How to Perform 3D Reconstruction from a Single Image
Novel View Synthesis, 3D Reconstruction, and Neural Radiance Fields (NeRF) from a Single Image Using Meta-Learning.
One of the main weaknesses of NeRF is that it requires a dense set of images to allow good-quality reconstruction. In this tutorial, we will see how incorporating prior knowledge through pre-training on multiple scenes allows reconstruction from a single image on a new unseen scene.
We are going to reproduce results from the paper Learned Initializations for Optimizing Coordinate-Based Neural Representations.
NeRF
Let us start by implementing the NeRF model which we already did in some of my previous posts, with more detailed explanations. For example, see this introduction to NeRF. What is great about that approach using Meta-Learning, is that the model does not need any conditioning (as opposed to approaches like pixelNeRF and GRF), all the prior knowledge is embedded in the initialization of the weights.
Note that the forward function does not take the view direction as input. This is because we follow the architecture from the paper which implements a simplified NeRF model. In more complex scenes or real-world applications, it would be best to incorporate the view direction to model the view-dependent radiance.
We can then move on to implementing the rendering function. Let us start by implementing a helper for computing the accumulated transmittance (Ti in the paper). This is a straightforward implementation of the equation from the initial NeRF paper.
The rendering function was already discussed in this post and therefore, I won’t spend time on it but I am adding it for completeness. If you want to deepen your knowledge of NeRF, I also have a 10-hour course about it on Udemy.
Meta-Learning
Now comes the interesting part of this paper, Meta-Learning, or learning to learn. In supervised learning, at each training iteration, we sample batches of data and do a gradient step so that the network learns the mapping from input to output. In Meta-Learning, at each iteration, we sample a task and teach the neural network to solve that task.
We can therefore implement a sample_task function that is equivalent to sample_batch in supervised learning. It returns a task to solve, which in our case is reconstructing a scene. Therefore, the function returns the ray associated with each pixel and its RGB color.
Then, solving a task means being able to fine-tune the NeRF model (initialized with the weights learned during Meta-Learning) on that task — even if we have only a few, or a single input view.
Why does Meta-Learning with NeRF work? By learning the initialization of the weights, the model’s weights are in a manifold where the representation is meaningful and where there is a strong inductive bias in learning proper geometries.
Once we have created the function to solve a task, which is just a standard supervised learning training loop, we can create the outer loop, i.e. implement the Meta-Learning algorithm. Here, we are going to use the reptile algorithm from the paper On First-Order Meta-Learning Algorithms
Helpers
Once our model and training look are ready, we are almost ready to start training. We can implement a function to load the data (we are using ShapeNet).
Putting it all together
Finally, all the pieces can be easily combined.
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