Researchers Propose Neural Density-Distance Field (NeDDF), a Distance Field Representation that is Reciprocally Constrained to the Density Field

Recent research has focused on employing coordinate-based neural networks, commonly referred to as neural fields, to represent 3D forms as an alternative to point clouds, voxels, meshes, and other representational methods. Neural Radiance Fields (NeRF) have demonstrated excellent quality for applications like new view-synthesis. However, many traditional approaches still demand strong beginning values for registration and localization tasks since NeRF only offers a small number of areas with smooth spatial density and color. The Neural Density-Distance Field is a proposed representation of the distance field that is reciprocally restricted to the density field (NeDDF). NeDDF provides object reconstruction quality equivalent to NeRF while achieving robust localization using distance fields.

The density field used in NeRF and the distance field used in NeuS are the two basic kinds of 3D shape representation in neural fields. Great-frequency structures like hair and transparent substances like smoke and water have high expressiveness in the density field. However, the field’s gradient is zero at most locations outside of the border. Building a convex objective function in a problem setting like registration is challenging. Even when the optimization converges, the distance field offers a gradient across an extensive range. In registration, it can create goal functions with high convexity.

Developing a conversion equation from distance to density may infer the field from the image using volume rendering. NeuS, for instance, presupposes that the density has a logistic distribution at the object’s surface. On the other hand, the convertible density field is severely constrained since they assume clear limits. The attention is on the Unsigned Distance Field (UDF), which ignores the surface direction of internal objects and can discriminate between internal and external objects based on both the gradient’s magnitude and the sign of the distance D.

The NeDDF features a converter that directly calculates the density in addition to a network that takes in a point and outputs the distance and its gradient. By interpreting D by the depth obtained from the volume rendering equation and fitting the density data of transparent objects to the mid-level gradient magnitude, they expand the distance field to recover arbitrary density distributions (b). This approach does not require density limitations when learning the distance field from pictures as NeuS does. In other words, while learning the density field, we may concurrently generate a consistent distance field with the same optimal values for the shape and camera posture.

NeDDF offers both effective registration of the related distance field and great expressiveness of the associated density field. Three contributions are made in the current paper: 

(1) Increasing the range of density distributions for which the distance field may be defined

(2) Outlining a technique that makes use of gradient and distance field data to recover the corresponding density from separate places

(3) Providing a solution to the distance gradient instability brought on by cusp points and sampling frequency

Additionally, experiments are used to assess the usefulness of the suggested strategy in terms of expressiveness and registration performance.

A PyTorch code implementation of the paper will be soon made available on GitHub.

This Article is written as a research summary article by Marktechpost Staff based on the research paper 'NEURAL DENSITY-DISTANCE FIELDS'. All Credit For This Research Goes To Researchers on This Project. Checkout the paper.

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