Geometry Distributions
This addresses limitations in 3D geometric learning for applications like mesh representation and rendering, though it appears incremental as it builds on diffusion models.
The paper tackles the problem of representing 3D geometry with neural networks, which struggle with thin structures and non-watertight shapes, by proposing a distribution-based representation that achieves high geometric fidelity without assumptions about surface properties.
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.