Method and apparatus for digital watermarking of three dimensional object

1. A method for 3D digital watermarking for a triangular mesh using one or more key parameters; comprising:

forming a Hamiltonian path of a desired length around a selected vertex in a selected direction of a spiral;

marking the selected vertex a dead end if there is a deadlock and continuing the spiral; and

applying a watermark by introducing points in a path order on edges of the spiral, wherein information is encoded at a partition of adjacent triangles at one or more of the points.

2. The method of claim 1 wherein the points have a random offset from the edges.

3. The method of claim 1 wherein the watermark includes an initial marker based on the one or more key parameters.

4. The method of claim 1 wherein the watermark is encrypted.

5. The method of claim 1 wherein the watermark includes a checksum.

6. The method of claim 1 wherein one or more labels are applied to the mesh.

7. A method of blind reading of a digital watermark from a three-dimensional mesh using one or more key parameters, comprising:

searching for a location of a watermark by searching vertices or triangles of the mesh;

recovering a Hamiltonian helical path having a length through one or more identified mesh triangles or vertices;

determining a presence of an initial marker to determine the presence of a label at a given point to restore a first path length of the initial marker to determine the presence of the initial marker;

building the path to a full path length; and

extracting information from a location of points on the path.

8. The method of claim 7 further comprising decoding the watermark content and a checksum verification.

9. A computer program product, stored on a non-transitory computer readable medium, comprising instructions that, when executed on one or more computers, cause the one or more computers to perform operations for a method for 3D digital watermarking for a triangular mesh using one or more key parameters,

forming a Hamiltonian path of a desired length around a selected vertex in a selected direction of a spiral;

marking the selected vertex a dead end if there is a deadlock and continuing the spiral; and

applying a watermark by introducing points in a path order on edges of the spiral, wherein information is encoded at a partition of adjacent triangles at one or more of the points.

10. The computer program product of claim 9 wherein the points have a random offset from the edges.

11. The computer program product of claim 9 wherein the watermark includes an initial marker based on the one or more key parameters.

12. The computer program product of claim 9 wherein the watermark is encrypted.

13. The computer program product of claim 9 wherein the watermark includes a checksum.

14. The computer program product of claim 9 wherein one or more labels are applied to the mesh.

15. A computer program product, stored on a non-transitory computer readable medium, comprising instructions that, when executed on one or more computers, cause the one or more computers to perform operations for a method of blind reading of a digital watermark from a three-dimensional mesh using one or more key parameters, comprising:

searching for a location of a watermark by searching vertices or triangles of the mesh;

recovering a Hamiltonian helical path having a length through one or more identified mesh triangles or vertices;

determining a presence of an initial marker to determine the presence of a label at a given point to restore a first path length of the initial marker to determine the presence of the initial marker;

building the path to a full path length; and

extracting information from a location of points on the path.

16. The computer program product of claim 15 further comprising decoding the watermark content and a checksum verification.