## 2 Materials and Methods
### Processing the Images  
#### 2.3.1 Image Segmentation  
To quantify the volumetric fractions of the different coarse aggregates (gravel, EVA, and fibers) using the Micro-CT images, firstly, grayscale segmentation was performed. This process consists of dividing the image into different regions with colors ranging in a certain number of intervals (classes) in which the different constituents are found, such that it is possible process the regions of interest individually. The most used techniques to segment grayscale images are based on thresholds. The Otsu and K-means [32; 33] methods stand out among thresholding techniques. In any given case, once the number of \(\mathcal{K}\) classes is determined, the method assigns to each pixel \(p\) of color \(x_{p}\in[0,255]\) (grayscale), one of the chosen colors \(X_{k}\), \(k=1,2,\ldots,\mathcal{K}\) to represent the segmented image. The way in which a class \(k\in[1,\mathcal{K}]\) is assigned to each pixel \(p\) depends on the thresholding method. The K-means method iteratively searches for the \(\mathcal{K}\) centroids (the colors) \(C_{k}\), \(k=1,2,\ldots,\mathcal{K}\) of the classes and assigns to each pixel \(p\) of color \(x_{p}\) the class \(k\) whose  
Figure 1: Segmentation of coarse aggregate for RC sample. (**a**) Micro-CT image. (**b**) K-means + open/close morphological operation segmentation. (**c**) Range-constraint Otsu segmentation. Figure 2: Segmentation of elements present in the cement paste for a EF25 sample. (**a**) Micro-CT image. (**b**) K-means + open/close morphological operation segmentation. (**c**) Range-constraint Otsu segmentation. centroid \(C_{\kappa}\) is closest, i.e., \(|x_{p}-C_{\kappa}|=\min_{k\in[1,\mathcal{K}]}|x_{p}-C_{k}|\). When all pixels have been assigned to a class, their centroids are updated as the mean of the colors of all pixels belonging to each class. Every time a centroid is updated (changes its value), the pixel distribution per class is repeated. The iterative process ends when no centroids are updated [33]. The Otsu method searches exhaustively for the \(\mathcal{K}-1\) thresholds between the classes \(l_{k},k=1,2,\ldots,\mathcal{K}-1\), such that \(l_{1}<l_{2}<\cdots<l_{\mathcal{K}-1}\), and assigns class \(k\) to a pixel \(p\) of color \(x_{p}\), if \(l_{k-1}\leq x_{p}<l_{k}\), for a \(k\in[1,\mathcal{K}]\). The grayscale boundaries are denoted by \(l_{0}=0\) (black) and \(l_{\mathcal{K}}=255\) (white). The choice between the \(\mathcal{K}(\mathcal{K}-1)/2\) color combinations of the \(\mathcal{K}\) thresholds \(l_{1},l_{2},\ldots,l_{\mathcal{K}}\) is made by choosing the color combination which maximizes the interclass variance of the image [32]. After several unsuccessful attempts to make a single segmentation with 5 classes representing: (1) cement mass, (2) pores, (3) gravel, (4) EVA, and (5) fiber, the decision was made to use two binary segmentations:  
1. Segmentation gravel + remainder = differentiation of the densest aggregate from the remaining aggregates, as shown in Figure 1b where the gravel is in white and the remainder in black. This segmentation was performed in two steps. First, the K-means method with 3 classes was used since 3 dominant shades of gray were identified. In this context, the centroids were \(C_{1}\) = dark gray, \(C_{2}\) = gray, and \(C_{3}\) = light gray. The color between the light gray and gray centroids was then used as the binary segmentation threshold, that is, we defined the \(l_{\textit{graved}}=(C_{2}+C_{3})/2\), so that pixels with colors greater than \(l_{\textit{graved}}\) were considered gravel and lesser values are part of the remainder. 2. Segmentation (pores, EVA, fiber, and exterior) + remainder = differentiation of the light aggregates, air, and pores from the remainder, as shown in Figure 2c, where pores, EVA, and fiber + area outside the sample (air) are black and the remainder of the image is white. This segmentation was performed using the range-constrained Otsu method [26] which lead to optimal threshold.