Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis (2111.04276v1)

Abstract: We introduce DMTet, a deep 3D conditional generative model that can synthesize high-resolution 3D shapes using simple user guides such as coarse voxels. It marries the merits of implicit and explicit 3D representations by leveraging a novel hybrid 3D representation. Compared to the current implicit approaches, which are trained to regress the signed distance values, DMTet directly optimizes for the reconstructed surface, which enables us to synthesize finer geometric details with fewer artifacts. Unlike deep 3D generative models that directly generate explicit representations such as meshes, our model can synthesize shapes with arbitrary topology. The core of DMTet includes a deformable tetrahedral grid that encodes a discretized signed distance function and a differentiable marching tetrahedra layer that converts the implicit signed distance representation to the explicit surface mesh representation. This combination allows joint optimization of the surface geometry and topology as well as generation of the hierarchy of subdivisions using reconstruction and adversarial losses defined explicitly on the surface mesh. Our approach significantly outperforms existing work on conditional shape synthesis from coarse voxel inputs, trained on a dataset of complex 3D animal shapes. Project page: https://nv-tlabs.github.io/DMTet/.

• The paper introduces DMT, which integrates implicit and explicit 3D representations to overcome traditional synthesis challenges.
• It employs a deformable tetrahedral grid with a differentiable marching tetrahedra layer to dynamically capture and refine local shape details.
• It achieves state-of-the-art results in point cloud reconstruction and 3D super-resolution while reducing computation time.

Deep Marching Tetrahedra: A Hybrid Representation for High-Resolution 3D Shape Synthesis

In the domain of 3D shape synthesis, the paper titled "Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis" presents an innovative method, abbreviated as DMT, for efficiently generating highly detailed 3D shapes. This research introduces a pioneering hybrid 3D representation that integrates both implicit and explicit methodologies, aimed at overcoming the limitations of existing approaches that separately utilize these methods.

Traditional methods often involve implicit representations such as signed distance functions (SDFs), which adeptly handle arbitrary complex geometries and topologies. However, these conventional approaches face challenges in achieving explicit geometric constraints, often resulting in surface artifacts. Alternatively, explicit representations, like meshes, offer tangible surface geometry but become complex when dealing with arbitrary topology. The DMT method directly addresses these limitations by leveraging a deformable tetrahedral grid to encode SDFs, coupled with a differentiable marching tetrahedra layer. This combination allows for dynamically adjusting grid resolution to capture local shape details efficiently, differentiating it from existing methods.

One key advantage of DMT is its ability to synthesize high-resolution 3D shapes from user-provided guides, such as coarse voxel grids, without being restricted to fixed topology templates. The deformable tetrahedral grid in DMT serves as a discretized spatial representation, where tetrahedrons are selectively subdivided and deformed to optimize surface geometry and topology jointly. This process is orchestrated through a learning framework that employs reconstruction and adversarial losses defined directly on the surface mesh, facilitating the recovery of high-quality shapes from minimal input.

In terms of performance, DMT achieves state-of-the-art results in point cloud reconstruction and 3D super-resolution tasks, particularly when compared to high-resolution isotropic grid approaches like marching cubes. This is achieved with the significant advantage of reducing computation time, exemplifying efficiency gains through adaptive resolution tailoring without compromising on the resolution of key geometric features.

The implications of this research extend to fields heavily reliant on high-quality 3D model generation, such as virtual reality, gaming, and digital content creation. DMT's hybrid representation potentially democratizes high-fidelity 3D asset creation by enabling non-expert users to produce intricate models from basic inputs, akin to popular voxel-based platforms like Minecraft.

Looking towards future developments, DMT's framework could be enhanced with adaptive learning mechanisms that further refine grid resolution and mesh optimization based on model complexity or application-specific requirements. Moreover, exploring this representation's application in real-time systems could open avenues for instantaneous high-resolution modeling, directly influencing interactive virtual environments and simulations.

From a theoretical standpoint, DMT consolidates the strengths of implicit and explicit representations, offering a cohesive solution to challenges in high-resolution 3D shape synthesis. Its approach could inspire similar hybrid models across other domains of artificial intelligence, where combining algorithmic efficiencies with robust learning frameworks becomes necessary for achieving practical applicability.