Orthogonal Rotation-Invariant Moments for Digital Image Processing
Orthogonal Rotation-Invariant Moments for Digital Image Processing
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DOI：
10.1109/tip.2007.916157
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发表时间：
2008-03
影响因子：
10.6
通讯作者：
H. Lin;J. Si;G. Abousleman
中科院分区：
文献类型：
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作者：
H. Lin;J. Si;G. Abousleman
正交旋转不变矩（ORIMs），如Zernike矩，被引入并定义在连续单元圆盘上，并已被证明是光学应用的强大工具。这些瞬间也被数字化，用于数字图像处理。不幸的是，数字化损害了矩的正交性，因此，数字orim无法表示图像中的细微细节，无法准确地重建图像。缓解数字化伪影的典型方法可以分为两类：(1)仔细选择一组像素作为接近单位磁盘的像素，并使用数值积分来确定ORIM值；(2)使用圆形表示像素，使其与单位磁盘相似，然后在极空间中计算orm。这些改进仍不足以保持orim的正交性。在本文中，与以往的方法相比，我们提出了一种不同的方法，使用数值优化技术来提高正交性。我们证明了改进正交性后，图像重建更加准确。仿真结果也表明，优化后的数字orim能够准确地重建图像，并能表现出图像的细微细节。
Orthogonal rotation-invariant moments (ORIMs), such as Zernike moments, are introduced and defined on a continuous unit disk and have been proven powerful tools in optics applications. These moments have also been digitized for applications in digital image processing. Unfortunately, digitization compromises the orthogonality of the moments and, therefore, digital ORIMs are incapable of representing subtle details in images and cannot accurately reconstruct images. Typical approaches to alleviate the digitization artifact can be divided into two categories: (1) careful selection of a set of pixels as close approximation to the unit disk and using numerical integration to determine the ORIM values, and (2) representing pixels using circular shapes such that they resemble that of the unit disk and then calculating ORIMs in polar space. These improvements still fall short of preserving the orthogonality of the ORIMs. In this paper, in contrast to the previous methods, we propose a different approach of using numerical optimization techniques to improve the orthogonality. We prove that with the improved orthogonality, image reconstruction becomes more accurate. Our simulation results also show that the optimized digital ORIMs can accurately reconstruct images and can represent subtle image details.