## 3 Results
### Extracting Profiles from the Images of Additively Manufactured Struts. Gaussian process modeling with the non-uniform sampling algorithm is applied to the sidewall profiles of AM fabricated struts. Figure 4a-c shows the CAD geometries of struts in 3 different printing angles (90\({}^{\circ}\), 75\({}^{\circ}\), and 60\({}^{\circ}\)) and printing directions. The layer thickness corresponds to 80 pixel units. The sidewall profiles of multiple AM fabricated struts with different angles (90\({}^{\circ}\), 75\({}^{\circ}\), and 60\({}^{\circ}\)) are shown in Figure 4d-f. The sidewall profile consists of multiple layers printed repeatedly layer-by-layer, and we assume that the spatial uncertainty in each printed layer is generated from an independent event, so that is not related to the neighboring layers. There are three parameters in Equation (1) that are reduced by considering the two ratios, \(\lambda_{b}/\lambda_{o}\) and \(\gamma/\lambda_{o}\). We manually segmented one printed layer in the image and varied the two ratios to determine the optimized parameter values to obtain the optimal match with respect to the manually segmented edge. After calibrating two ratios in the level set method, the same algorithm is applied to the remaining layers to extract the edge information from the image. \begin{table}
\begin{tabular}{l c c c} \hline  & \(\
u\) **(2)** & \(\phi\) **(2)** & \(\theta\) **(0.4)** \\ \hline
1 st sampled locations (14 points) & 2.011 \(\pm\) 0.027 & 2.052 \(\pm\) 0.028 & 0.416 \(\pm\) 0.012 \\
2 nd sampled locations (20 points) & 1.978 \(\pm\) 0.025 & 2.063 \(\pm\) 0.030 & 0.418 \(\pm\) 0.009 \\
3 rd sampled locations (31 points) & 1.971 \(\pm\) 0.016 & 2.055 \(\pm\) 0.029 & 0.415 \(\pm\) 0.007 \\ \hline \end{tabular}
\end{table} 
Table 2: Estimated hyperparameters in the covariance function for the test problem. The given values are denoted in the parentheses. Figure 3: Probability density functions (PDFs) of the estimated parameters in Matérn covariance function: (**a**) \(\
u\), (**b**) \(\phi\), and (**c**) \(\theta\). The blue line is a part of the given prior PDF at the displayed region and blue histogram is the frequency of sampled parameters from the posterior PDF. The red curve is a fitted normal distribution to the histogram. The histograms and the prior PDFs are not in the same scale. Figure 4g-i shows the binary masks of the images after segmentation in which the white pixels represent the segmented region of the strut and the black pixels denote the background region. Given the smooth intensity gradient from the center to the edge of the image, the segmentation at the edges of the images is inaccurate in the 75\({}^{\circ}\) and 60\({}^{\circ}\) cases in Figure 4h,i. The artifact from the background inhomogeneity can be easily removed by measuring and compensating the intensity gradient in the background. The compensation is not applied in the study to minimize the manual intervention. A more systematic approach to reduce the effect from the local inhomogeneity is given in [33]. The edge profile is extracted by collecting the outermost pixels in the left and right sidewalls of binary masks. Figure 5a,b shows the extracted edge profiles in the left and right sidewalls of each printed layer, respectively. It is clear that the side profile of all layers show consistent trend depending on the printing angle. This characteristic staircase profile is caused by the light absorption and scattering in the resin vat and light penetration during the curing of upper layer. In a manner similar to the test case, the mean of all observations, which represents the staircase profile, is subtracted from the sidewall profile; thus, the roughness spatial uncertainty is independent of the printed angle. The mean profile is obtained by simple summation of all side profiles in each printing angles. The summation averages out the local roughness from the mean profile. The mean trends extracted from all observations and the roughness extracted spatial uncertainties are shown in Figure 5c-f, respectively.