In this paper, a new geometric structure of projective invariants is proposed. Compared with the traditional invariant calculation method based on 3D reconstruction, this method is comparable in the reliability of invariant calculation. According to this method, the only thing needed to find out is the geometric relationship between 3D points and 2D points, and the invariant can be obtained by using a single frame image. In the method based on 3D reconstruction, the basic matrix of two images is estimated first, and then, the 3D projective invariants are calculated according to the basic matrix. Therefore, in terms of algorithm complexity, the method proposed in this paper is superior to the traditional method. In this paper, we also study the projection transformation from a 3D point to a 2D point in space. According to this relationship, the geometric invariant relationships of other point structures can be easily derived, which have important applications in model-based object recognition. At the same time, the experimental results show that the eight-point structure invariants proposed in this paper can effectively describe the essential characteristics of the 3D structure of the target, without the influence of view, scaling, lighting, and other link factors, and have good stability and reliability.

中文翻译：

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空间点单元结构的不变量及其应用

本文提出了射影不变量的新几何结构。与基于3D重构的传统不变式计算方法相比，该方法在不变性计算的可靠性方面具有可比性。根据该方法，唯一需要找出的是3D点和2D点之间的几何关系，并且可以使用单个帧图像获得不变性。在基于3D重建的方法中，首先估计两个图像的基本矩阵，然后根据该基本矩阵计算3D投影不变式。因此，在算法复杂度方面，本文提出的方法优于传统方法。在本文中，我们还研究了空间中从3D点到2D点的投影变换。根据这种关系，可以很容易地推导出其他点结构的几何不变性关系，这些关系在基于模型的目标识别中具有重要的应用。同时，实验结果表明，本文提出的八点结构不变量可以有效地描述目标3D结构的基本特征，而不受视图，缩放，照明和其他链接因素的影响，并且具有良好的稳定性和可靠性。