Power Diagram Enhanced Adaptive Isosurface Extraction from Signed Distance Fields (2506.09579v2)

Abstract: Extracting high-fidelity mesh surfaces from Signed Distance Fields has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain namely, how to automatically capture the intricate geometric and topological structures encoded in the zero level set of SDFs. In this paper, we present a novel isosurface extraction algorithm that introduces two key innovations: 1. An incrementally constructed power diagram through the addition of sample points, which enables repeated updates to the extracted surface via its dual regular Delaunay tetrahedralization; and 2. An adaptive point insertion strategy that identifies regions exhibiting the greatest discrepancy between the current mesh and the underlying continuous surface. As the teaser figure shows, our framework progressively refines the extracted mesh with minimal computational cost until it sufficiently approximates the underlying surface. Experimental results demonstrate that our approach outperforms sofa methods, particularly for models with intricate geometric variations and complex topologies.

• The paper introduces a novel algorithm that leverages incremental power diagram construction to enhance isosurface extraction from SDFs.
• It employs an adaptive point insertion strategy to refine areas with large mesh-surface discrepancies, capturing intricate geometric details.
• Experimental results demonstrate superior performance over traditional methods, enabling accurate and efficient 3D surface modeling.

Power Diagram Enhanced Adaptive Isosurface Extraction from Signed Distance Fields

The paper "Power Diagram Enhanced Adaptive Isosurface Extraction from Signed Distance Fields" presents a sophisticated algorithm for the extraction of high-fidelity mesh surfaces from Signed Distance Fields (SDFs), an intrinsic representation in geometry processing. This work introduces significant advancements over traditional methods like Marching Cubes and Neural Dual Contouring, addressing key challenges in automatically capturing intricate geometric and topological structures encoded within SDFs.

Key Innovations

The researchers propose two critical innovations that form the backbone of the new algorithm:

1. Incremental Power Diagram Construction: The algorithm constructs a power diagram by incrementally adding sample points. This approach employs the dual, regular Delaunay tetrahedralization, which allows the surface extraction to be dynamically updated. The utilization of SDF values at sample points as weights facilitates more adaptive surface refinement.
2. Adaptive Point Insertion Strategy: A novel strategy for point insertion is introduced, which identifies regions of the mesh that exhibit the largest discrepancy between the current mesh and the underlying continuous surface. This enables focused refinement where it is most needed.

Experimental Results

The experimental validation demonstrates that this adaptive framework excels in extracting mesh surfaces with geometrically complex variations and topologies. The results indicate the method's superiority in capturing fine details compared to state-of-the-art methods. The algorithm iteratively refines the mesh, achieving geometrically accurate results with minimal computational overhead.

Implications and Future Directions

The algorithm has significant implications for practical applications in 3D modeling, computer graphics, and possibly in medical imaging where precision and detail are critical. Theoretically, it paves the way for further exploration into adaptive mesh processing algorithms by highlighting the utility of dual structures like Delaunay tetrahedralization in conjunction with power diagrams.

For future work, the authors suggest addressing limitations such as the dependency on SDF gradient information, which may not always be readily available or efficiently processable. Additionally, optimizing the algorithm to reduce computation cost and query count during surface evaluation could further enhance its efficiency.

Overall, this paper contributes a notable advancement in the field of geometry processing, offering an efficient and effective solution to surface extraction from SDFs. As the algorithm supports localized updates, it holds potential for dynamic and real-time applications in computer graphics. Further development could see these techniques integrated into broader AI-driven 3D modeling platforms, continuing to refine and expand upon the foundational advancements presented here.