Modeling 3D Surface Manifolds with a Locally Conditioned Atlas

TL;DR

The paper tackles the issue of discontinuities in patch-based 3D surface reconstructions from point clouds. It introduces LoCondA, a Locally Conditioned Atlas that combines a Continuous Atlas with a two-part architecture: Part A uses a pretrained hypernetwork-based autoencoder to map point clouds to a surface prior, and Part B uses a locally conditioned atlas to place and stitch patches on the surface. Key contributions include the Continuous Atlas formulation, a local conditioning mechanism to share information across patches, and an empirical demonstration of watertight, topologically diverse meshes with competitive generative and reconstruction performance on ShapeNet. This approach enables scalable, high-quality 3D mesh reconstructions suitable for real-world applications where seamless stitching and topology flexibility are essential.

Abstract

Recently proposed 3D object reconstruction methods represent a mesh with an atlas - a set of planar patches approximating the surface. However, their application in a real-world scenario is limited since the surfaces of reconstructed objects contain discontinuities, which degrades the quality of the final mesh. This is mainly caused by independent processing of individual patches, and in this work, we postulate to mitigate this limitation by preserving local consistency around patch vertices. To that end, we introduce a Locally Conditioned Atlas (LoCondA), a framework for representing a 3D object hierarchically in a generative model. Firstly, the model maps a point cloud of an object into a sphere. Secondly, by leveraging a spherical prior, we enforce the mapping to be locally consistent on the sphere and on the target object. This way, we can sample a mesh quad on that sphere and project it back onto the object's manifold. With LoCondA, we can produce topologically diverse objects while maintaining quads to be stitched together. We show that the proposed approach provides structurally coherent reconstructions while producing meshes of quality comparable to the competitors.

Figures (5)

• Figure 1: LoCondA extends a base generative hypermodel (Part A) by taking a point $p$ on the surface $S$ and mapping it to a patch covering a neighborhood of $p$ (Part B).
• Figure 2: Visualization of patches from the airplane. Parts next to each other are structurally similar and construct smooth surfaces.
• Figure 3: Mesh representations generated by our LoCondA (HyperCloud) method.
• Figure 4: Mesh representations generated by our LoCondA (HyperCloud) method with different number of patches.
• Figure 5: Mesh interpolation generated by our LoCondA (HyperCloud) method.