Here, we intend to introduce a fast and non-rigid global registration for simple planar closed curves relatively to the planar Special Affine group SA(2,R). In previous work, Ghorbel (1998) has been introduced a complete and stable set of invariant for simple closed planar curves which is invariant jointly under its original parametrization and special planar affine transformations. Such property allows us a robust reconstruction of the considered object up to a special affine transformation. In this paper, several numerical difficulties of the computation of the proposed reconstruction are considered. The robustness of this inverse problem with respect to noise and reasonable deformations of non-rigid shape is demonstrated experimentally. The proposed new registration is based, on the one hand, on the shift theorem relating to the group SA(2,R) and, on the other hand, on the invertibility of the set of invariant. Since this shift theorem allows the extraction of a pose parameters exciting between reference and target objects. The low algorithmic complexity is due to the fact that the computation of the inverse descriptors are based essentially on the Fast Fourier Transformation (FFT) algorithm. Experiments are conducted on different known datasets such as MPEG-7, MCD, Kimia-99, Kimia216, ETH-80 and Swedish leaf datasets. Promising results on the sense of shape retrieval and shape recognition rates will also be demonstrated.

在这里，我们打算为相对于平面特殊仿射群SA（2，R）的简单平面闭合曲线引入快速且非刚性的全局配准。在以前的工作中，Ghorbel（1998）为简单的闭合平面曲线引入了一套完整且稳定的不变量，在其原始的参数化和特殊的平面仿射变换下它们是不变的。这种特性使我们能够对所考虑的对象进行鲁棒的重构，直到进行特殊的仿射变换为止。在本文中，考虑了所提出的重构计算的几个数值困难。实验证明了该反问题相对于噪声的鲁棒性和非刚性形状的合理变形。一方面，拟议的新注册基于与组SA（2，R），另一方面，则表示不变集的可逆性。由于该移位定理允许提取在参考对象与目标对象之间令人兴奋的姿势参数。较低的算法复杂度是由于以下事实：逆描述符的计算基本上基于快速傅立叶变换（FFT）算法。在不同的已知数据集（例如MPEG-7，MCD，Kimia-99，Kimia216，ETH-80和瑞典叶数据集）上进行了实验。在形状检索和形状识别率方面的有希望的结果也将得到证明。较低的算法复杂度是由于以下事实：逆描述符的计算基本上基于快速傅立叶变换（FFT）算法。在不同的已知数据集（例如MPEG-7，MCD，Kimia-99，Kimia216，ETH-80和瑞典叶数据集）上进行了实验。在形状检索和形状识别率方面的有希望的结果也将得到证明。较低的算法复杂度是由于以下事实：逆描述符的计算基本上基于快速傅立叶变换（FFT）算法。实验针对不同的已知数据集进行，例如MPEG-7，MCD，Kimia-99，Kimia216，ETH-80和Swedish叶数据集。在形状检索和形状识别率方面的有希望的结果也将得到证明。