The growing capabilities of neural rendering have increased the demand for new techniques that enable the intuitive editing of 3D objects, particularly when they are represented as neural implicit surfaces. In this paper, we present a novel neural algorithm to parameterize neural implicit surfaces to simple parametric domains, such as spheres, cubes or polycubes, where 3D radiance field can be represented as a 2D field, thereby facilitating visualization and various editing tasks. Technically, our method computes a bi-directional deformation between 3D objects and their chosen parametric domains, eliminating the need for any prior information. We adopt a forward mapping of points on the zero level set of the 3D object to a parametric domain, followed by a backward mapping through inverse deformation. To ensure the map is bijective, we employ a cycle loss while optimizing the smoothness of both deformations. Additionally, we leverage a Laplacian regularizer to effectively control angle distortion and offer the flexibility to choose from a range of parametric domains for managing area distortion. Designed for compatibility, our framework integrates seamlessly with existing neural rendering pipelines, taking multi-view images as input to reconstruct 3D geometry and compute the corresponding texture map. We also introduce a simple yet effective technique for intrinsic radiance decomposition, facilitating both view-independent material editing and view-dependent shading editing. Our method allows for the immediate rendering of edited textures through volume rendering, without the need for network re-training. Moreover, our approach supports the co-parameterization of multiple objects and enables texture transfer between them. We demonstrate the effectiveness of our method on images of human heads and man-made objects. We will make the source code publicly available.

翻译：随着神经渲染能力的不断增强，人们对能够实现三维物体直观编辑的新技术需求日益增长，尤其是当物体以神经隐式曲面表示时。本文提出了一种新颖的神经算法，可将神经隐式曲面参数化到简单的参数域（如球体、立方体或多立方体），使得三维辐射场可表示为二维场，从而便于可视化及各类编辑任务。在技术层面，我们的方法通过计算三维物体与其选定参数域之间的双向形变，无需任何先验信息。我们采用从三维物体零水平集上的点到参数域的正向映射，随后通过逆形变进行反向映射。为确保映射是双射的，我们引入循环损失，同时优化两个形变的光滑性。此外，我们利用拉普拉斯正则化有效控制角度扭曲，并提供选择多种参数域的灵活性以管理面积扭曲。本框架设计具有兼容性，可无缝集成到现有神经渲染管线中，以多视角图像为输入重建三维几何并计算对应的纹理映射。我们还提出一种简单而有效的本征辐射分解技术，便于实现视角无关的材料编辑与视角相关的明暗编辑。通过体渲染可直接呈现编辑后的纹理，无需重新训练网络。此外，我们的方法支持多个物体的协同参数化，并实现它们之间的纹理迁移。我们在人头与人造物体的图像上验证了方法的有效性。源代码将公开发布。