MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram

Conceptos Básicos

Novel framework for computing topology-preserving medial axis with geometric convergence.

Resumen

Introduces a novel topology-preserving medial axis computation framework based on volumetric restricted power diagram (RPD).
Utilizes fractional Euler characteristic algorithm for efficient GPU-based computation of Euler characteristic.
Compares with existing methods and highlights advantages in adaptively revising the medial mesh.
Demonstrates topology preservation and geometric convergence in medial axis computation.

Estadísticas

The volumetric RPD discretizes the input 3D volume into sub-regions given a set of medial spheres.
Our method is the first to adaptively revise the medial mesh without modifying the dependent structure globally.
Compared with MATFP, our method offers geometrically comparable results with fewer spheres.

Citas

"Our method can preserve the topology while keeping a competitive reconstruction quality."
"Our adaptive refinement strategy results in a lower number of generated medial spheres."

Ideas clave extraídas de

MATTopo

by Ningna Wang,... a las arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18761.pdf

Consultas más profundas

How does the use of volumetric RPD impact the computational time compared to surface-based methods

The use of volumetric Restricted Power Diagram (RPD) can impact computational time compared to surface-based methods due to the nature of the calculations involved. Volumetric RPD requires cutting tets by half-spaces inside the volume, which can be more computationally intensive than surface-based methods that operate on the boundary of the shape. The process of dividing the input volumetric domain into sub-regions using RPD and computing the intersection of tetrahedral mesh with power cells can be more complex and time-consuming. Additionally, the need to update the RPD partially for each new medial sphere added in the volumetric approach can also contribute to increased computational time compared to surface-based methods.

What are the potential limitations of using a smaller value for the geometric error bound 𝛿𝜖

Using a smaller value for the geometric error bound 𝛿𝜖 can have potential limitations in terms of the reconstruction quality and accuracy of the generated medial mesh. A smaller 𝛿𝜖 value would lead to a more stringent criterion for adding new non-feature spheres based on the distance from surface samples to the enveloping volume of the medial mesh. This could result in a smoother medial mesh around non-feature regions, as more non-feature spheres are sampled to reduce the error. However, setting 𝛿𝜖 too small may lead to over-sampling and unnecessary addition of new spheres, potentially impacting the overall efficiency of the algorithm. It is essential to strike a balance between the geometric error bound and the reconstruction quality to achieve optimal results.

How might the concept of topology preservation in medial axis computation be applied in other fields beyond CAD models

The concept of topology preservation in medial axis computation can be applied beyond CAD models in various fields where shape analysis and feature extraction are essential. For example:

Medical Imaging: In medical imaging, preserving the topology of anatomical structures such as blood vessels, organs, or tumors can aid in accurate diagnosis and treatment planning. Medial axis computation with topology preservation can help in extracting essential features and understanding the spatial relationships within the body.
Robotics: In robotics, understanding the topology of objects in the environment is crucial for navigation, manipulation, and object recognition tasks. Medial axis computation with topology preservation can assist robots in identifying key features and planning efficient paths.
Geographic Information Systems (GIS): Topology preservation in medial axis computation can be valuable in GIS applications for analyzing terrain features, road networks, or urban structures. It can help in extracting meaningful information and understanding the connectivity of geographic elements.
Manufacturing and Industrial Design: In manufacturing and industrial design, preserving the topology of complex shapes and structures is essential for optimizing processes, ensuring structural integrity, and enhancing product design. Medial axis computation with topology preservation can aid in feature extraction and shape analysis for improved manufacturing processes.