物體邊界的描述或辨識在影像處理和模式識別領域□是很重要的課題，傅立葉描述子在這方面顯示出有用的特性。藉由描繪閉合的輪廓曲線得到的週期函數，可以用傅立葉級數來表現。這些係數因為對大小、角方向、位置以及起始條件不敏感而使得傅立葉描述子在形狀識別方面廣被利用。
本篇論文□，將對兩種傅立葉描述子理論作一番回顧與評論。探討傅立葉描述子的一些特性，並且推出用來計算多邊形曲線的傅立葉描述子的演算流程。我們可以將其應用在針對灰階影像作改良的內插方法上，以物件的形狀為基礎作考量。該新方法使用多邊形來逼近物件的形狀，並且使用該多邊形向量作參考軸來進行內插。此處理工作不僅可以得到更佳的內插結果，也使得傅立葉描述子的應用不再侷限於二值影像□。

Description or discrimination of boundary curves is an important problem in image processing and pattern recognition. Fourier descriptors have been shown to be useful in this respect. The periodic function which is obtained by tracing the closed contour can be expressed in a Fourier series. These descriptors have been used for shape discrimination noting that the coefficients are invariant to size, angular orientation, position, and starting conditions.
In this paper, a critical review is given of two kinds of Fourier descriptors. Some properties of the Fourier descriptors are given and algorithms for computing the Fourier descriptors of the polygonal curve are proposed. We can apply them to an improved shaped-based interpolation method for grey-level images. The new method uses polygon to approximate the object shape and performs the interpolation using polygon vertices as references. This process is not only able to achieve a better interpolation but also its application is not limited to binary images.

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