture itself
[ 1 -3 1]
kernel, i.e. identity laplacian = identity - filter
You see, #3 looks blurry because some high frequencies were subtracted.