CONACYT-Universidad de Quintana Roo, Boulevar Bahía s/n, Chetumal, 77019, Quintana Roo, México and Universidad de las Américas Puebla, Sta. Catarina Mártir, San Andrés Cholula, 72810, Puebla, México.
Universidad de Quintana Roo, Boulevar Bahía s/n, Chetumal, 77019, Quintana Roo, México.
Phys Rev E. 2018 Feb;97(2-1):023304. doi: 10.1103/PhysRevE.97.023304.
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 scanning electron microscopy or other microscopy techniques. Among them, binarization and decimation are critical in order to compute the correlation functions that characterize the microstructure of the above-mentioned materials. In this study, we present a theoretical analysis of the effects of the image-size reduction, due to the progressive and sequential decimation of the original image. Three different decimation procedures (random, bilinear, and bicubic) were implemented and their consequences on the discrete correlation functions (two-point, line-path, and pore-size distribution) and the coarseness (derived from the local volume fraction) are reported and analyzed. The chosen statistical descriptors (correlation functions and coarseness) are typically employed to characterize and reconstruct heterogeneous materials. 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 (reference function). In contrast, when the decimated image does not hold 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 difference, between the discrete correlation functions of the decimated images and the reference functions, 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 on 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.
多相材料（如多孔介质和电极材料）的特性描述和重构需要应用图像处理方法对扫描电子显微镜或其他显微镜技术获取的数据进行处理。其中，二值化和降采样对于计算描述上述材料微观结构的相关函数至关重要。在本研究中，我们对由于原始图像的逐步和顺序降采样导致的图像尺寸减小的影响进行了理论分析。实施了三种不同的降采样过程（随机、双线性和双三次），并报告和分析了它们对离散相关函数（两点、线路径和孔径分布）和粗糙度（由局部体积分数导出）的影响。所选的统计描述符（相关函数和粗糙度）通常用于描述和重构多相材料。对每个相关函数都进行了归一化。当降采样图像中没有显著损失统计信息时，其归一化相关函数可以通过原始图像的趋势（参考函数）进行预测。相反，当降采样图像不具有原始图像的统计证据时，归一化相关函数会偏离参考函数。此外，通过离散相关函数的平均平方差的等权重和，得到了一个整体误差的定义。在逐渐降采样的早期阶段，误差相对较小且与降采样过程无关。在参考函数的相关长度定义的阈值之上，误差成为降采样步骤数的函数。在这个阶段，一些统计信息丢失，误差取决于降采样过程。这些结果可以帮助我们在进行降采样过程时限制可以承受的信息量，以减少特征描述或重构技术所消耗的时间，同时保持数字化样本的统计质量。
