Neural Vector Fields for Implicit Surface Representation and Inference
- URL: http://arxiv.org/abs/2204.06552v3
- Date: Fri, 7 Apr 2023 15:15:46 GMT
- Title: Neural Vector Fields for Implicit Surface Representation and Inference
- Authors: Edoardo Mello Rella, Ajad Chhatkuli, Ender Konukoglu, and Luc Van Gool
- Abstract summary: Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately.
We develop a novel and yet a fundamental representation considering unit vectors in 3D space and call it Vector Field (VF)
We show the advantages of VF representation, in learning open, closed, or multi-layered as well as piecewise planar surfaces.
- Score: 73.25812045209001
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Implicit fields have recently shown increasing success in representing and
learning 3D shapes accurately. Signed distance fields and occupancy fields are
decades old and still the preferred representations, both with well-studied
properties, despite their restriction to closed surfaces. With neural networks,
several other variations and training principles have been proposed with the
goal to represent all classes of shapes. In this paper, we develop a novel and
yet a fundamental representation considering unit vectors in 3D space and call
it Vector Field (VF): at each point in $\mathbb{R}^3$, VF is directed at the
closest point on the surface. We theoretically demonstrate that VF can be
easily transformed to surface density by computing the flux density. Unlike
other standard representations, VF directly encodes an important physical
property of the surface, its normal. We further show the advantages of VF
representation, in learning open, closed, or multi-layered as well as piecewise
planar surfaces. We compare our method on several datasets including ShapeNet
where the proposed new neural implicit field shows superior accuracy in
representing any type of shape, outperforming other standard methods. Code is
available at https://github.com/edomel/ImplicitVF.
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