3D Mesh Watermarking via Local Vertex Position Modification
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Solution Overview
Problem
Existing 3D mesh watermarking techniques face challenges in creating cropping-invariant feature points that are imperceptible and controllable, as they often rely on public umbilical points, making them susceptible to attacks and compromising the quality of the 3D object.
Innovation Solution
A method that introduces feature points with characteristics dependent on a secret key and watermark payload, modifying the local neighborhood of vertices to create landmarks that are approximately aligned with a secret signature, allowing for blind recovery and minimizing distortion, thereby improving robustness against cropping.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If feature points are created using public umbilical points or mesh prongs, then the watermarking process becomes simpler and more controllable, but the feature points become noticeable and susceptible to attacks
Solution Approach 1:
The patent transforms feature points by modifying local vertex positions to match target parameters derived from a secret key and watermark payload. This changes the geometric parameters of local neighborhoods to create controllable, imperceptible feature points that are aligned with secret signatures rather than relying on public umbilical points
Solution Approach 2:
The patent introduces an intermediary optimization process that mediates between the original mesh geometry and the desired feature point characteristics. The optimization algorithm adjusts vertex positions to minimize distortion while achieving target signature values, creating a bridge between simplicity and security
2Loss of information
If watermarking is achieved by perturbing vertices according to a pseudo-random bumped surface, then the watermark can be embedded, but the quality of the 3D object deteriorates due to visible distortion
Solution Approach 1:
The patent applies local quality by modifying only the local neighborhood of selected vertices rather than applying global pseudo-random perturbations. Each modification is localized to create specific feature points with target signatures, minimizing overall distortion and preserving the global quality of the 3D object while still embedding watermark information
Solution Approach 2:
The patent uses partial action by selectively modifying only the necessary local neighborhoods to create feature points with correct signatures, rather than applying excessive pseudo-random bumping across the entire mesh. This partial modification approach achieves watermark embedding with minimal impact on overall object quality
3Ease of operation
If feature points are placed at uncontrollable locations like umbilical points, then the watermarking process is simpler, but the feature points become targetable by adversaries
Solution Approach 1:
The patent applies preliminary action by pre-computing target signatures from secret keys and watermark payloads before modifying the mesh. This allows the system to control exactly where feature points will be created and what their characteristics will be, preventing adversaries from targeting predictable locations while maintaining a systematic watermarking process
Solution Approach 2:
The patent introduces asymmetry by using secret key-dependent target signatures that create feature points at non-standard, unpredictable locations. This breaks the symmetry of public umbilical points and creates an asymmetric relationship between the watermarking system and potential attackers, enhancing security while maintaining operational simplicity through the optimized modification process
Data Source
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AI summary
The invention relates to a method for watermarking a three-dimensional object. The watermarking method comprises computing an original signature of a local neighborhood of a current vertex among the plurality of vertices of the three-dimensional object; obtaining a target signature from the original signature and a watermark payload; and modifying said local neighborhood wherein a position of at least one vertex of said local neighborhood is modified such that a modified signature of said modified local neighborhood is close to said target signature and wherein at least a vertex of said modified local neighborhood is not modified. The invention further relates to a method for obtaining payload from a three-dimensional object wherein a signature of a local neighborhood of at least one vertex among a plurality of vertices is close to a target signature and wherein the target signature is obtained using an original signature corresponding to an original three-dimensional object and using a watermark payload. The invention further relates to a 3D object carrying a watermark and to devices for implementing the disclosed methods.