I-Filtering: Implicit Filtering for Learning Neural Distance Functions from 3D Point Clouds | JoVE Visualize

Area of Science:

Computer Vision
Computer Graphics
Geometric Deep Learning

Background:

Neural implicit functions like signed distance functions (SDFs) and unsigned distance functions (UDFs) excel at shape geometry fitting.
Inferring continuous distance fields from discrete, unoriented point clouds remains challenging, often resulting in rough surfaces that miss fine geometric details.

Purpose of the Study:

To propose a novel non-linear implicit filter for smoothing implicit fields while preserving high-frequency geometric details.
To extend implicit filtering to non-zero level sets for consistent regularization of the zero level set.
To adapt the filtering method for UDFs using a gradient immutable training schema and improve sparse-view reconstruction.

Main Methods:

A non-linear implicit filter is proposed to smooth the implicit field by filtering the surface (zero level set) using neighbor points and gradients of the SDF.
The filtering is extended to non-zero level sets by moving input point clouds along the gradient, ensuring consistency across level sets.
A gradient immutable training schema is developed to apply the filter to UDFs, addressing non-differentiability at the zero level set.

Main Results:

The proposed implicit filtering method effectively smooths implicit fields while preserving fine geometric details like edges and corners.
The method demonstrates improved performance in surface reconstruction from objects, complex scenes, and multi-view images.
Significant improvements are observed in sparse-view reconstruction, point normal estimation, and point cloud upsampling tasks compared to state-of-the-art methods.

Conclusions:

The novel implicit filter enhances the accuracy and detail preservation of neural implicit functions for 3D shape representation.
The gradient immutable training schema successfully adapts the filtering technique for UDFs, broadening its applicability.
The method offers a robust solution for various geometric deep learning tasks, including reconstruction, normal estimation, and upsampling.