2D Low Band Power Calculation for a Region inside an Image

I have to calculate the "Low Band Power" for a region (not always rectangular) inside an Image. So my questions are:

How can I calculate the Low Band Power?

The idea is to follow this three steps:

1. FI = Calculation of the 2D Fourier Transform with fft2
2. LBFI = perform the lowpass filtering with a filter formed by a series of zeros outside of a circle
3. PSD = Calculation of the Power

In code

 FI = fft2(img);
 LBFI = fftshift(H).*FI;   % where H is the circle
 PSD = sum(sum(abs(LBFI).^2))

Is there a way to adapt this algoritm for a not rectangular region?

I don't know if there's a way to make something similar, maybe with another alghoritms withouth the calculation of the fft. Any suggestion?