FOURIER DESCRIPTORS FOR PLANE CLOSED CURVES
FOURIER DESCRIPTORS FOR PLANE CLOSED CURVES
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DOI：
10.1109/tc.1972.5008949
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发表时间：
1972-01-01
影响因子：
3.7
通讯作者：
ROSKIES, RZ
中科院分区：
文献类型：
--
作者：
ZAHN, CT;ROSKIES, RZ
本文利用Cosgriff [1]的傅立叶描述子FD，提出了一种分析和综合平面闭曲线的方法。曲线通过自起点以来曲线方向的累积变化以参数方式表示为弧长的函数。该函数以傅立叶级数展开，系数以幅度/相位角形式排列。它表明，振幅是纯粹的形式不变，以及某些简单的函数的相位角。旋转和轴对称直接与傅立叶描述符的简单性质有关。形状相似性或对称性的分析可以基于这些关系;闭合对称曲线也可以从几乎任意的傅立叶描述符合成。它建立了傅立叶级数展开是最佳的和唯一的关于获得系数不敏感的起点。文中给出了几个实例，说明傅立叶描述子作为形状判别特征的有效性，并用计算机生成和绘制了一些有趣的对称曲线。
A method for the analysis and synthesis of closed curves in the plane is developed using the Fourier descriptors FD's of Cosgriff [1]. A curve is represented parametrically as a function of arc length by the accumulated change in direction of the curve since the starting point. This function is expanded in a Fourier series and the coefficients are arranged in the amplitude/phase-angle form. It is shown that the amplitudes are pure form invariants as well as are certain simple functions of phase angles. Rotational and axial symmetry are related directly to simple properties of the Fourier descriptors. An analysis of shape similarity or symmetry can be based on these relationships; also closed symmetric curves can be synthesized from almost arbitrary Fourier descriptors. It is established that the Fourier series expansion is optimal and unique with respect to obtaining coefficients insensitive to starting point. Several examples are provided to indicate the usefulness of Fourier descriptors as features for shape discrimination and a number of interesting symmetric curves are generated by computer and plotted out.