Thank you every one for your valuable answers and consideration.
But I think that i don't explain my question as well.
So, to be more explicit, I attached here an article that contains an example of exactly what I seek. Indeed, from Fig. 3 of this this paper, the authors consider the horizontal directions - according to my view point - as the mostly vertical ones and vice versa (what I thought that are vertical, they are considered to be mostly horizontal).
Can anyone explain me this fact?
http://minhdo.ece.illinois.edu/publications/contourlet_txform.pdf
Direction of what, movement or image components(lines/ edges .etcc)?
Please see sent message : I think there is an error (omitted "j" or pi /4 or wrong vector calculation)
x=[1 -2 1]
y=[1;-2;1]
d2x=filter2(x,image)
d2y=filter2(y,image)
grad=sqrt(d2x^2+d2y^2)
direc=atan(d2y/d2x)
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