Efficient Plane Arrangement for Scalable Low-Poly Surface and Volume Modeling

Belangrijkste concepten

An efficient plane arrangement mechanism that enables the construction of concise polyhedral decompositions for low-polygon surface and volume modeling from complex 3D data.

Samenvatting

The paper presents a scalable plane arrangement method for generating low-polygon surface and volume meshes from 3D point clouds. The key contributions are:

1. An ordering scheme for the plane insertion operations that prioritizes splits creating cells that cannot be split further and balances the number of polygons in the cells.
2. The direct use of input points during arrangement construction to replace costly intersection tests with simple point-plane orientation checks.
3. A remeshing and simplification technique to extract low-polygon surface meshes and lightweight convex decompositions of volumes from the arrangement.

The proposed method significantly outperforms existing plane arrangement algorithms in terms of complexity and runtime, while producing state-of-the-art results for low-poly surface and volume modeling tasks. Experiments on the Thingi10k dataset and comparisons to baselines demonstrate the effectiveness of the approach.

Statistieken

The average number of polyhedral cells in the decompositions produced by our method is 73 for simple models, 256 for moderate models, and 705 for complex models.
The average number of polygonal facets in the reconstructed surface meshes is 53 for simple models, 167 for moderate models, and 478 for complex models.
The average symmetric Chamfer distance between the ground truth and reconstructed meshes is 0.193 for simple models, 0.254 for moderate models, and 0.224 for complex models.
The average symmetric Hausdorff distance between the ground truth and reconstructed meshes is 1.15 for simple models, 2.32 for moderate models, and 2.78 for complex models.
The average construction time of our method is 3.06 seconds for simple models, 16.3 seconds for moderate models, and 68.1 seconds for complex models.

Citaten

"The key contribution of our work is an efficient mechanism for constructing more concise arrangements in less time than existing methods."
"We directly exploit input points to avoid unnecessary splitting operations and replace intersection tests between polyhedral cells and polygons with simply point-plane orientation tests."
"We carefully order the plane insertion operations to further lower the computational complexity of the algorithm."

Belangrijkste Inzichten Gedestilleerd Uit

Concise Plane Arrangements for Low-Poly Surface and Volume Modelling

by Raphael Sulz... om arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.06154.pdf

Diepere vragen

How could the plane detection step be improved to further enhance the quality and compactness of the reconstructed models?

In order to enhance the quality and compactness of the reconstructed models through improved plane detection, several strategies can be implemented:

Refinement of Plane Fitting Algorithms: Utilizing more advanced plane fitting algorithms that can accurately capture the underlying geometry of the surfaces in the point cloud data. This can involve incorporating robust estimation techniques to handle outliers and noise effectively.

Adaptive Plane Detection: Implementing adaptive plane detection methods that can adjust the parameters based on the local geometry of the point cloud. This can help in capturing intricate details and complex structures more accurately.

Multi-Scale Plane Detection: Employing multi-scale plane detection techniques to capture planes at different levels of detail. This can help in representing the geometry of the object more comprehensively.

Feature-Based Plane Detection: Integrating feature-based plane detection methods that can identify salient features in the point cloud data and use them to guide the plane fitting process. This can lead to more meaningful and compact plane arrangements.

Incorporating Semantic Information: Utilizing semantic information from the point cloud data to guide the plane detection process. This can help in identifying regions of interest and improving the overall reconstruction quality.

By incorporating these enhancements in the plane detection step, the quality and compactness of the reconstructed models can be significantly improved.

What are the potential limitations of the plane arrangement approach compared to other surface and volume modeling techniques, such as neural network-based methods?

While plane arrangement approaches offer several advantages for surface and volume modeling, they also have some limitations compared to neural network-based methods:

Complexity of Geometry Representation: Plane arrangement methods rely on decomposing the geometry into planar regions, which may not capture complex geometries with high fidelity compared to neural network-based methods that can learn intricate shapes directly from the data.

Scalability: Plane arrangement algorithms may face scalability issues when dealing with a large number of input planes, leading to computational challenges. In contrast, neural network-based methods can handle larger datasets more efficiently.

Generalization: Neural network-based methods have the potential to generalize well to unseen data and diverse shapes, whereas plane arrangement approaches may struggle with generalization, especially for complex or irregular geometries.

Training Data Dependency: Neural network-based methods require extensive training data to learn the underlying patterns in the geometry, while plane arrangement methods rely more on geometric principles and may not require as much training data.

Flexibility: Neural network-based methods offer more flexibility in modeling different types of geometries and can adapt to various reconstruction tasks, whereas plane arrangement approaches are more tailored to specific geometric decomposition tasks.

While plane arrangement methods excel in certain aspects such as watertightness and geometric guarantees, they may have limitations in handling complex and diverse geometries compared to neural network-based methods.

Could the proposed plane arrangement algorithm be extended to handle dynamic 3D scenes or deformable objects?

The proposed plane arrangement algorithm can be extended to handle dynamic 3D scenes or deformable objects with certain modifications and considerations:

Dynamic Scene Handling: For dynamic scenes, the algorithm would need to incorporate mechanisms to update the plane arrangement in real-time as the scene changes. This could involve dynamic data structures and algorithms to adapt to the evolving geometry.

Deformable Object Modeling: To handle deformable objects, the algorithm would need to account for the changing shape of the objects over time. This could involve integrating techniques for tracking deformations and updating the plane arrangement accordingly.

Temporal Consistency: Ensuring temporal consistency in the plane arrangement to maintain coherence between consecutive frames in dynamic scenes or deformable objects. This could involve incorporating motion estimation and tracking to guide the arrangement process.

Physics-Based Modeling: Introducing physics-based constraints and simulations to handle interactions between objects in dynamic scenes or deformable objects. This could enhance the realism of the reconstructed models and improve the accuracy of the plane arrangement.

By incorporating these considerations and modifications, the plane arrangement algorithm can be extended to effectively handle dynamic 3D scenes and deformable objects, providing a robust framework for surface and volume modeling in dynamic environments.