# 3D Reconstruction of Celadon from a 2D Image: Application to Path Tracing and VR
###### Abstract  
We present a straightforward approach for reconstructing 3D eladon models from a single 2D image. The celadon is a historical example of the surface of revolution. Our approach uses a surface of revolution technique to generate the basic shape of the celadon and then applies texture mapping to create a realistic appearance. The process involves detecting the contour and corners of the celadon image, determining an axis of revolution, generating a profile curve, and finally constructing a 3D celadon model. Additionally, we create models as triangular meshes at multiple resolutions, employing a B-spline curve as the profile curve. It enhances the adaptability of the models for various purposes. We render various scenes using a path tracer to assess the suitability of the generated 3D celadon models and generate a VR celadon museum with the models. Overall, our approach offers a simple and efficient solution for reconstructing a 3D celadon model, generating VR content, and demonstrating extensive applicability across numerous disciplines. 3D reconstruction; surface of revolution; celadon; VR museum; path tracing +
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From a geometric perspective, the celadon is shaped like a surface of revolution. This unique characteristic simplifies the creation of 3D data compared to other complex 3D objects. Surfaces of revolution can be defined using only two parameters: a profile curve \(C\) and an axis of revolution A. Accurately representing the profile curve is the key to successful 3D reconstructions. We first extract a profile polyline using image processing techniques that consider the celadon in the input image as a surface of revolution. The profile polyline can be converted to the B-spline profile curve \(C\) by curve fitting [13; 14]. B-spline curves are locally defined splines representing various geometry types by adjusting degrees, knots, and control points [15; 16]. This property represents the profile curve at different resolutions with fewer data, maintaining the shape of the celadon. Fitting the profile polyline to the B-spline profile curve offers several advantages over other algorithms [17; 18; 19; 20; 21] in that the B-spline can offer superior curve representation and accuracy compared to these algorithms. Based on the process, we generate 3D celadon models by rotating the curve around the axis. The final step is to generate textures that include the colors and patterns of the celadon and apply these to the 3D models. To do so, we first separate a celadon region from a background in the input image. Then, we automatically generate rectangular-shaped texture images using linear interpolation. Applying the generated textures to the celadons will help to analyze and understand them. There are several ways to represent 3D data, such as triangular mesh, point clouds, voxels, and implicit surfaces. We construct 3D celadon models in the triangular mesh, put the generated textures on them, and render in various scenes using a path tracer [22]. When rendering a scene using a path tracer, selecting a value of samples per pixel (SPP) \(\sigma\) is crucial because it is a trade-off between image quality and rendering speed. The main contributions of this work can be summarized as follows:  
* We propose a general guideline for obtaining a 3D celadon model from one single 2D image without requiring any additional inputs. * Our method considers the celadon in the input images as a surface of revolution and extracts a profile polyline and an axis of revolution from it. * Using the fitted B-spline profile curve, we can generate 3D models at various resolutions we want. * We automatically generate a texture image of the celadon by separating a region of the celadon from a background in the input image and applying linear interpolation. * We produce various scenes with our 3D celadon models using a path tracer [22] and assess their suitability.