K-Planes: Explicit Radiance Fields in Space, Time, and Appearance (2301.10241v2)

Abstract: We introduce k-planes, a white-box model for radiance fields in arbitrary dimensions. Our model uses d choose 2 planes to represent a d-dimensional scene, providing a seamless way to go from static (d=3) to dynamic (d=4) scenes. This planar factorization makes adding dimension-specific priors easy, e.g. temporal smoothness and multi-resolution spatial structure, and induces a natural decomposition of static and dynamic components of a scene. We use a linear feature decoder with a learned color basis that yields similar performance as a nonlinear black-box MLP decoder. Across a range of synthetic and real, static and dynamic, fixed and varying appearance scenes, k-planes yields competitive and often state-of-the-art reconstruction fidelity with low memory usage, achieving 1000x compression over a full 4D grid, and fast optimization with a pure PyTorch implementation. For video results and code, please see https://sarafridov.github.io/K-Planes.

• The paper introduces a planar factorization method that decomposes d-dimensional scenes into K-planes, achieving state-of-the-art reconstruction fidelity.
• It simplifies radiance representation by decoupling static and dynamic elements, enabling faster optimization and significant memory efficiency.
• The methodology enhances interpretability and scalability in volumetric rendering, offering practical benefits for VR, video synthesis, and real-time applications.

Overview of "$K$-Planes: Explicit Radiance Fields in Space, Time, and Appearance"

This paper introduces a novel method for representing radiance fields across various dimensions using a new approach termed "$K$-planes." The $K$-planes model employs a planar factorization of $d$-dimensional spaces, simplifying the volumetric rendering process and enhancing scalability concerning both optimization time and model size. This method is particularly advantageous for tackling 3D static volumes, photo collections with varying appearances, and 4D dynamic videos.

Theoretical Contributions and Methodology

The proposed methodology of $K$-planes hinges on a white-box model that leverages $\binom{d}{2}$ planes to depict a $d$-dimensional scene. This innovative planar factorization permits seamless transitions from static 3D scenes to dynamic 4D scenarios. The authors introduce the concept with an emphasis on simplicity, interpretability, compactness, and speed, all without relying on Multi-Layer Perceptrons (MLPs) which are often utilized in black-box models.

One of the key insights of this work is the decomposition of 4D volumes into six planes—three representing spatial axes and three representing spatiotemporal changes. This structure inherently separates static and dynamic elements of a scene, allowing for targeted regularization, such as encouraging temporal smoothness. The simplifying premise of using planes drawn from combinations of dimensions allows for effective mutual exclusion of unnecessary memory usage.

Numerical Results and Claims

The experiments conducted on a variety of datasets, including synthetic and real scenes, demonstrate that $K$-planes can achieve competitive, and often state-of-the-art, reconstruction fidelity. Notably, the model manages this performance with significantly reduced memory usage, achieving up to 1000x compression over a full 4D grid representation. Furthermore, training is efficient, reported to be orders of magnitude faster than previous implicit models, thanks to an implementation realized purely in PyTorch.

The paper also compares $K$-planes to several benchmarks in different scene settings. For static scenes, it holds its own against models such as TensoRF and Instant-NGP, while in dynamic scenarios, it is competitive with, or superior to, approaches like DyNeRF and NeRF-W in reconstruction quality, especially given its explicit model nature and reduced computational cost.

Practical and Theoretical Implications

Practically, the $K$-planes model can be optimized and rendered swiftly without the need for specialized hardware or custom CUDA kernels. This could democratize sophisticated volumetric rendering tasks, making them more accessible to those with standard computational resources. The interpretability of the model, coupled with its efficiency, suggests practical applications in VR, video synthesis, and potentially real-time rendering systems.

Theoretically, this work contributes an exemplary case of factorization that bypasses the traditional complexities associated with higher-dimensional radiance fields. It opens avenues for coupling explicit representations with feature decompositions that do not rely heavily on deep networks, promoting comprehensible and adjustable rendering systems.

Prospective Future Developments

Researchers in AI and computer vision may find the $K$-planes approach conducive to expanding the applications of explicit radiance fields to even broader domains, perhaps extending further into 5D or more complex scenes with intricate dynamic and appearance variations. Moreover, enhancing the basis functions beyond learned linear ones could further refine the adaptability and precision of the model, particularly in challenging lighting conditions or with significant occlusions.

In summary, "$K$-Planes: Explicit Radiance Fields in Space, Time, and Appearance" offers a succinct yet powerful tool for efficient volumetric rendering. Its design philosophy prioritizes simplicity, speed, and interpretable outputs, serving as a compelling proposition in contemporary research on neural rendering and scene representation.