Gastón A Ayubi, Bartlomiej Kowalski, Alfredo Dubra
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Like a previously defined <math><mi>N</mi> <mi>W</mi> <mi>C</mi> <mi>C</mi></math> with binary weights, the proposed generalizations enable the registration of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling. All <math><mi>N</mi> <mi>C</mi> <mi>C</mi></math> definitions discussed here are provided with discrete Fourier transform ( <math><mi>D</mi> <mi>F</mi> <mi>T</mi></math> ) formulations for fast computation. Practical aspects of <math><mi>N</mi> <mi>C</mi> <mi>C</mi></math> computational implementation are briefly discussed, and a convenient function to calculate the overlap of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling is introduced, together with its <math><mi>D</mi> <mi>F</mi> <mi>T</mi></math> formulation. Finally, examples illustrate the benefit of the proposed normalized cross-correlation functions.</p>","PeriodicalId":74366,"journal":{"name":"Optics continuum","volume":"3 5","pages":"649-665"},"PeriodicalIF":1.4000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12448653/pdf/","citationCount":"0","resultStr":"{\"title\":\"Normalized weighted cross correlation for multi-channel image registration.\",\"authors\":\"Gastón A Ayubi, Bartlomiej Kowalski, Alfredo Dubra\",\"doi\":\"10.1364/OPTCON.525065\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The normalized cross-correlation ( <math><mi>N</mi> <mi>C</mi> <mi>C</mi></math> ) is widely used for image registration due to its simple geometrical interpretation and being feature-agnostic. Here, after reviewing <math><mi>N</mi> <mi>C</mi> <mi>C</mi></math> definitions for images with an arbitrary number of dimensions and channels, we propose a generalization in which each pixel value of each channel can be individually weighted using real non-negative numbers. This generalized normalized weighted cross-correlation ( <math><mi>N</mi> <mi>W</mi> <mi>C</mi> <mi>C</mi></math> ) and its zero-mean equivalent ( <math><mi>Z</mi> <mi>N</mi> <mi>W</mi> <mi>C</mi> <mi>C</mi></math> ) can be used, for example, to prioritize pixels based on signal-to-noise ratio. Like a previously defined <math><mi>N</mi> <mi>W</mi> <mi>C</mi> <mi>C</mi></math> with binary weights, the proposed generalizations enable the registration of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling. 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引用次数: 0
摘要
归一化互相关(ncc - C)因其几何解释简单、特征不确定而被广泛应用于图像配准。这里,在回顾了具有任意数量维度和通道的图像的ncc定义之后,我们提出了一种概化方法,其中每个通道的每个像素值可以使用实数非负数单独加权。例如,这种广义归一化加权互相关(N W C C)及其零均值当量(Z N W C C)可用于根据信噪比对像素进行优先排序。就像之前定义的具有二元权值的nwcc一样,所提出的概化方法可以对具有不规则边界和/或稀疏采样的均匀(但不一定是各向同性)采样图像进行配准。这里讨论的所有nc定义都提供了用于快速计算的离散傅里叶变换(dft)公式。简要讨论了ncc计算实现的实际方面,并介绍了一个方便的函数来计算具有不规则边界和/或稀疏采样的均匀但不一定是各向同性的采样图像的重叠,以及它的D - F - T公式。最后,举例说明了所提出的归一化互相关函数的好处。
Normalized weighted cross correlation for multi-channel image registration.
The normalized cross-correlation ( ) is widely used for image registration due to its simple geometrical interpretation and being feature-agnostic. Here, after reviewing definitions for images with an arbitrary number of dimensions and channels, we propose a generalization in which each pixel value of each channel can be individually weighted using real non-negative numbers. This generalized normalized weighted cross-correlation ( ) and its zero-mean equivalent ( ) can be used, for example, to prioritize pixels based on signal-to-noise ratio. Like a previously defined with binary weights, the proposed generalizations enable the registration of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling. All definitions discussed here are provided with discrete Fourier transform ( ) formulations for fast computation. Practical aspects of computational implementation are briefly discussed, and a convenient function to calculate the overlap of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling is introduced, together with its formulation. Finally, examples illustrate the benefit of the proposed normalized cross-correlation functions.