Triangulation Method for Non-2-Manifold Surface Meshes
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Solution Overview
Problem
Standard triangulation methods fail to effectively handle non-2-manifold surface meshes, particularly in medical applications where multiple organs with common boundaries are represented, leading to segmentation errors due to ambiguous image features at 3D T-junctions.
Innovation Solution
A method that decomposes T-junctions into triangles and 2-point-polygons, ensuring each triangle has exactly three neighbors, allowing for the application of standard triangulation methods by connecting surface parts of different organs via 2-point-polygons, and using region growing and curvature-adaptive thinning to reduce voxel numbers while preserving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If standard triangulation methods are used on non-2-manifold surface meshes representing multiple organs with common boundaries, then the segmentation process becomes simpler, but segmentation errors occur due to ambiguous image features at 3D T-junctions
Solution Approach 1:
The patent applies segmentation by dividing the non-2-manifold surface mesh into multiple 2-manifold components, each representing a distinct organ or structure. This is achieved by identifying and separating regions connected through T-junctions, allowing standard triangulation methods to be applied reliably to each segment while maintaining overall structural accuracy
Solution Approach 2:
The patent introduces an intermediary representation layer between the original non-2-manifold mesh and the final triangulated surfaces. This intermediary structure resolves ambiguous T-junctions by creating explicit separation interfaces, enabling accurate segmentation without directly processing the problematic non-2-manifold geometry
2Reliability
If T-junctions are decomposed into triangles and 2-point-polygons to enable standard triangulation methods, then triangulation reliability improves, but the complexity of the mesh structure increases
Solution Approach 1:
The decomposition of T-junctions into separate triangles and 2-point-polygons applies segmentation by breaking down complex junction structures into simpler, well-defined geometric primitives. This segmentation enables standard triangulation algorithms to process each component reliably while maintaining the overall mesh topology
Solution Approach 2:
The patent applies local quality by treating different regions of the mesh with appropriate geometric representations. T-junction areas are locally transformed into 2-point-polygons with specific properties, while other regions maintain standard triangular structures, optimizing both reliability and complexity management
3Productivity
If region growing and curvature-adaptive thinning are applied to reduce voxel numbers, then the number of triangles decreases improving productivity, but measurement precision may be affected
Solution Approach 1:
The patent applies parameter changes by dynamically adjusting mesh density based on local curvature characteristics. Regions with high curvature retain higher voxel resolution to maintain measurement precision, while low-curvature areas undergo aggressive thinning to reduce triangle count and improve processing efficiency
Solution Approach 2:
Curvature-adaptive thinning applies local quality by differentiating between critical and non-critical regions. Surface areas requiring high precision (e.g., organ boundaries with complex geometry) maintain fine resolution, while flat or gently curving regions are coarsened, optimizing the balance between accuracy and productivity
Data Source
AI summary
An exemplary embodiment of the invention provides a method for producing a triangulation of a surface of a physical object the method comprising the steps of generating an intermediate mesh representation of the surface out of surface voxels (102) and detecting at least one T-junction in the intermediate mesh representation (103). The method further comprising the steps of decomposing of the at least one T-junction into at least one triangle and at least one two-point-polygon (104), and generating the triangulation of the surface out of the modelled intermediate mesh representation (107).