LinPrim: Linear Primitives for Differentiable Volumetric Rendering

TL;DR

This paper introduces linear primitive-based volumetric scene representations using octahedra and tetrahedra, enabling efficient differentiable rendering and comparable reconstruction quality with fewer primitives.

Contribution

It presents a novel differentiable rasterizer for linear primitives, offering an alternative to NeRF and 3D Gaussian representations with real-time capabilities.

Findings

Comparable performance to state-of-the-art methods

Fewer primitives needed for similar fidelity

Provides insights into 3D representation fidelity

Abstract

Volumetric rendering has become central to modern novel view synthesis methods, which use differentiable rendering to optimize 3D scene representations directly from observed views. While many recent works build on NeRF or 3D Gaussians, we explore an alternative volumetric scene representation. More specifically, we introduce two new scene representations based on linear primitives - octahedra and tetrahedra - both of which define homogeneous volumes bounded by triangular faces. To optimize these primitives, we present a differentiable rasterizer that runs efficiently on GPUs, allowing end-to-end gradient-based optimization while maintaining real-time rendering capabilities. Through experiments on real-world datasets, we demonstrate comparable performance to state-of-the-art volumetric methods while requiring fewer primitives to achieve similar reconstruction fidelity. Our findings deepen the understanding of 3D representations by providing insights into the fidelity and performance characteristics of transparent polyhedra and suggest that adopting novel primitives can expand the available design space.