This is part of my journey of learning NeRF.

# 1. Introduction to NeRF

## What is NeRF

Reference: Original NeRF paper; an online ariticle

NeRF 想做这样一件事，不需要中间三维重建的过程，仅根据位姿内参和图像，直接合成新视角下的图像。为此 NeRF 引入了辐射场的概念，这在图形学中是非常重要的概念，在此我们给出渲染方程的定义：

### SDF - Signed Distance Function

SDF是一种计算图形学中定义距离的函数。SDF定义了空间中的点到隐式曲面的距离，该点在曲面内外决定了其SDF的正负性。

## Features of NeRF

• Representation can be discrete or continuous. but the discrete representation will be a big one if you have more dimensions, e.g., 3 dim.
• Actually the Plenoxels try to use 3D grids to store the fields. Fast, however, too much memory.
1. Compactness 紧致:
2. Regularization: nn itself as inductive bias makes it easy to learn
3. Domain Agonostic: cheap to add a dimension
• also problems
• Editability / Manipulability
• Computational Complexity
• Spectral Bias

## Problem Formulation

• Input: multiview images
• Output: 3D Geometry and appearance
• Objective:

$\arg \min_x\|y-F(x)\|+\lambda P(x)$

y is multiview images, F is forward mapping, x is the desired 3D reconstruction.

F can be differentiable, then you can supervise this.

• nn本身就是某种constraints，你就不需要加太多handicraft constraints