ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction

Standard pipelines for physics-ready 3D reconstruction rely on a decoupled two-stage paradigm: extracting surface geometry followed by an error-prone tetrahedralization process. While recent Lagrangian methods like TetSphere Splatting attempt to bypass this by directly optimizing volumetric primitives, their homeomorphic constraints prevent topology-adaptive optimization. Consequently, they produce disjoint tetrahedra rather than a single connected mesh, rendering the structures unsuitable for further physical simulations. To address this, we propose a topology-adaptive framework for holistic tetrahedral mesh reconstruction through end-to-end topological and geometric optimization. First, by coupling Gaussian spheres to tetrahedral elements and leveraging edge connections, we estimate a continuous opacity field for differentiable element pruning. Next, jointly minimizing mesh smoothing energy and multi-view Gaussian rendering error drives alternating geometric refinement while preserving topological adaptivity. Consequently, our approach effectively constructs a unified and topologically coherent tetrahedral mesh. Extensive experiments demonstrate that our method outperforms state-of-the-art techniques by achieving superior geometric accuracy and producing coherent, single-connected tetrahedral meshes, thereby effectively bypassing the error-prone conventional tetrahedralization step for reconstructed surface meshes and streamlining downstream physical simulation.

Reconstructing surface meshes from multi-view images has remained a core challenge in recent years. Most existing methods, whether implicit or explicit, depend on intermediate representations and post-processing steps like Marching Cubes or TSDF fusion, often resulting in artifacts and fragmented geometry. Directly optimizing explicit meshes is a promising approach. However, it presents two critical challenges. The first is how to adaptively refine mesh topology to capture detail without introducing degenerate faces. The second is how to maintain consistent UV coordinates for high-fidelity texturing as the mesh structure evolves. To overcome these, we propose ExMesh, a novel framework that directly optimizes explicit meshes by integrating differentiable optimization with discrete topology updates. Specifically, we introduce an adaptive vertex splitting and merging strategy, along with real-time UV maintenance, to enable coarse-to-fine optimization while preserving geometric integrity. To our knowledge, ExMesh is the first framework to seamlessly integrate discrete topology operations into a continuous differentiable optimization pipeline. Extensive experiments demonstrate that ExMesh achieves a balance among accuracy, computational efficiency, and mesh conciseness.

Differentiable rendering has emerged as a powerful approach for 3D reconstruction and novel view synthesis. State-of-the-art differentiable rendering methods combine a variety of custom representations of 3D geometry and appearance with specialized renderers. However, most downstream tasks in computer graphics rely on 3D meshes. While prior work has attempted differentiable rendering with mesh representations, these approaches are limited to object-centric scenes and fail to reconstruct large-scale, unbounded scenes. In this work, we introduce Meshtryoshka, a novel mesh differentiable rendering framework that combines an off-the-shelf triangle rasterizer with a 3D representation that consists of nested mesh shells which resemble a matryoshka doll. In every forward pass, the mesh shells are extracted anew from a 3D signed distance function via iso-surface extraction, and the opacities for each vertex are computed as a function of signed distance. Each mesh shell is then rasterized independently, and the final image is created via alpha compositing. Crucially, mesh vertex positions are updated only indirectly via gradients that flow through the opacity values into the signed distance function, and hence, our method is compatible with off-the-shelf mesh renderers that need not be differentiable with respect to vertex positions. On object-centric scenes, our method performs competitively with surface-based differentiable rendering techniques. Our differentiable mesh rendering method scales to unbounded, real-world 3D scenes, where it yields high-quality novel view synthesis results approaching those of state-of-the-art, non-mesh methods. Our method suggests that it may be possible to solve the differentiable rendering problem without relying on specialized renderers, only using conventional tools from the computer graphics toolbox.