Neural Density-Distance Fields

European Conference on Computer Vision (ECCV) 2022

1University of Tsukuba 2Waseda University 3National Institute of Advanced Industrial Science and Technology (AIST) 4Hiroshima University


We propose Neural Density-Distance Field (NeDDF), a novel 3D representation that reciprocally constrains the distance and density fields. NeDDF makes it possible to define a distance field for objects with indefinite boundaries, such as smoke, hairballs, and glass, without losing density information.

The figure visualizes (left) the 2D slice for each field with iron, hair, and glass spheres, and (right) the plots of 1D slices for each field.

NeRF provides no distance information. Unsigned Distance Field (UDF) cannot handle some cases correctly, such as (a) ambiguous density changes such as a hairball or (b) low densities such as a glass ball.

Proposed NeDDF can represent both cases properly. NeDDF represents ambiguous density changes by the gradient value of distance fields, and low densities by the minimal value of distance fields.


We derive an expression that converts the distance and its gradient into density using the fact that the distance field is an integral of a polynomial about density.

By using the expression, a density field consistent with the distance field represented by the neural field can be obtained in a differentiable form.

Result: camera pose estimation

By applying the distance field obtained by NeDDF, it is possible to take the reprojection error with the pseudo corresponding points in addition to the conventional photometric error. Combining these two errors enables highly accurate camera pose estimation even when the initial pose is poor and the overlap of silhouettes is small.


  title={Neural Density-Distance Fields},
  author={Ueda, Itsuki and Fukuhara, Yoshihiro and Kataoka, Hirokatsu and Aizawa, Hiroaki and Shishido, Hidehiko and Kitahara, Itaru},
  booktitle={Proceedings of the European Conference on Computer Vision},