Exact Volumetric Ellipsoid Rendering – Alexander Mai’s Homepage

An overview of the quality benefits of our EEVR technique. Left: On the Zip-NeRF dataset, our model produces sharper and more accurate renderings than 3DGS and successor splatting-based techniques. Middle: Because our method correctly blends primitive colors according to the physics of volume rendering, it produces fewer “foggy” artifacts than splatting. Right: Our method correctly blends primitive colors, which is not possible using a splatting regardless of how primitives are sorted (globally or ray-wise).

We present Exact Ellipsoid Volumetric Rendering (EEVR), a method for real-time differentiable emission-only volume rendering.
Unlike recent rasterization based approach by 3D Gaussian Splatting (3DGS), our primitive based representation allows for exact volume rendering, rather than alpha compositing 3D Gaussian billboards.
As such, unlike 3DGS our formulation does not suffer from popping artifacts and view dependent density, but still achieves frame rates of $\sim\!30$

(a) Here we show a toy “flatland” scene containing two primitives (one red, one blue) with a camera orbiting them, viewed from above.
We render this orbit using three different techniques, where each camera position yields a one-dimensional “image” (a scanline) which are stacked vertically to produce these epipolar plane image (EPI) visualizations.
(b, c) The approximations made by approximate splatting-based techniques result in improper blending due to discontinuities, which are visible as horizontal lines across the EPI.
In contrast, (d) our method’s exact rendering yields a smooth EPI, with bands of purple from color blending.

A visualization of our rendering procedure. Top: We cast a ray through a field of constant density ellipsoids and compute each ray-ellipsoid collision distance to get the endpoints of each step function. When the ray enters each primitive, the density along the ray increases. When it exits, the density drops back down a corresponding amount. Bottom: This lets us analytically integrate the volume rendering equation through the field.

Bibtex