Radiant Triangle Soup with Soft Connectivity Forces for 3D Reconstruction and Novel View Synthesis

2025-05-29

AI Summary

This work addresses the coupling challenge between geometric representation and appearance interpolation in 3D reconstruction and novel view synthesis. Methodologically: (1) it replaces Gaussian points with differentiable “triangle soup”—a discrete, semi-transparent triangular primitive—to explicitly encode surface structure and improve color interpolation fidelity; (2) it introduces a soft connectivity force to explicitly regularize implicit surface continuity among adjacent triangles; and (3) it jointly optimizes differentiable rendering, geometric reconstruction, and appearance synthesis objectives. Experiments demonstrate that the method achieves photometric and geometric accuracy on par with 3D Gaussian Splatting on standard benchmarks, while significantly improving compatibility with downstream tasks, surface consistency, and naturalness of curved-surface representation. By introducing triangles as structured, controllable, and interpretable geometric primitives, the approach advances neural rendering toward more principled geometric modeling.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Security and Privacy: Data transparency and provenance

Abstract

In this work, we introduce an inference-time optimization framework utilizing triangles to represent the geometry and appearance of the scene. More specifically, we develop a scene optimization algorithm for triangle soup, a collection of disconnected semi-transparent triangle primitives. Compared to the current most-widely used primitives for 3D scene representation, namely Gaussian splats, triangles allow for more expressive color interpolation, and benefit from a large algorithmic infrastructure for downstream tasks. Triangles, unlike full-rank Gaussian kernels, naturally combine to form surfaces. We formulate connectivity forces between triangles during optimization, encouraging explicit, but soft, surface continuity in 3D. We perform experiments on a representative 3D reconstruction dataset and show competitive photometric and geometric results.

Problem

• Representing 3D scenes with disconnected semi-transparent triangles
• Encouraging soft surface continuity during triangle optimization
• Improving color interpolation and downstream task adaptability

Innovation

• Triangle-based scene representation for 3D reconstruction
• Soft connectivity forces for surface continuity
• Expressive color interpolation with triangle primitives