# How to implement Fourier Descriptor of an image?

I want to implement Fourier Descriptor of an object. I have read link. However, I have some questions about normalizing Fourier Descriptor.

First, if I want to normalize the position of the starting point, according to the above link, This is done by subtracting the phase of the second Fourier descriptor $\phi_1$ from the phase of all Fourier descriptors and weighting by $k$; that is:

$a(k)=a(k)e^{-j \phi_1 k}$

Is the weight $k$ equal to the $k$ in $a(k)$ ?

Second, how could I do in order to achieve rotational invariance when I implement Fourier descriptor ? Thank you very much for your reply.

• So if I want to normalize the FD I need to take the following step? 1) Set $a(0)=0$. 2) Divide all the Fourier descriptors with the magnitude of the second one. $a(1)=r_1e^{j\phi_1}$ $a(k)=\frac{a(k)}{\lVert a(1) \rVert}$ 3) Subtracting the phase of the second Fourier descriptor $\phi_1$ from the phase of all Fourier descriptors and weighting by $k$. $a(k)=a(k)e^{-j \phi_1 k}$ (4)implement rotational invariant: $a(k)=a(k)e^{-j \phi_1}$ – Kuo Feb 14 '15 at 11:33