# PRIF: Primary Ray-based Implicit Function

arXiv: https://arxiv.org/abs/2208.06143 · HTML: https://mlsanity.com/paper/2208.06143/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 55 references that are in the map.
- First posted on arXiv 12 Aug 2022.

## Builds on (most cited first, 30 of 39)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Combining Implicit Function Learning and Parametric Models for 3D Human Reconstruction](https://mlsanity.com/paper/2007.11432/) (2020)
- [Learning to Infer Implicit Surfaces without 3D Supervision](https://mlsanity.com/paper/1911.00767/) (2019)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)

## Built on by (most cited first, 17 of 17)

- [Pointersect: Neural Rendering with Cloud-Ray Intersection](https://mlsanity.com/paper/2304.12390/) (2023)
- [Learning to Estimate 6DoF Pose from Limited Data: A Few-Shot, Generalizable Approach using RGB Images](https://mlsanity.com/paper/2306.07598/) (2023)
- [RayDF: Neural Ray-surface Distance Fields with Multi-view Consistency](https://mlsanity.com/paper/2310.19629/) (2023)
- [3D Motion Magnification: Visualizing Subtle Motions with Time Varying Radiance Fields](https://mlsanity.com/paper/2308.03757/) (2023)
- [VIINTER: View Interpolation with Implicit Neural Representations of Images](https://mlsanity.com/paper/2211.00722/) (2022)
- [Reconstructive Latent-Space Neural Radiance Fields for Efficient 3D Scene Representations](https://mlsanity.com/paper/2310.17880/) (2023)
- [Progressive Multi-scale Light Field Networks](https://mlsanity.com/paper/2208.06710/) (2022)
- [MARF: The Medial Atom Ray Field Object Representation](https://mlsanity.com/paper/2307.00037/) (2023)
- [Continuous Levels of Detail for Light Field Networks](https://mlsanity.com/paper/2309.11591/) (2023)
- [Efficient Visibility Approximation for Game AI using Neural Omnidirectional Distance Fields](https://mlsanity.com/paper/2407.03330/) (2024)
- [RayletDF: Raylet Distance Fields for Generalizable 3D Surface Reconstruction from Point Clouds or Gaussians](https://mlsanity.com/paper/2508.09830/) (2025)
- [Shape Representation using Gaussian Process mixture models](https://mlsanity.com/paper/2604.00862/) (2026)
- [ConVRT: Consistent Video Restoration Through Turbulence with Test-time Optimization of Neural Video Representations](https://mlsanity.com/paper/2312.04679/) (2023)
- [TaylorGrid: Towards Fast and High-Quality Implicit Field Learning via Direct Taylor-based Grid Optimization](https://mlsanity.com/paper/2402.14415/) (2024)
- [Probabilistic Directed Distance Fields for Ray-Based Shape Representations](https://mlsanity.com/paper/2404.09081/) (2024)
- [COBRA -- COnfidence score Based on shape Regression Analysis for method-independent quality assessment of object pose estimation from single images](https://mlsanity.com/paper/2404.16471/) (2024)
- [N-BVH: Neural ray queries with bounding volume hierarchies](https://mlsanity.com/paper/2405.16237/) (2024)

## Abstract (arXiv)

We introduce a new implicit shape representation called Primary Ray-based Implicit Function (PRIF). In contrast to most existing approaches based on the signed distance function (SDF) which handles spatial locations, our representation operates on oriented rays. Specifically, PRIF is formulated to directly produce the surface hit point of a given input ray, without the expensive sphere-tracing operations, hence enabling efficient shape extraction and differentiable rendering. We demonstrate that neural networks trained to encode PRIF achieve successes in various tasks including single shape representation, category-wise shape generation, shape completion from sparse or noisy observations, inverse rendering for camera pose estimation, and neural rendering with color.