DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fields (2401.09736v5)

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 DDM, an efficient, effective, robust, and differentiable distance metric for 3D geometry data. Specifically, we construct DDM 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 DDM, 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 DDM achieves significantly higher accuracy under all tasks. As a generic distance metric, DDM has the potential to advance the field of 3D geometric modeling. The source code is available at https://github.com/rsy6318/DDM.

• The paper introduces DirDist, a metric that uses directional distance fields to compare 3D models without relying on explicit point correspondence.
• It demonstrates that DirDist achieves higher accuracy and efficiency compared to traditional approaches like Chamfer Distance and point-to-face metrics.
• Experimental results confirm DirDist's versatility in both rigid and non-rigid registrations, making it a practical tool for diverse 3D modeling tasks.

Introduction to DirDist: A New Metric for 3D Model Comparison

3D geometric models are at the heart of many applications, from computer graphics to robotics. For these applications to work seamlessly, a reliable method to measure the difference or discrepancy between two 3D models is essential. Traditionally, measures like Chamfer Distance (CD) and point-to-face (P2F) distances have been deployed, but they come with limitations. They either overlook the surface continuity or are computationally intensive. Researchers have now developed a novel distance metric called DirDist, which rethinks the approach to comparing 3D models by using an implicit representation known as the directional distance field (DDF).

Advantages of Directional Distance Fields

The DDF represents an implicit field constructed for any 3D model, capturing the local surface geometry without the need for direct point correspondence – a major bottleneck in earlier methods. This representation allows DirDist to associate reference points between models efficiently. Moreover, DirDist blends the advantages of both robustness and computational convenience, a blend not common with existing metrics.

Application to 3D Geometric Modeling Tasks

The practicality of DirDist has been tested across various fundamental 3D geometric modeling tasks, such as template surface fitting and registration - both rigid and non-rigid. Significantly, DirDist proves its versatility in both optimization-based and unsupervised learning-based contexts. When integrated into these tasks, DirDist not only speeds up the process but also achieves higher accuracy compared to conventional methods.

Experimentation and Results

The performance and efficiency of DirDist were thoroughly vetted through experiments involving the above mentioned 3D geometric modeling tasks. The researchers conducted comparative studies against widely used metrics such as CD, P2F, and Earth Mover’s Distance (EMD), which demonstrated the superiority of DirDist in terms of accuracy and computational resources required. Furthermore, extensive ablation studies confirm the robustness of DirDist across different settings and scenarios, including noisy and outlier-prone data.

Conclusion and Implications

The introduction of DirDist represents a significant advance in the field of 3D geometric modeling. Its ability to accurately, efficiently, and robustly handle the comparison of 3D models addresses many existing challenges. The source code for DirDist has been made publicly available, allowing researchers and developers to utilize this new metric for various 3D geometry processing tasks and innovate further based on this work. This could potentially lead to improvements in a wide array of technologies reliant on 3D modeling, from virtual reality to autonomous navigation.