3D Reconstruction Using Tetrahedral Meshing for Non-Regular Point Clouds
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Solution Overview
Problem
Existing methods for 3D reconstruction of real scenes from point clouds are limited by their inability to accurately handle non-regular structures, require smoothness hypotheses, and are sensitive to noise and outliers, often resulting in incomplete or inaccurate reconstructions due to high computational demands.
Innovation Solution
A computer-implemented method for 3D reconstruction that uses tetrahedral meshing to determine an open triangulated surface representing the skin of a structure, penalizing high-ranked triangles based on a lexicographic order that minimizes triangle size and maintains consistency with given labels, allowing for robust handling of non-regular point clouds and large datasets without manual parameter tuning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing methods for 3D reconstruction are used, then the reconstruction process can be completed, but the accuracy is reduced due to sensitivity to noise and outliers
Solution Approach 1:
The patent applies preliminary action by performing tetrahedral meshing on the point cloud before surface reconstruction. This preprocessing step creates a structured geometric framework that filters out noise and outliers early in the process, allowing the subsequent surface extraction to operate on cleaned, structured data rather than raw noisy points
Solution Approach 2:
The patent introduces an intermediary structure (tetrahedral mesh) between the raw point cloud and the final surface reconstruction. This intermediate representation serves as a mediator that transforms unstructured noisy data into a structured format, enabling more robust surface extraction while maintaining accuracy
2Productivity
If existing 3D reconstruction methods are used, then the process can handle various structures, but the computational complexity increases leading to incomplete reconstructions
Solution Approach 1:
The patent applies segmentation by dividing the point cloud into tetrahedral elements through meshing. This breaks down the complex global reconstruction problem into smaller local tetrahedral units that can be processed efficiently, reducing overall computational complexity while maintaining complete coverage of the structure
Solution Approach 2:
The patent changes the parameter representation from unstructured point coordinates to structured tetrahedral mesh parameters. This transformation enables more efficient computational operations during surface extraction, improving productivity while managing complexity through the regular structure of the mesh
3Ease of manufacture
If smoothness hypotheses are applied in 3D reconstruction, then the computational process is simplified, but the ability to handle non-regular structures is reduced
Solution Approach 1:
The patent applies local quality by allowing different regions of the mesh to have different properties. The tetrahedral meshing approach enables local adaptation to non-regular structures while maintaining overall process simplicity, as each tetrahedron can conform to local geometric features without requiring global smoothness assumptions
Data Source
AI summary
A 3D reconstruction method including obtaining a first open triangulated surface consisting of triangles of a tetrahedral meshing of a point cloud and determining a second open triangulated surface. The determining explores candidate open triangulated surfaces each being a set of triangles of the meshing and penalizes a high rank of the candidates according to a lexicographic order based on a triangle order and ordering a candidate having triangles decreasingly ordered according to a triangle order penalizing triangle size, relative to another candidate having triangles decreasingly ordered according to the triangle order. The second surface violates consistency of a labelling of the meshing with two labels. A triangle respects labelling consistency when it belongs to the first surface and separates two tetrahedrons having different labels, or when it does not belong to the first surface and separates two tetrahedrons having a same label.