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arXiv 2410.19085cs.CVcs.AIeess.IV
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互相关模板匹配中的一个反例

A Counterexample in Cross-Correlation Template Matching

Texas A&M University(得克萨斯农工大学)

Serap A. Savari

AI总结:

论文针对一维空间受限分段常数函数的含噪离散配准,给出互相关模板匹配失效的反例,并证明结合差分序列、阈值化与动态规划可在一定噪声条件下同时完成对齐和分割。

摘要:

采样和量化是信号与图像处理中的标准做法,但对其影响的理论理解仍不完整。我们考虑当底层函数为一维空间受限分段常数函数时的离散图像配准问题。对于理想无噪声采样,函数支撑集每个区域的采样数量通常取决于采样网格的位置。因此,如果函数的采样含有噪声,图像配准就需要对数据序列进行对齐与分割。对齐图像的一种流行策略是从互相关模板匹配中选取最大值。为推动研究同时解决分割问题的更鲁棒、更准确的方法,我们给出了一个一维空间受限分段常数函数的例子:在含噪采样上,互相关技术可能表现很差。尽管早期改进该方法的途径涉及归一化,但我们的例子在所处设定下提示了一种新策略。差分序列、阈值化和动态规划是图像处理中众所周知的技术。我们证明,在关于噪声的某些条件下,它们是正确对齐并分割含噪数据序列的工具。我们还讨论了在更一般情况下可能出现的一些潜在困难。

英文摘要:

Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional spatially-limited piecewise constant function. For ideal noiseless sampling the number of samples from each region of the support of the function generally depends on the placement of the sampling grid. Therefore, if the samples of the function are noisy, then image registration requires alignment and segmentation of the data sequences. One popular strategy for aligning images is selecting the maximum from cross-correlation template matching. To motivate more robust and accurate approaches which also address segmentation, we provide an example of a one-dimensional spatially-limited piecewise constant function for which the cross-correlation technique can perform poorly on noisy samples. While earlier approaches to improve the method involve normalization, our example suggests a novel strategy in our setting. Difference sequences, thresholding, and dynamic programming are well-known techniques in image processing. We prove that they are tools to correctly align and segment noisy data sequences under some conditions on the noise. We also address some of the potential difficulties that could arise in a more general case.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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