The procedure discussed in Section 11.2.3 for using Fourier descriptors consists of expres...

The procedure discussed in Section 11.2.3 for using Fourier descriptors consists of expressing the coordinates of a contour as complex numbers, taking the DFT of these numbers, and keeping only a few components of the DFT as descriptors of the boundary shape. The inverse DFT is then an approximation to the original contour. What class of contour shapes would have a DFT consisting of real numbers and how would the axis system in Fig. have to be set up to obtain these real numbers?

FIGURE A digital boundary and its representation as a complex sequence.The points (x0, y0) and (x1, y1) shown are (arbitrarily) the first two points in the sequence.