Encoding patient contours using Fourier descriptors for computer treatment planning

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Abstract
Frequently it is desirable to digitize patient''s external and internal contours from computer-assisted tomography (CAT) scan images and to use them for computer treatment planning. After the contours are digitized, each contour could contain over 1000 points. It is a common practice to reduce the number of contour points by interpolation methods in order to use them in a treatment planning program, and in order to save storage space. This paper describes an alternative method for encoding contours. The x-y coordinates of each contour point are represented as a complex number, x + jy. The discrete Fourier transform (DFT) of the array of complex numbers is then computed. Only the 50 lowest frequency components of the DFT are retained. Each contour is then represented by these 50 complex numbers, known as Fourier descriptors. The original contour is restored by performing the inverse Fourier transform. All the frequency components higher than 50 are assumed to be zero during the inverse Fourier transform. The algorithm is described in detail.

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