[AI from Scratch] Episode 209: Neural Radiance Fields (NeRF)

Recap: Diffusion Models

In the previous episode, we discussed Diffusion Models, explaining their mechanisms, applications, and differences from other generative models like GANs and VAEs. Diffusion models are gaining attention for their ability to generate high-quality data and overcome the limitations of previous approaches. This time, we will delve into Neural Radiance Fields (NeRF), a technology used for 3D scene reconstruction. NeRF enables the creation of high-fidelity 3D scenes from images or videos, making it a promising tool in fields such as VR, AR, and film production. We will explore its mechanisms and specific applications in detail.

What Are Neural Radiance Fields (NeRF)?

1. Basic Concept of NeRF

Neural Radiance Fields (NeRF) use neural networks to model the radiance (brightness) properties of a 3D scene, allowing for high-precision 3D reconstruction from 2D images. Unlike traditional 3D reconstruction techniques, NeRF learns the radiance and volumetric density at every point in the scene and uses this information to generate images from new viewpoints.

Specifically, the neural network takes as input the coordinates (x, y, z) of each point and the viewing direction (θ, φ), and outputs the corresponding radiance and density. This approach enables the creation of realistic images that adapt to changes in perspective.

2. An Analogy for Understanding NeRF

NeRF can be likened to “sculpting with light.” Traditional 3D modeling techniques focus on explicitly shaping objects, like sculpting with clay. In contrast, NeRF simulates how light interacts with the object’s surface and reaches the observer. By calculating light reflections and interactions, it reproduces the object’s shape and texture, resulting in 3D scenes with realistic shading and reflections.

How Does NeRF Work?

1. Estimating Radiance and Density

The core of NeRF involves estimating radiance and volumetric density using a neural network. Radiance represents the intensity of light emitted from a specific point in a certain direction, while density indicates the concentration of material at that point.

The neural network learns these values for each point in 3D space, taking the 3D coordinates and viewing direction as inputs and outputting the corresponding radiance and density.

2. Volume Rendering

Another critical element of NeRF is volume rendering, a process that calculates the integration of light along the line of sight based on the radiance and density of each point in the scene. The line of sight extends from the camera through various points in the scene, and the rendering process accounts for both the absorption and emission of light along this path.

During this volume rendering process, the neural network uses the radiance and density information it has learned to reconstruct images from any viewpoint. This allows for realistic 3D visualization from multiple angles.

3. Training Process

Training a NeRF model requires 2D images captured from multiple camera angles. These images serve as the basis for training the neural network to estimate radiance and density accurately.

The steps include:

1. Collecting 2D Images: Capture images of the scene from various angles, recording the camera positions and viewing directions.
2. Training the Neural Network: The network learns to approximate the integration of radiance and density along the light paths represented by the pixels in these images. By repeating this process, the model learns the entire 3D structure of the scene.

Applications of NeRF

1. Virtual Reality (VR) and Augmented Reality (AR)

NeRF plays an innovative role in VR and AR. For example, it enables precise scanning of real-world objects and spaces, which can then be reused as VR/AR content. This capability allows for the reproduction of real buildings and interiors in virtual spaces, offering realistic 3D experiences.

2. Film Production and Gaming

NeRF holds great potential in film and game production. Traditional CG technology often requires manual modeling, which is time-consuming. NeRF, however, can quickly convert real-world sets or locations into 3D models, reducing production time and costs.

3. Medical and Scientific Visualization

NeRF is also used for the 3D reconstruction of medical images, such as CT scans and MRIs. By creating detailed 3D models based on cross-sectional images of complex structures within the human body, it aids doctors in diagnosis and treatment planning. In science, it is applied to visualize physical phenomena and display simulation results in 3D.

Comparison with Other 3D Reconstruction Techniques

1. Differences from Traditional 3D Modeling Techniques

Traditional 3D modeling techniques, such as polygon meshes or point clouds, require explicit definition of object shapes and surface properties, often demanding significant time and effort. In contrast, NeRF learns the radiance and density of the entire scene, allowing for the reconstruction of objects with complex shapes and textures more efficiently.

2. Differences from SLAM (Simultaneous Localization and Mapping)

SLAM is a technique widely used in robotics and AR to create maps of environments while simultaneously locating the camera or robot within that map. While SLAM is excellent for real-time mapping, it struggles to reproduce detailed textures and shading like NeRF. Although NeRF has higher computational costs, it achieves more precise 3D scene reconstruction.

Challenges of NeRF

1. High Computational Cost

Although NeRF enables high-precision 3D reconstruction, it requires significant computational resources. Especially when reconstructing large scenes at high resolutions, the inference process can be time-consuming. While several methods have been proposed to improve computational efficiency, achieving real-time 3D reconstruction remains challenging.

2. Data Preparation

Training NeRF requires numerous images and corresponding camera position information. If it is difficult to collect data or obtain accurate camera positions, the reconstruction accuracy may decrease. Thus, data preparation can be more demanding compared to traditional methods.

Summary

This episode explained the mechanisms and applications of Neural Radiance Fields (NeRF) and compared them with other 3D reconstruction techniques. NeRF is a powerful technology capable of reconstructing realistic and high-precision 3D scenes from images or videos, and it has applications in fields like VR/AR, film production, and healthcare. However, challenges such as computational cost and data preparation remain, highlighting the need for further technological advancements.

Next Episode Preview

Next time, we will review Chapter 7 and conduct a knowledge check, summarizing what we have learned about generative models so far and deepening our understanding. Stay tuned!

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Annotations

1. Volume Rendering: A technique for generating images by considering the absorption and emission of light within a 3D space.
2. SLAM (Simultaneous Localization and Mapping): A method where robots or cameras simultaneously map the environment and locate their own position.
3. Radiance: The measure of light intensity emitted in a specific direction from a point.