# 3D Reconstruction of Celadon from a 2D Image: Application to Path Tracing and VR
## 4 Experimental Results  
Our approach was implemented on a Windows PC with an Intel Core i7-11700 2.5 GHz processor, 32 GB of RAM, and an NVIDIA GeForce RTX 3070 graphics card, using Python 3.11.1. We experimented with eight celadon examples [34] by processing their 2D input images to generate corresponding 3D models. In order to simplify data acquisition, we limited ourselves to using one image per celadon. For rendering the 3D celadon models in various scenes and evaluating their suitability in different environments [35], we employed the Mitsuba 3 renderer [22]. Furthermore, we used Unreal Engine 5 [36] to construct a VR celadon museum exhibiting the models. Figure 5 shows the results of the 3D reconstruction for the celadons, from \(\mathcal{P}_{0}\) to \(\mathcal{P}_{7}\). The first row of Figure 5 shows input 2D celadon images. The second row shows each image's axis of revolution **A** and profile curve \(C\), shown in blue and black, and the third row shows their texture images. The last row shows the generated 3D celadon models for each input image based on their **A**, \(C\), and texture images. Figure 4: The rendered images of a \(\mathcal{P}_{0}\) model by rotating it 360\({}^{\circ}\) in a 60\({}^{\circ}\) interval. Figure 5: Geometric data generated by our 3D reconstruction algorithm from input image: axis of revolution **A**, profile curve \(C\), generated texture image, and generated 3D model with texture. Table 1 presents numerical information, such as the computing time for each step of the 3D reconstruction process. Image processing took a similar time for all examples. However, the non-uniformly splitting B-spline curve can impact the resulting 3D model's generation time. As the number of divided domains increases, the number of points and faces in the corresponding 3D model also increases, resulting in slower 3D model generation. The number of divided domains depends on the curvature variations of each profile curve of the celadon, so it has a unique value according to the celadon examples. Meanwhile, we computed the approximation error of the B-spline profile curve \(C\) by measuring the one-sided Hausdorff distance to the profile polyline curve with [PERSON]'s approximation technique [14]. As shown in Table 1, the B-spline profile curve \(C\) approximations are considered to be accurate since their approximation errors are at most 2.33 pixels. Through several rendering tests, we decided to set the SPP value \(\sigma\) to 64 for low quality and 1024 for high quality and selected HD (\(1280\times 720\)), FHD (\(1920\times 1080\)), and 4K (\(3840\times 2160\)) as the image resolutions to experiment. The scenes were rendered using these two \(\sigma\) values and three image resolutions. Since our GPU hardware does not support \(\sigma\) to 1024 in 4K, we selected 512 for high quality in 4K. The rendering times for each scene at different resolutions and \(\sigma\) values are displayed in Table 2, with each scene represented by a subscript. The results show that the rendering time for each scene is proportional to the image resolution and \(\sigma\). In particular, the scene \(\mathcal{S}_{showcase}\), as shown in Figure 1 with a celadon encased in glasses, is rendered slowly as brighter scenes \(\mathcal{S}_{lifting}\), \(\mathcal{S}_{kitchen}\), and \(\mathcal{S}_{lounge}\) because path tracing the glass material requires high computational costs. Figure 6a shows the scenes without our 3D reconstructed celadon models, and Figure 6b includes them, with \(\sigma=1024\) and HD resolution. Please note that all scenes were rendered with a GPU and then denoised using an Opti AI-accelerated Denoiser [37]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Celadon**} & \multicolumn{3}{c}{**Image Processing**} & \multicolumn{3}{c}{**B-Spline**} & \multicolumn{3}{c}{**3D Model**} & \multirow{2}{*}{ \begin{tabular}{c} **Approx.** \\ **Error** \\ **(Pixels)** \\ \end{tabular}  } \\ \cline{2-2} \cline{6-9}  & \begin{tabular}{c} **Time (ms)** \\ \end{tabular}  &