Li Erbo, Mo Hanlin, Xu Dong, Li Hua
IEEE Trans Pattern Anal Mach Intell. 2019 May;41(5):1144-1157. doi: 10.1109/TPAMI.2018.2832060. Epub 2018 May 1.
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.
在本文中，我们利用加权矩的有限组合证明了图像射影矩不变量的存在性，其中相对射影微分不变量作为权函数。我们给出了一些以这种方式构造的实例，并分析了可能影响性能的问题。采取了一些步骤来估计离散图像的偏导数，并设计了一种新方法来归一化离散图像的像素数量，以最小化射影变换前后的变化。我们使用流行的图像数据库和真实图像进行了实验来测试性能。结果表明，本文提出的不变量在图像检索和分类中比其他先前使用的矩不变量具有更好的稳定性和可区分性。用户无需知道二维射影变换的参数，就可以直接从不同视角提取给定平面物体图像的不变特征。因此，射影矩不变量在平面物体识别、图像描述和分类方面可能具有潜在的用途。
