Representing 3D Shapes with Probabilistic Directed Distance Fields

TL;DR

This paper introduces Probabilistic Directed Distance Fields (PDDFs), a novel implicit shape representation enabling fast, differentiable rendering and detailed geometric analysis, suitable for various 3D understanding tasks.

Contribution

The work proposes PDDFs, a new implicit shape representation that models discontinuities probabilistically, allowing efficient rendering and geometry extraction in 3D shape modeling.

Findings

Achieved fast depth map rendering with a single pass per pixel.

Enabled differential surface geometry extraction such as normals and curvatures.

Demonstrated strong performance in shape fitting, 3D-aware image modeling, and single-image 3D reconstruction.

Abstract

Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or meshes), while relatively easily rendered, often suffer from limited geometric fidelity or topological constraints. On the other hand, implicit representations (occupancy, distance, or radiance fields) preserve greater fidelity, but suffer from complex or inefficient rendering processes, limiting scalability. In this work, we endeavour to address both shortcomings with a novel shape representation that allows fast differentiable rendering within an implicit architecture. Building on implicit distance representations, we define Directed Distance Fields (DDFs), which map an oriented point (position and direction) to surface visibility and depth. Such a field can render a depth map with a single forward pass per pixel, enable differential surface geometry extraction (e.g., surface normals and curvatures) via network derivatives, be easily composed, and permit extraction of classical unsigned distance fields. Using probabilistic DDFs (PDDFs), we show how to model inherent discontinuities in the underlying field. Finally, we apply our method to fitting single shapes, unpaired 3D-aware generative image modelling, and single-image 3D reconstruction tasks, showcasing strong performance with simple architectural components via the versatility of our representation.