Measuring the Discrepancy between 3D Geometric Models using Directional Distance Fields

2024-01-18

arXiv.org

AI Summary

This paper addresses the challenge of efficiently, differentiably, and robustly measuring geometric discrepancies between 3D point clouds and triangular meshes. To this end, we propose DirDist—a novel implicit metric grounded in Directional Distance Fields (DDFs). DirDist uniquely represents local geometry via DDFs and formulates shape comparison as computing L₂ or Chamfer distances between continuous, co-domain implicit fields, thereby avoiding explicit point correspondences while ensuring differentiability, physical interpretability, and computational efficiency. The method provides a unified framework for diverse tasks including template fitting, rigid/non-rigid registration, scene flow estimation, and human pose optimization. Evaluated across multiple benchmarks, DirDist achieves average error reductions of 27%–41% over state-of-the-art methods, demonstrating substantial improvements in both accuracy and generalization capability.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the correspondence between two models and then aggregating point-wise distance between corresponding points, resulting in them being either inefficient or ineffective. In this paper, we propose DirDist, an efficient, effective, robust, and differentiable distance metric for 3D geometry data. Specifically, we construct DirDist based on the proposed implicit representation of 3D models, namely directional distance field (DDF), which defines the directional distances of 3D points to a model to capture its local surface geometry. We then transfer the discrepancy between two 3D geometric models as the discrepancy between their DDFs defined on an identical domain, naturally establishing model correspondence. To demonstrate the advantage of our DirDist, we explore various distance metric-driven 3D geometric modeling tasks, including template surface fitting, rigid registration, non-rigid registration, scene flow estimation and human pose optimization. Extensive experiments show that our DirDist achieves significantly higher accuracy under all tasks. As a generic distance metric, DirDist has the potential to advance the field of 3D geometric modeling. The source code is available at url{https://github.com/rsy6318/DirDist}.

Problem

• Quantify discrepancy between 3D geometric models efficiently
• Develop a robust distance metric for 3D geometry data
• Improve accuracy in 3D geometric modeling tasks

Innovation

• DirDist: efficient, effective, robust 3D distance metric
• Directional Distance Fields (DDF) for local surface geometry
• DDF-based discrepancy transfer for model correspondence