In this paper, we have proved the existence of projective moment invariants of images using finite combinations of weighted moments, with relative projective differential invariants as weight functions. We have given some instances constructed in that way, and analyzed possible issues could affect the performance. Some procedures are taken to estimate partial derivatives of discrete images, and a new method is designed to normalize the number of pixels for discrete images to minimize the changes before and after the projective transformation. We have carried out experiments using popular image databases and real images to test the performance. And the results show that the invariants proposed in this paper have better stability and discriminability than other previously used moment invariants in image retrieval and classification. Users can directly extract invariant features of images for a given planar object from different viewpoints without knowing the parameters of the 2D projective transformations. Therefore, the projective moment invariant could be potentially useful for planar object recognition, image description and classification.

中文翻译：

---

图像投影不变量

在本文中，我们使用加权矩的有限组合证明了图像的射影矩不变量的存在，其中相对射影微分不变量作为权重函数。我们给出了以此方式构造的一些实例，并分析了可能影响性能的问题。采取一些程序来估计离散图像的偏导数，并设计了一种新方法来标准化离散图像的像素数，以最小化投影变换前后的变化。我们已经使用流行的图像数据库和真实图像进行了实验，以测试性能。结果表明，本文提出的不变量在图像检索和分类中比以前使用的其他矩不变量具有更好的稳定性和可判别性。用户可以直接从不同的角度提取给定平面对象的图像不变性，而无需知道2D投影变换的参数。因此，投影矩不变性可能对平面物体识别，图像描述和分类很有用。