Gaußsches Splatting

The 2023 paper by Kerbl and colleagues studies view synthesis with a set of explicit 3D Gaussians. The representation count varies with the scene and optimization; calling it necessarily millions of blobs is not a definition. Each primitive has a position, anisotropic shape, opacity, and appearance parameters. Covariance describes the ellipsoidal shape and orientation, while spherical-harmonic coefficients allow direction-dependent appearance. This is an appearance model rather than a guarantee of physical relighting or perfect reflections. The original method starts from sparse points provided by structure from motion, with captured images and cameras supplying training observations. Optimization adjusts Gaussian properties to reduce image residuals. It also changes representation density. Small Gaussians in under-reconstructed regions can be cloned, while large ones with significant reconstruction variation can be split into smaller primitives. Pruning removes selected unneeded or nearly transparent primitives according to the method. The paper’s density-control language concerns the population of Gaussians, distinct from NeRF’s volume-density value at a spatial point. Rendering projects primitives to the image, sorts contributions, and alpha-blends them through a tile-based, visibility-aware process. This avoids the original NeRF-style repeated network queries along each ray, but runtime comparisons still require an identified implementation, hardware, and scene. The Gaussian covariance is parameterized through scale and rotation factors, rather than freely changing arbitrary matrix entries. A normalized rotation quaternion supplies a valid rotation, and the resulting factorization preserves a positive-semidefinite covariance form. The method reports strong tested rendering results and also discusses artifacts in poorly observed regions.