Sometimes it is necessary to know the transformation to apply to a mapping shape in order to locate its true place. Such an operation can be computed if a corresponding reference object exists and we can identify corresponding points in both shapes. Nevertheless our approach does not need to match any corresponding point beforehand. The method proposed defines a polygon in the frequency domain—two periodic functions are derived from a polygonal or polygon. According to the theory of elliptic Fourier descriptors those two periodic functions can be expressed by Fourier expansions. The transformation can be computed using the coefficients of the harmonics from the corresponding shapes without taking into account where each polygon vertex is placed in the spatial domain. The transformation parameters will be derived by a least squares approach. The geomatics and geosciences applications of this method go from photogrammetry, geographic information system, computer vision, to cadaster and real estates.

中文翻译：

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基于傅立叶的映射形状之间的自动转换—地籍和土地注册处的应用

有时，必须知道要应用于映射形状的变换才能找到其真实位置。如果存在相应的参考对象，则可以计算出这种操作，并且我们可以识别两种形状中的相应点。然而，我们的方法不需要事先匹配任何对应点。所提出的方法在频域中定义了一个多边形-从一个多边形或多边形派生出两个周期函数。根据椭圆傅立叶描述符理论，这两个周期函数可以通过傅立叶展开表示。可以使用来自相应形状的谐波系数来计算变换，而无需考虑每个多边形顶点在空间域中的放置位置。变换参数将通过最小二乘法得出。