Volumetric rendering and neural radiance fields

From: hu-po

Nerfack, short for “Nerf acceleration toolkit,” is a recently released paper from the University of California, Berkeley, focused on accelerating Neural Radiance Fields (NeRFs) [00:01:33]. It is designed to be a user-friendly Python API, ready for plug-and-play acceleration for most NeRF models [00:03:33].

Understanding Neural Radiance Fields (NeRFs)

Neural Radiance Fields are a popular type of volumetric rendering used for 3D representation [00:02:00] [00:02:50]. They involve training a neural network, typically a Multi-Layer Perceptron (MLP), to encode the view-dependent appearance of a scene [00:03:01]. The network takes a view vector (the direction from which the scene is to be rendered) and returns pixel values [00:03:11].

Volumetric Rendering and Ray Marching

The key characteristic of NeRFs is their volumetric rendering algorithm, known as ray marching [00:03:38]. This process casts a ray into the 3D space, generates discrete samples along that ray, and accumulates colors to determine the final pixel value [00:06:12] [00:13:41]. Each sample point along the ray provides a color and an opacity (alpha) value from the neural network [00:07:17]. These are then summed up to get the pixel’s color [00:08:00]. This ray marching process is differentiable, allowing NeRFs to be trained using backpropagation [00:03:43].

Limitations of Vanilla NeRFs

A significant limitation of the original NeRF model is its training time, often taking two days to converge on a single scene [00:03:51]. While some specialized implementations, like Nvidia’s Instant NGP, have reduced training and rendering times, they often rely on proprietary CUDA code, limiting their general applicability [00:09:04].

Comparison with Other 3D Representations

• Voxel-based Radiance Fields: These break up space into small squares (voxels) [00:04:40]. While they can vary in resolution (e.g., using Octrees where voxels with information are subdivided), they are generally less flexible than MLP-based NeRFs [00:05:05].
• Arbitrary Properties: NeRFs are not limited to predicting only color and opacity; they can predict an arbitrary number of properties like specularity or roughness. In the future, this could extend to physics-based properties (e.g., hardness, elasticity) to enable physics simulations where objects are also represented by MLPs [00:27:35].

Nerfack’s Acceleration Techniques

Nerfack aims to address the computational intensity of NeRFs, particularly their long training times [00:13:10]. The core of its efficiency comes from intelligently skipping unnecessary computations during ray marching and rendering [00:16:17].

Efficient Ray Marching

The primary bottleneck in NeRF efficiency is evaluating the Radiance Field for each sample [00:13:38]. Nerfack improves this by reducing the number of samples [00:14:40].

• Skipping Empty or Occluded Space: Samples that have very low opacity (empty space) or are occluded by denser objects (low transmittance) contribute little to the final image. Nerfack safely skips evaluating these samples, saving inference time [00:14:47]. For example, in a dense Lego scene, this pruning can eliminate 98% of samples [00:20:58].
• Occupancy Grid: During training, a binary grid is cached and updated to store which areas of the scene are empty [00:18:18]. This helps identify regions not worth rendering [00:18:42]. Rays can be terminated if their transmittance falls below a certain threshold [00:19:34].

Optimizing Computation and GPU Optimization Techniques

• Parallelization: Nerfack minimizes operations parallelized across rays, instead preferring to parallelize across samples, especially since sample opacity and density are independent of the rays [00:24:04]. This “clever mapping” helps optimally utilize the GPU [00:24:43].
• Coarse-to-Fine Sampling: Instead of uniformly sampling many points along a ray, NeRFack can initially perform a coarse sampling. Once regions of high opacity are identified, it can then densely sample around the object’s surface, further reducing unnecessary computations [00:42:22].

Support for Unbounded and Dynamic Scenes

While many NeRF papers focus on bounded static scenes (an object confined within a specific 3D volume) [00:25:09], Nerfack extends its techniques to support:

• Unbounded Scenes: For scenes with vast backgrounds that extend to infinity, Nerfack incorporates a scene contraction idea from MIP-NeRF 360, applying a nonlinear function to map unbounded space into a finite grid [00:25:10].
• Dynamic Scenes: For scenes where objects are moving and changing over time, an additional time dimension is conditioned on the neural network, making the rendering more computationally intensive [00:47:45].

Differentiable Volume Rendering

The process of accumulating sample colors along rays into pixel colors is called differentiable rendering [00:26:31]. Because the functions involved (like opacity changes along a ray) are smooth and differentiable, it’s possible to use gradient descent to minimize errors between observed images and rendered views [00:27:00] [00:38:38]. Nerfack disables gradients during certain parts of ray marching to minimize computation [00:20:04].

Implementation and Performance

Python API and PyTorch

Nerfack provides a user-friendly Python API, built on PyTorch [00:31:00] [00:59:03]. Users primarily need to define two functions for their Radiance Field:

1. Sigma FN: Queries the density (opacity) at given positions along a ray, which only depends on the (x, y, z) position [00:32:50].
2. RGB Sigma FN: Queries both color and density, where color depends on both the (x, y, z) position and the view angle (direction of the ray) [00:34:06].

The API handles the complex ray marching and differentiable rendering steps, including parameters like near/far planes and early stopping thresholds for opacity and transmittance [00:35:54].

Performance Benchmarks

Nerfack demonstrates significant speed improvements while maintaining or improving quality (measured by PSNR - Peak Signal-to-Noise Ratio) [00:41:40].

• Static Scenes: For a standard NeRF model (8-layer MLP) on datasets like “Lego” and “Drum,” Nerfack can train a model in about 4 minutes, compared to two days for vanilla NeRF [00:41:20].
• Dynamic Scenes: For dynamic scenes (e.g., D-NeRF synthetic dataset with moving figures), Nerfack can train in approximately one hour, a significant reduction from two days [00:46:36] [00:48:08].
• Memory Footprint: Training memory footprint is around 10-11 gigabytes, making it compatible with high-end consumer GPUs [00:40:20].

Comparison with Neural Radiance Fields NeRF Models

Nerfack is compared against models like Instant NGP and MIP-NeRF 360, showing comparable or better performance [00:43:31]. Instant NGP, for example, uses background augmentation techniques (changing the background of training images using the alpha channel) to improve its NeRF [00:44:15].

Practical Demonstration

The process of using Nerfack involves:

1. Setting up a Python Virtual Environment: This isolates project dependencies [00:49:36].
2. Cloning the Repository: Obtaining the Nerfack codebase [00:51:36].
3. Installing Dependencies: Using pip install nerfack and additional libraries like imageio and tqdm [00:51:00].
4. Resolving CUDA Issues: Potential compatibility issues between PyTorch and the installed CUDA version might require specific PyTorch versions or environment variable adjustments [00:54:40].
5. Downloading Data: NeRF models are trained on hundreds of pictures from various camera poses, which are typically downloaded as a dataset (e.g., Nerf Synthetic dataset containing objects like a Lego truck) [01:00:31].
6. Running Training: Executing a training script with specified parameters (e.g., scene, train/test split, learning rate, epochs) [01:23:08].
7. Monitoring and Visualization: Observing GPU utilization, training progress, and output images (color image and opacity mask) [01:16:54]. Even with reduced training steps, a basic output can be quickly generated, demonstrating the efficiency of the acceleration [01:27:11].