Graph Representation for 3D Object Symmetry Detection
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Solution Overview
Problem
Existing methods for constructing high-level representations of 3D models struggle with symmetry detection due to missing data and noise, often resulting in false results and requiring user-defined criteria, which limits their effectiveness in capturing the hierarchical structures of man-made objects.
Innovation Solution
A method that generates an initial graph representation for 3D objects by selecting nodes with the largest distance within symmetric groups, expanding sub-graphs, and using Earth Mover's Distance to refine symmetry results, allowing for the contraction of sub-graphs into new nodes and updating the graph representation to achieve a hierarchical structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If symmetry detection is performed on 3D models with missing data and noise, then symmetry groups can be identified, but false results are generated
Solution Approach 1:
The patent employs feedback mechanisms where the graph representation construction process continuously refines symmetry detection results. The algorithm uses the constructed graph to verify and correct initial symmetry detection, iteratively improving accuracy by feeding back the structural relationships discovered in the graph representation to adjust symmetry group assignments and eliminate false detections.
Solution Approach 2:
The patent introduces an intermediate graph representation structure that mediates between raw 3D model data and final symmetry detection results. This graph serves as an intermediary layer that captures geometric and topological relationships, allowing the system to reason about symmetry in a structured manner that is more robust to noise and missing data than direct symmetry detection methods.
2Extent of automation
If high-level representation is built on user-defined criteria, then hierarchical structure can be constructed, but the method requires manual intervention and lacks automation
Solution Approach 1:
The patent implements self-service through an automated algorithm that constructs hierarchical graph representations without requiring user-defined criteria. The system autonomously analyzes the 3D model's geometric and topological properties, automatically identifies symmetry groups, and builds the hierarchical structure based on intrinsic model characteristics rather than external user specifications.
Solution Approach 2:
The patent replaces the manual mechanical process of user-defined criteria with an automated computational system. Instead of users manually specifying hierarchical relationships and symmetry criteria, the system uses algorithmic processing to automatically discover and encode these structures from the 3D model data, substituting human intervention with computational analysis.
3Reliability
If symmetry hierarchy method is used on models with excellent symmetry, then hierarchical representation is achieved, but it fails on models with missing data or noise
Solution Approach 1:
The patent applies parameter changes by transforming the 3D model data into a graph representation where nodes and edges encode geometric and topological relationships. This parameter transformation allows the system to work with varying data qualities, as the graph structure preserves essential relational information even when raw geometric data is noisy or incomplete, making the symmetry hierarchy construction more robust.
Solution Approach 2:
The patent uses a composite approach by combining multiple types of information (geometric properties, topological relationships, symmetry indicators) into a unified graph representation. This composite structure integrates different data aspects that complement each other, allowing the system to maintain reliability in symmetry hierarchy construction even when individual data sources are degraded by noise or missing values.
Data Source
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AI summary
It is provided a method for constructing a graph representation for a 3D object, wherein comprising the steps of generating an initial graph representation for the 3D object, wherein a node in the initial graph representation corresponds to a component of the 3D object and a symmetric indication value uniquely identifying a symmetric group is associated with a symmetric node; selecting two nodes from one symmetric group that has the most symmetric nodes, wherein the distance between the two nodes are the largest among distance between any other two nodes within the symmetric group; obtaining two set of nodes by expanding separately from the two nodes to their directly connected nodes, wherein if a node is connected directly to both two nodes, the node is excluded from the two set of nodes; and if determining that the two sets of nodes match, updating the graph representation by grouping each set of nodes into one node.