Bi-directional Deformation for Parameterization of Neural Implicit Surfaces

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.