摘要翻译：
多孔介质和电极材料等非均匀材料的表征和重建涉及到图像处理方法对显微技术获取的数据的应用。在这项研究中，我们提出了一个理论分析的影响，图像尺寸缩小，由于逐步抽取原始图像。实现了三种不同的抽取过程，并报告和分析了它们对离散相关函数和粗糙度的影响。对每个相关函数进行了归一化。当抽取图像的统计信息损失不大时，根据原始图像的趋势预测其归一化相关函数。相反，当抽取图像不代表原始图像的统计证据时，归一化相关函数偏离参考函数。此外，差的平方的平均加权和导致了总误差的定义。在逐步抽取的第一阶段，误差保持相对较小，并独立于抽取程序。在由参考函数的相关长度定义的阈值以上，误差成为抽取步数的函数。在这个阶段，一些统计信息丢失，误差变得依赖于抽取过程。这些结果可以帮助我们限制在抽取过程中可以损失的信息量，以减少计算和存储成本，当我们旨在减少表征或重建技术所消耗的时间时，同时保持数字化样本的统计质量。
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英文标题：
《Effect of the image resolution on the statistical descriptors of
  heterogeneous media》
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作者：
Rene Ledesma-Alonso and Romeli Barbosa and Jaime Ortegon
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最新提交年份：
2017
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Image and Video Processing        图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
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一级分类：Physics        物理学
二级分类：Materials Science        材料科学
分类描述：Techniques, synthesis, characterization, structure.  Structural phase transitions, mechanical properties, phonons. Defects, adsorbates, interfaces
技术，合成，表征，结构。结构相变，力学性质，声子。缺陷，吸附质，界面
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英文摘要：
  The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by microscopy techniques. In this study, we present a theoretical analysis of the effects of the image size reduction, due to a gradual decimation of the original image. Three different decimation procedures were implemented and their consequences on the discrete correlation functions and the coarseness are reported and analyzed. A normalization for each of the correlation functions has been performed. When the loss of statistical information has not been significant for a decimated image, its normalized correlation function is forecast by the trend of the original image. In contrast, when the decimated image does not represent the statistical evidence of the original one, the normalized correlation function diverts from the reference function. Moreover, the equally weighted sum of the average of the squared differences leads to a definition of an overall error. During the first stages of the gradual decimation, the error remains relatively small and independent of the decimation procedure. Above a threshold defined by the correlation length of the reference function, the error becomes a function of the number of decimation steps. At this stage, some statistical information is lost and the error becomes dependent of the decimation procedure. These results may help us to restrict the amount of information that one can afford to lose during a decimation process, in order to reduce the computational and memory cost, when one aims to diminish the time consumed by a characterization or reconstruction technique, yet maintaining the statistical quality of the digitized sample.
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PDF链接：
https://arxiv.org/pdf/1712.03183