GEOMetrics: Exploiting Geometric Structure for Graph-Encoded Objects

TL;DR

GEOMetrics leverages the geometric structure of graph-encoded 3D objects to improve mesh reconstruction, achieving state-of-the-art results with efficient adaptive meshes by combining specialized graph convolutions, heuristics, and multi-level training.

Contribution

The paper introduces a novel system that exploits geometric structure in graph-encoded objects through a graph convolutional update, an adaptive splitting heuristic, and a dual-level training objective.

Findings

Achieves state-of-the-art 3D reconstruction performance on ShapeNet.

Produces smaller, adaptive meshes with detailed surface representation.

Demonstrates improved visual and numerical results over existing methods.

Abstract

Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to compromises with respect to performance or resolution. In this paper, we argue that the graph representation of geometric objects allows for additional structure, which should be leveraged for enhanced reconstruction. Thus, we propose a system which properly benefits from the advantages of the geometric structure of graph encoded objects by introducing (1) a graph convolutional update preserving vertex information; (2) an adaptive splitting heuristic allowing detail to emerge; and (3) a training objective operating both on the local surfaces defined by vertices as well as the global structure defined by the mesh. Our proposed method is evaluated on the task of 3D object reconstruction from images with the ShapeNet dataset, where we demonstrate state of the art performance, both visually and numerically, while having far smaller space requirements by generating adaptive meshes