3D Mesh Watermarking via Topological Index Modification
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Solution Overview
Problem
Conventional 3D mesh watermarking algorithms deform the shape of the model, reducing precision, making them unsuitable for high-precision applications in rapid prototyping and aerospace manufacturing, where integrity authentication is crucial.
Innovation Solution
A method that embeds a watermark by setting a reference coordinate system using 1-ring values of vertices, sorting them, and modifying index values of polygonal faces to embed bit-information without deforming the model, allowing for robust authentication and information hiding while preserving precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If conventional 3D mesh watermarking algorithms are used to embed watermarks, then watermark embedding capability is achieved, but the shape of the model is deformed and precision is reduced
Solution Approach 1:
The patent segments the 3D mesh model into vertices, edges, and polygonal faces, and further divides vertices into groups based on their spatial relationships (1-ring neighbors). The watermark is embedded by modifying indices within these segmented groups rather than directly altering vertex coordinates, thus avoiding shape deformation while preserving the ability to embed watermark information.
Solution Approach 2:
Instead of changing geometric parameters (vertex coordinates) that affect model shape, the patent changes topological parameters (indices of vertices in polygonal faces). This parameter transformation allows watermark embedding without affecting the actual geometry and precision of the 3D model.
2Loss of information
If watermark is embedded by modifying vertex coordinates or geometric properties, then watermark embedding is achieved, but model integrity and shape accuracy are compromised
Solution Approach 1:
The patent uses indices of vertices as an intermediary to embed watermark information. Rather than directly modifying vertex coordinates or geometric properties, the watermark is hidden within the index values that reference vertices in polygonal faces. This intermediary approach allows watermark embedding without directly affecting the model's shape or geometric integrity.
Solution Approach 2:
The patent creates a copy of the index structure (a parallel representation of vertex relationships) and embeds the watermark in this copied structure. The original geometric data remains unchanged, while the copied index information carries the watermark, effectively separating watermark embedding from shape modification.
3Reliability
If cryptographic techniques are used for data authentication, then security is improved, but applicability in rapid prototyping workflow is limited due to demodulation requirements
Solution Approach 1:
The patent makes the 3D mesh model itself carry its authentication information through embedded watermarks in its structure. The model authenticates itself without requiring external cryptographic verification systems or demodulation processes. This self-service approach maintains reliability while being fully compatible with existing rapid prototyping workflows.
4Loss of information
If watermark embedding modifies geometric properties of the model, then watermark capacity is increased, but manufacturing precision for high-precision fields is reduced
Solution Approach 1:
The patent transforms the embedding target from geometric parameters (coordinates, lengths, areas) to topological parameters (indices, connectivity relationships). This parameter change enables substantial watermark capacity through index modifications while completely preserving geometric precision, making the technique suitable for high-precision manufacturing applications.
Data Source
AI summary
Provided are a watermarking method and a watermarking apparatus for a mesh mode, which are applicable to a system which requires high precision, such as a rapid prototyping system. A reference coordinate system is set using 1-ring values of vertices of a 3D mesh model. The vertices are sorted based on the set reference coordinate system, and bit-information of the watermark consisting of bit string is, respectively, embedded into each of polygonal faces of the 3D mesh model in the sorted order.The present invention is advantageous in that the shape of the model is not deformed even when watermarked, and therefore the present invention is useful in a rapid prototyping system which requires high precision for the purpose of authenticating data integrity. The present invention can be also used for the purpose of marking contents without the need for storing, and for the purpose of information hiding.