An Introduction to NeRF: Neural Radiance Fields

 Neural Radiance Fields (NeRF) is a machine learning model that can generate high-resolution, photorealistic 3D models of scenes or objects from a set of 2D images. It does this by learning a continuous 3D function that maps positions in 3D space to the radiance (intensity and color) of the light that would be observed at that position in the scene.

To create a NeRF model, the model is trained on a dataset of 2D images of the scene or object, along with their corresponding 3D positions and orientations. The model learns to predict the radiance at each 3D position in the scene by using a combination of convolutional neural networks (CNNs) and a differentiable renderer.

Why Use Neural Fields?

The Neural Fields model has a number of key features that make it particularly well-suited for generating high-quality 3D models from 2D images:

Continuity: Because the NeRF model learns a continuous 3D function, it can generate smooth, continuous 3D models that do not have any "gaps" or "holes" in them. This is in contrast to methods that rely on discrete 3D points or voxels, which can result in models with discontinuities or artifacts.

High resolution: The NeRF model is able to generate high-resolution 3D models, with fine details and accurate shading. This makes it well-suited for applications where high-quality, photorealistic models are required.

Photorealism: The NeRF model is able to generate 3D models that are visually indistinguishable from real photographs of the scene or object. This makes it particularly useful for applications where realism is important, such as in computer graphics or virtual reality.

Efficient rendering: The NeRF model is able to efficiently render 3D models from any viewpoint, making it possible to interactively explore the model from different angles. This makes it well-suited for applications where real-time rendering is important, such as in virtual reality or augmented reality.

In the context of Neural Radiance Fields (NeRF), the term "fields" refers to the continuous 3D function learned by the model. Specifically, the NeRF model learns a function that maps positions in 3D space to the radiance (intensity and color) of the light that would be observed at that position in the scene.

This function is called a "radiance field," because it encodes the radiance of the light at each position in the scene. The term "Neural Radiance Fields" refers to the fact that this function is learned using a neural network. In short, the concept of fields is a central idea in the NeRF model, as it allows the model to generate continuous, smooth 3D models that do not have any gaps or discontinuities.

What are the steps to train a NeRF

According to the original paper of NeRF, here are the general steps to train a Neural Radiance Fields (NeRF) model:

• Collect a dataset of 2D images of the scene or object, along with their corresponding 3D positions and orientations.
• Preprocess the data by applying any necessary transformations or augmentations to the images and 3D positions.
• Define the neural network architecture of the NeRF model, including the number and types of layers, the number of channels in each layer, and any other hyperparameters.
• Initialize the weights of the neural network.
• Define the loss function that will be used to train the NeRF model. This loss function should measure the difference between the predicted radiance at each position in the scene and the true radiance at that position.
• Train the NeRF model by minimizing the loss function using an optimization algorithm, such as stochastic gradient descent (SGD). This involves feeding the model a batch of images and 3D positions, computing the loss, and updating the weights of the neural network using the gradients of the loss with respect to the weights.
• Continue training the NeRF model until the loss reaches a satisfactory level, or until a predetermined number of training, iterations has been reached.
• Evaluate the performance of the trained NeRF model on a separate test dataset to ensure that it is able to accurately generate 3D models of the scene or object.

Typical Neural Field Algorithm

As explained in the NeRF original paper, the mathematical process of reconstructing a 3D scene or object from 2D images using a Neural Radiance Fields (NeRF) model can be explained as follows:

The NeRF model is first described as a neural field, denoted as Φ:X→Y, which maps positions in 3D space (denoted as x_recon ∈ X) to field quantities (denoted as y_recon ∈ Y). The field quantities could represent various properties of the scene or object, such as the radiance (intensity and color) of the light at each position, or other features of the scene. The 2D images of the scene or object are also described as a neural field, denoted as Ω:S→T, which maps sensor coordinates (denoted as x_sens ∈ S) to measurements (denoted as t_sens ∈ T). The measurements could represent the pixel values in the 2D images, or other features extracted from the images. There is also the "forward map," denoted as F:(X→Y)→(S→T), which is a mapping between the two neural fields. The forward map is differentiable, which means that the gradients of the mapping can be calculated.

The paper also suggests that the process of reconstructing the 3D scene or object involves solving an optimization problem to calculate the neural field Φ. This optimization problem likely involves minimizing a loss function that measures the difference between the predicted field quantities (y_recon) and the true field quantities (t_sens) using the forward map and the 2D images as input.

Neural Radiance Fields (NeRFs) for view synthesis

Neural Radiance Fields (NeRFs) can be used for view synthesis, which is the process of generating new views of a scene or object from a set of existing views. This can be useful in a variety of applications, such as virtual reality, augmented reality, and computer graphics.

To use NeRFs for view synthesis, the model is first trained on a dataset of 2D images of the scene or object, along with their corresponding 3D positions and orientations. The model learns to predict the radiance (intensity and color) of light at each position in the 3D scene or object.

Once the NeRF model is trained, it can be used to generate new views of the scene or object from any viewpoint. To do this, the model takes a 2D image as input and uses its convolutional neural networks (CNNs) to extract features from the image. It then uses these features and the attention mechanism to generate a 3D model of the scene or object that is consistent with the input image. The model can then render the 3D model from any viewpoint to generate a new 2D image of the scene or object.

At last, NeRFs-based models are a powerful tool for view synthesis, as they can generate high-quality, photorealistic views of a scene or object from any viewpoint, using only a small number of input images. This makes them particularly useful for applications where real-time rendering is important, such as in virtual reality or augmented reality.

Next Steps: in this article, we presented a simple introduction to NERF and why it is important, in our next article we will cover some more technical aspects of this topic including its implementation in TensorFlow and Pytorch. Until then, stay tuned.

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