### Abstract

We introduce a technique for pairwise registration of neural fields that extends classical optimization-based local registration (i.e. ICP) to operate on Neural Radiance Fields (NeRF) – neural 3D scene representations trained from collections ofcalibrated images. NeRF does not decompose illumination and color, so to make registration invariant to illumination, we introduce the concept of a “surface field” – a field distilled from a pre-trained NeRF model that measures the likelihood of a point being on the surface of an object. We then cast nerf2nerf registration as a robust optimization that iteratively seeks a rigid transformation that aligns the surface fields of the two scenes. We evaluate the effectiveness of our technique by introducing a dataset of pre-trained NeRF scenes – our synthetic scenes enable quantitative evaluations and comparisons to classical registration techniques, while our real scenes demonstrate the validity of our technique in real-world scenarios.

### Surface Field

*t*measures the differential probability of hitting a particle at a point (view-independent). Transmittance is the probability that a ray hits no solid particle on its way to the point (view-dependent), and can be derived directly from density through integration along the ray. Using the multiplication theorem for independent events, we can then define the differential probability of hitting a

*surface*while looking from a certain viewing direction as the product of density and transmittance (view-dependent):

*o*through the point

*x*:

### Energy-based Optimization

*Keypoint Energy*and

*Matching Energy*. Keypoint energy provides an initial approximate solution by minimizing the ditance between manually annotated keypoint coordinates, and is then gradually annealed through the optimization. The robust matching energy compares the surface field of the two scenes on an active set of samples, given the current estimate of the rigid transform. To make the comparison robust to outliers, we utilize a robust kernel and apply it on our residuals.

### Sampling

*in close correspondence*,

*not too close to current set of samples*and

*are close to surface*.

### Results

Bench | Bust | Jar |

### Video

### Citation

### Acknowledgements

The website template was borrowed from Dor Verbin.