A Survey on 3D Gaussian Splatting(2)-优快云博客

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Structure

Problem Formulation

Radiance Field

A radiance field is a representation of light distribution in a three-dimensional space, which captures how light interacts with surfaces and materials in the environment.

Mathematically, a radiance field can be described as a function $L{:}\mathbb{R}^5\mapsto\mathbb{R}^+$ , where $L(x, y, z, \theta , \phi )$ maps a point in space $(x, y, z )$ , and a direction specified by spherical coordinates $(\theta , \phi )$ , to a non-negative radiance value.

Radiance fields can be encapsulated through implicit or explicit representations, each with specific advantages for scene representation and rendering.

Implicit Radiance Field

An implicit radiance field represents light distribution in a scene without explicitly defining the geometry of the scene.

In the deep learning era, it often uses neural networks to learn a continuous volumetric scene representation. The most prominent example is NeRF.

In NeRF, the MLP network is used to map a set of spatial coordinates