ReMatching: Low-Resolution Representations for Efficient Shape Correspondence

Khái niệm cốt lõi

The author introduces ReMatching, a novel shape correspondence solution based on the functional maps framework, utilizing a new re-meshing paradigm to target shape-matching tasks efficiently on meshes with millions of vertices. The core of the procedure is a time-efficient remeshing algorithm that constructs a low-resolution geometry while conservatively acting on the original topology and metric.

Tóm tắt

The content discusses ReMatching, a method for efficient shape correspondence using low-resolution representations. It introduces a novel approach based on functional maps and re-meshing algorithms to handle dense shapes effectively. The method is compared with state-of-the-art pipelines, showcasing its efficiency and effectiveness in quality and computational cost.
The authors address the fundamental topic of finding semantically meaningful correspondences between discrete surfaces. They introduce ReMatching as a solution based on the functional maps framework, aiming to define correspondences between functions rather than point-wise correspondences. Various approaches within this framework are explored to improve computation and extend functionality to different bases.
The method involves three main steps: computing low-resolution meshes, applying existing pipelines for functional mapping, and extending the correspondence to original meshes efficiently. The benefits of remeshing are highlighted, showing improved accuracy in mapping by removing small disconnected components post-remeshing.
Experimental evaluations demonstrate the scalability and performance of ReMatching compared to other methods on datasets like SHREC19 and TOSCA. Results show superior accuracy and efficiency in handling high-resolution meshes while maintaining stability even under altered geometries. Further comparisons with SFM and other remeshing algorithms emphasize the advantages of ReMatching in achieving meaningful shape correspondences.

Thống kê

Despite the mesh density shown in Figure 1, the computation took ~ 2 minutes.
We compare our solution against well-established isotropic and anisotropic remeshing algorithms (IRM [HDD∗93, BPR∗06] and ARM [NLG15]), as well as the scalable functional maps (SFM) approach proposed by Magnet et al. [MO23].
To further ease alignment of Laplacian spectra, we post-process remeshed shapes produced with IRM, ARM, and our algorithm.
Our technique outperforms SFM and achieves better results than using IRM remeshing strategy.
Our method achieves better time performance than other remeshing algorithms like SMD and IEM.

Trích dẫn

"Our pipeline relies on an efficient remeshing algorithm that can quickly reduce mesh size while preserving geometry."
"We introduce a new scalable functional map pipeline handling very dense meshes efficiently."
"Our experimental evaluation proved that our procedure is effective on various types of shapes at different resolutions."

Thông tin chi tiết chính được chắt lọc từ

ReMatching

by Fili... lúc arxiv.org 03-12-2024

https://arxiv.org/pdf/2305.09274.pdf

Yêu cầu sâu hơn

How does ReMatching compare to traditional methods for shape correspondence beyond just efficiency?

ReMatching offers several advantages over traditional methods for shape correspondence. Firstly, it introduces a novel approach based on low-resolution representations that enable efficient computation of functional maps between dense shapes. This allows for scalable shape matching tasks even on meshes with millions of vertices, where traditional methods may struggle or require significant computational resources. Additionally, ReMatching provides a time-efficient remeshing algorithm that constructs a low-resolution geometry while conservatively maintaining the original topology and metric. This ensures accurate and stable results in shape correspondence tasks.
Moreover, ReMatching extends the estimated correspondences from the low-resolution representation to the original meshes efficiently. By leveraging fast solutions for extending scalar maps from the remeshed shapes to the high-resolution surfaces, it enables suitable bases for function transfer and shape matching. Overall, ReMatching not only improves efficiency but also enhances effectiveness through quantitative and qualitative comparisons with state-of-the-art pipelines in terms of quality and computational cost.

What potential limitations or challenges could arise when implementing ReMatching in practical applications?

While ReMatching offers significant benefits in terms of scalability and efficiency for shape correspondence tasks, there are some potential limitations or challenges that could arise during implementation:

Accuracy vs Efficiency Trade-off: There might be a trade-off between accuracy and efficiency when using low-resolution representations for shape correspondence. Balancing these factors to ensure both accurate results and fast computations can be challenging.

Topology Preservation: Ensuring that the remeshing algorithm preserves the original topology while reducing mesh complexity is crucial but may pose challenges, especially with highly detailed or complex shapes.

Handling Non-Manifold Surfaces: Dealing with non-manifold surfaces or shapes with intricate geometries can introduce complexities in computing correspondences accurately across different resolutions.

Parameter Tuning: Fine-tuning parameters such as sampling density, resolution reduction levels, or extension mapping techniques may require expertise to optimize performance effectively.

Scalability Issues: While designed for scalability on large meshes, implementing ReMatching on extremely high-resolution models may still present computational challenges due to memory constraints or processing power limitations.

How might advancements in computational geometry impact the future development of shape correspondence techniques?

Advancements in computational geometry play a crucial role in shaping future developments of shape correspondence techniques by enabling more sophisticated algorithms and approaches:

Enhanced Algorithmic Efficiency: Improved algorithms leveraging concepts from computational geometry can lead to faster and more optimized solutions for solving complex geometric problems involved in shape correspondence tasks.

Geometric Data Processing Techniques: Advancements such as spectral mesh processing algorithms can enhance geometric data analysis capabilities essential for accurate shape matching by extracting meaningful features from 3D models efficiently.

3 .Topological Analysis Tools: Advanced topological analysis tools derived from computational geometry principles can provide deeper insights into surface connectivity patterns within shapes, aiding in better understanding relationships between different regions during correspondence computations.
4 .Machine Learning Integration: Integrating machine learning techniques with advanced geometric algorithms can lead to innovative approaches that combine data-driven methodologies with geometric principles to improve accuracy and robustness in shape matching processes.
5 .Real-time Applications: Progression towards real-time applications driven by advancements like parallel computing architectures will enable rapid processing speeds required for interactive 3D modeling environments where quick feedback is essential.
These advancements will likely pave the way for more efficient,
accurate,and versatile solutionsinshapecorrespondence,redefiningthe possibilitiesforapplicationsinscienceandindustry.