The rendering procedure used by neural radiance fields (NeRF) samples a scene with single 3D points along each ray and may therefore produce renderings that are excessively blurred or aliased when training or testing images observe scene content at different resolutions. The solution presented in this paper, called mip-NeRF (a NeRF variant inspired by mipmapping), casts cones instead of rays and renders anti-aliased conical frustums instead of points. By efficiently approximating the conical frustums with multivariate Gaussians and computing integrated positional encoding (IPE), mip-NeRF addresses the aliasing issue while being 7% faster than NeRF, using half the parameters. Mip-NeRF reduces average error rates by 17% on single-scale and 60% on multiscale benchmarks compared to NeRF.

Neural radiance fields (NeRF) represent scenes as continuous volumetric functions parameterized by neural networks, mapping 3D coordinates and viewing directions to color and density. NeRF has demonstrated remarkable quality for novel view synthesis. However, NeRF's rendering procedure queries the scene representation at individual 3D points along each ray, which means that the same MLP is used to represent scene content at all scales. This lack of scale awareness causes aliasing artifacts: when an image observes a distant region, a single point query does not capture the fact that the corresponding pixel covers a large volume of 3D space. While supersampling (casting multiple rays per pixel) can reduce aliasing, it is prohibitively expensive for NeRF.

In traditional computer graphics, anti-aliasing is addressed through two approaches: supersampling (casting multiple rays per pixel) and prefiltering (using multiscale representations such as mipmaps). Prefiltering is computationally efficient because "filtered versions of scene content can be precomputed ahead of time." However, in the context of view synthesis, the scene geometry is unknown at test time, making precomputation infeasible. Coordinate-based neural representations like NeRF use positional encoding to enable MLPs to represent high-frequency content, but standard positional encoding operates on individual points and has no notion of the volume being integrated over.

Instead of casting infinitesimally thin rays as in NeRF, mip-NeRF casts cones from each pixel, where the cone's radius at the image plane corresponds to the pixel's footprint. Along each cone, the scene is sampled by dividing the cone into conical frustums — truncated cone segments between consecutive depth values [t_0, t_1]. Each frustum is then approximated by a multivariate Gaussian with mean and covariance derived from the frustum geometry. The mean position along the ray includes a correction term: mu_t = t_mu + 2*t_mu*t_delta^2 / (3*t_mu^2 + t_delta^2), and the variance components sigma_t^2 (along-ray) and sigma_r^2 (cross-ray) capture the extent of the frustum in both directions.

The key technical contribution is Integrated Positional Encoding (IPE), which computes the expected positional encoding over the Gaussian approximation of each conical frustum. For a Gaussian with mean mu and variance sigma^2, the expected sine and cosine values have closed-form solutions: E[sin(x)] = sin(mu) * exp(-sigma^2/2) and E[cos(x)] = cos(mu) * exp(-sigma^2/2). This creates "anti-aliased positional encoding features" that naturally encode the size and shape of the integrated volume. Critically, high-frequency components are attenuated when their period is smaller than the integrated region, while lower frequencies pass through unaffected — exactly mirroring the behavior of a prefiltered multiscale representation.

Mip-NeRF uses a single MLP rather than NeRF's separate coarse and fine networks, since the IPE features already encode scale information that makes the coarse network redundant. For each pixel, n+1 depths are sampled, generating n IPE features for adjacent depth intervals. The volume rendering equation remains identical to NeRF's standard formulation. The training objective is: min sum(lambda * ||C*(r) - C(r; Theta, t^c)||^2 + ||C*(r) - C(r; Theta, t^f)||^2) with lambda=0.1 and a "blurpool" filter applied to sampling weights to prevent missed content in empty regions. This architectural simplification reduces parameters from 1,191K to 612K (48% reduction).

On the standard single-scale Blender dataset, mip-NeRF improves PSNR from 31.74 to 33.09 dB, SSIM from 0.953 to 0.961, and LPIPS from 0.050 to 0.043, representing a ~17% average error reduction. On the newly created multiscale Blender dataset (images downsampled by 2x, 4x, and 8x), the improvements are far more dramatic: average error drops from 0.0288 to 0.0114 — a 60% reduction. At 1/8 resolution, SSIM improves from 0.8709 to 0.9833. Crucially, mip-NeRF matches the accuracy of brute-force supersampled NeRF (casting 128 rays per pixel) while being 22x faster. Training takes 2.84 hours vs. NeRF's 3.05 hours (7% faster). Ablation studies confirm that removing IPE degrades performance to baseline NeRF levels, and the single MLP is 20% faster with halved parameters.

Mip-NeRF addresses the fundamental aliasing problem in neural radiance fields by replacing point sampling with cone tracing and integrated positional encoding. The approach draws on classical prefiltering concepts from computer graphics to create a continuously-valued multiscale scene representation. The resulting model is faster, smaller, and significantly more accurate than NeRF, particularly in multiscale settings. The key insight — that positional encoding can be extended to encode regions rather than points — opens the door to further extensions of coordinate-based neural representations that reason about scale and extent.