## 2 Materials and Methods
### Methodology
#### 2.2.2 Data Preprocessing  
Obtention of Projection Images  
The approach to UT-XCT volume registration was a 2D image registration of projections. During a pre-processing step, both volumes were manually aligned in the 3D space. The XCT projections were the result of the summation of several consecutive images (parallel to the composite surface) at different depths in the volume, whereas the maximum operator was used to obtain the projections at different depths in the US volume (Equation (1) defines the determination of a projection). The number of images to be included in each projection (k parameter) was manually selected to identify sufficient similar structures in the XCT and US projections. The process is defined below.  
Let \(I=\{1,\ldots,1\}\) denote the indices of the rows of a matrix \(A\).  
Let \(J=\{1,\ldots,m\}\) denote the indices of the columns of matrix \(A\)  
Let \(K=\{1,\ldots,n\}\) denote the indices of the slices of matrix \(A\)  
\(I\), \(J\), \(K\) are oriented to the height, width and thickness of the coupon, respectively  
Let \(a_{ij,k}\) denote the value of the element \(A[i,j,k]\)  
Let \(F\) be the summation operation in the case of XCT. The maximum operation in the case of the ultrasonic data  
\[projection=U_{ij}=F(a_{ij})_{k=k_{1}}^{k_{2}},\quad i=1,\ldots,l\quad j=1, \ldots,m;\ k_{1}\,\text{and}\,k_{2}\,\text{found experimentally}. \tag{1}\]  
The summation operation was found to be better suited for XCT because it highlights regions (white areas in Figure 2) and provides more microstructural information. After extracting all the images, histogram matching was applied to ultrasonic projections, and their pixel values were normalized in the interval [0,1]. This was performed to offset the differing intensity across the width due to ultrasound wave attenuation. This methodology output a total of 12 images for two 5 mm-thick coupons. The XCT images were scaled to fit the size of the PA projections, which was equal to 470 \(\times\) 120 mm.  
Figure 2: Detail of a pair of projections illustrating the keypoints identifying common voids.  
2D Registration of Projections  
The registration was carried out on each pair of images. The XCT projection was used as a reference, and the ultrasonic projection as a moving image. We tested several automatic methods, and, as shown in Figure 2, the use of manually placed landmarks in common structures yielded the best results. The main obstacle to automated registration was that equivalent keypoints in the image pairs could not be identified automatically. The image registration algorithm is detailed in [36].  
Labels  
The registration was performed on gray-level XCT projections. The XCT-label projections were obtained through the segmentation of the gray-level XCT projections, which was performed using the local segmentation Sauvola filter algorithm (implemented in ImageJ).  
A second labeling was performed as a result of the resolution differences between XCT and UT, which is explained in the discussion. To perform manual annotation, the registered projections of XCT and UT were superimposed, and the annotation was performed based on human criteria.