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Neural radiance fields

3 min readadvancedUpdated 28 Sept 2026
1 · In one line

A neural radiance field maps a 3D position and viewing direction to density and view-dependent color.

1 · What it is

A NeRF is a continuous scene function represented by a neural network. Its inputs are a spatial position and viewing direction. Its outputs are volume density and view-dependent color.

Rendering marches a camera ray through the scene. Each sampled point and the ray direction enter the network. Classical volume rendering then accumulates the returned colors and densities into one pixel. Because this procedure is differentiable, the original method optimizes the field from images with known camera poses.

The original representation is optimized for each scene independently. mip-NeRF replaces narrow ray samples with anti-aliased conical frustums. Instant-NGP augments a small neural network with a multiresolution hash table of trainable feature vectors. NeRF++ describes a spatial parameterization issue for unbounded 360-degree captures, while pixelNeRF conditions a scene representation on one or a few images.

2 · Why it exists

Novel views can be rendered from a continuous scene representation learned from posed images.

Scene functionThe original NeRF represents a static scene as a continuous five-dimensional function.
View dependenceThe function includes position and viewing direction so emitted color may change with direction.
Differentiable imageVolume rendering connects sampled colors and densities to a rendered pixel.
3 · How it works

Follow one camera ray into one rendered pixel.

NeRF repeatedly queries one continuous field along each ray, then composites the returned colors and densities.
  1. 1 · castMarch a camera ray through the scene and choose sample positions.
  2. 2 · querySend each position and the viewing direction through the neural field.
  3. 3 · predictObtain volume density and view-dependent RGB color at every sample.
  4. 4 · compositeAccumulate the sampled colors and densities into a pixel with volume rendering.

The field is continuous; rendering evaluates it at a discrete set of positions along each ray.

4 · Where it's used
WhoWhat they askWhat it works with
Graphics researcher“What color should this unseen camera view contain?”Field samples along camera rays
Capture engineer“Are image camera poses available for optimization?”Calibrated input views
Rendering engineer“Which samples contribute most to a pixel?”Density-derived volume-rendering weights
5 · What it solves, and what it doesn't
solves
  • The original NeRF renders new views from images with known camera poses.
  • mip-NeRF renders anti-aliased conical frustums instead of rays.
  • Instant-NGP uses a trainable multiresolution hash encoding with a smaller neural network.
doesn't solve
  • The original method optimizes a representation for each scene independently.
  • Standard parameterization is problematic for unbounded scenes captured in 360 degrees.
  • The original method requires images with known camera poses.
6 · Go deeper
Computer vision3D generation modelsNeural networksPositional encodingText-to-image models

Sources used

This explainer is written in original language. The links below support its factual claims.

  1. paperNeRF Representing Scenes as Neural Radiance Fields for View Synthesis, Mildenhall et al. · read 28 Sept 2026
  2. papermip-NeRF, Barron et al. · read 28 Sept 2026
  3. paperInstant Neural Graphics Primitives with a Multiresolution Hash Encoding, Müller et al. · read 28 Sept 2026
  4. paperNeRF++, Zhang et al. · read 28 Sept 2026
  5. paperpixelNeRF, Yu et al. · read 28 Sept 2026
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