VF-NeRF: Viewshed Fields for Rigid Neural Radiance Field Registration

Core Concepts

VF-NeRF introduces Viewshed Fields (VF), an implicit function that determines the likelihood of 3D points being observed by the original cameras, to enable efficient and accurate rigid registration between two Neural Radiance Fields (NeRFs).

Abstract

The paper proposes a method called VF-NeRF for registering two NeRFs when the original camera positions are not given. The key novelty is the introduction of Viewshed Fields (VF), an implicit function that captures the likelihood of 3D points being observed by the original cameras.
The VF is learned during NeRF training using Normalizing Flows, which maps oriented points (3D location and viewing direction) to a Gaussian distribution in latent space. During registration, high VF score points are sampled from the Gaussian to generate novel views that are used to optimize the 6-DoF transformation between the two NeRFs.
The paper also shows how VF can be used to initialize the registration process by generating a 3D point cloud, and to guide the optimization by selecting high quality rays. Extensive experiments on various datasets, including real-world casually captured scenes and synthetic Objaverse scenes, demonstrate that VF-NeRF achieves state-of-the-art results on NeRF registration tasks.

Stats

The paper reports the following key metrics:

Root Mean Square (RMS) error of the estimated rotation (∆R) and translation (∆t) compared to the ground truth transformation.
The results are reported for different levels of overlap between the two NeRFs being registered: full overlap, partial overlap, and no overlap.

Quotes

"VF is an implicit function, similar to NeRF, that, given an oriented point (i.e., a 3D point and a viewing direction), outputs a scalar that represents how well was the 3D point covered, from a specific direction, by the original set of images that was used to create the NeRF."
"We generate meaningful novel views to support NeRF registration task. We use a generative method, based on Normalizing Flows, to generate high score VF points. These points are then used to set the parameters of virtual cameras which, in turn, produce images of the scene that are used to solve the NeRF registration problem."

Key Insights Distilled From

VF-NeRF

by Leo Segre,Sh... at arxiv.org 04-05-2024

https://arxiv.org/pdf/2404.03349.pdf

Deeper Inquiries

How can VF-NeRF be extended to handle non-rigid transformations between NeRFs?

To extend VF-NeRF to handle non-rigid transformations between NeRFs, we can incorporate deformable registration techniques. Instead of assuming a rigid transformation, we can introduce a deformation field that captures the non-rigid deformations between the scenes. This deformation field can be learned using neural networks or other deformable registration methods. By incorporating the deformation field into the registration process, VF-NeRF can align the scenes even in the presence of non-rigid transformations.

What are the limitations of the photometric loss used in VF-NeRF, and how could it be improved to handle more challenging scenes?

One limitation of the photometric loss used in VF-NeRF is its sensitivity to textureless surfaces or scenes with poor lighting conditions. In such cases, the photometric loss may not provide accurate alignment between the scenes. To improve this, additional cues such as geometric consistency or semantic information can be incorporated into the loss function. By combining photometric, geometric, and semantic losses, VF-NeRF can handle more challenging scenes with varying textures and lighting conditions, providing a more robust registration process.

Could the VF representation be used for other applications beyond NeRF registration, such as scene understanding or 3D reconstruction?

Yes, the VF representation can be applied to various other applications beyond NeRF registration. For scene understanding, VF can be used to analyze the visibility of objects in a scene from different viewpoints, aiding in tasks such as object detection or scene segmentation. In 3D reconstruction, VF can assist in generating novel views of a scene, which can be valuable for creating detailed 3D models or enhancing the quality of reconstructed scenes. Additionally, VF can be utilized in applications like augmented reality for accurate scene rendering and virtual object placement based on visibility analysis. The versatility of VF makes it a valuable tool for a wide range of computer vision tasks beyond NeRF registration.