GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models

We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes. Instead of optimizing the parameterization of each shape independently, our method learns a neural generative model that predicts a continuous mapping from the unit sphere to shapes in a dataset. Under this formulation, spherical parameterizations are obtained through the inverse mappings of the learned generator, which encourages similar shapes to share consistent parameterizations. To make this formulation practical, we address several key challenges in learning such a generative model. First, we introduce a continuous neural deformation model that predicts surface points from sphere coordinates and latent shape codes, avoiding discretization artifacts common in mesh-based formulations. Second, we augment the training space with intermediate shapes that bridge the sphere and input shapes, allowing the model to learn meaningful deformations across a heterogeneous shape collection. Third, we compute reliable initial correspondences by propagating mappings along a spanning tree of training shapes in the latent space. Experiments on the ShapeNet dataset demonstrate that our approach significantly reduces geometric distortion and improves cross-shape consistency compared with state-of-the-art spherical parameterization methods.

Hierarchical Neural Surfaces for 3D Mesh Compression

Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts of traditional implicit representations of 3D geometries, such as signed distance functions. However, the triangle mesh-based representation of geometry remains the most widely used representation in the industry, while building INRs capable of generating them has been sparsely studied. In this paper, we present a method for building compact INRs of zero-genus 3D manifolds. Our method relies on creating a spherical parameterization of a given 3D mesh - mapping the surface of a mesh to that of a unit sphere - then constructing an INR that encodes the displacement vector field defined continuously on its surface that regenerates the original shape. The compactness of our representation can be attributed to its hierarchical structure, wherein it first recovers the coarse structure of the encoded surface before adding high-frequency details to it. Once the INR is computed, 3D meshes of arbitrary resolution/connectivity can be decoded from it. The decoding can be performed in real time while achieving a state-of-the-art trade-off between reconstruction quality and the size of the compressed representations.

GeoScaler: Geometry and Rendering-Aware Downsampling of 3D Mesh Textures

High-resolution texture maps are necessary for representing real-world objects accurately with 3D meshes. The large sizes of textures can bottleneck the real-time rendering of high-quality virtual 3D scenes on devices having low computational budgets and limited memory. Downsampling the texture maps directly addresses the issue, albeit at the cost of visual fidelity. Traditionally, downsampling of texture maps is performed using methods like bicubic interpolation and the Lanczos algorithm. These methods ignore the geometric layout of the mesh and its UV parametrization and also do not account for the rendering process used to obtain the final visualization that the users will experience. Towards filling these gaps, we introduce GeoScaler, which is a method of downsampling texture maps of 3D meshes while incorporating geometric cues, and by maximizing the visual fidelity of the rendered views of the textured meshes. We show that the textures generated by GeoScaler deliver significantly better quality rendered images compared to those generated by traditional downsampling methods