1. Progressive compression invariant semi-fragile watermarks for 3D meshes
Author:Puneet Maheshwari, Parag Agarwal, Balakrishnan Prabhakaran
Source: MM&Sec’07, September 20–21, 2007, Dallas, Texas, USA
Presenter: Wu Yenlang 1

2. Outline Introduction Scheme design Watermarking algorithm Conclusion
Clustering
Ordering
Geometry based watermarking
Conclusion 2

3. Introduction
The purpose of this paper is to suggest a methodology that identifies the 3D points (vertices) that are present in every refinement resulting from the CPM [9], PM [7] and PFS [11] algorithms.
Since these points (vertices) define the shape of the object, it is also necessary that during watermarking we do not lose the shape of the 3D object due to the encoding.
Digital Watermarking has found applications in authenticating 3D models by using the loss of the watermark as an evidence for tampering of the 3D shape of the data.
There are many ways of representing 3D models but the most commonly used method is triangulated meshes. 3D meshes can be represented using geometric information defined by a set of 3D vertices (points), and the topological information defined as edge between vertices.
....
Therefore, reduction in distortion achieving imperceptibility of the watermark is also necessary. 3

4. Scheme design 4

5. Scheme design
(0,0)

6. Scheme design
(0,0)

7. Scheme design
(0,0)

8. Scheme design
(0,0)

9. Clustering
(0,0)

10. Clustering (4,5) (8,5) (1,4) (5,4) (10,4) (3,0) (7,3) (3,2) (1,2)
(5,1)
(10,0)
(0,0)

11. Clustering (4,5) (8,5) (1,4) (5,4) (10,4) (3,0) (7,3) (3,2) (1,2)
(5,1)
(10,0)
(0,0)

12. Clustering (4,5) (8,5) (1,4) (5,4) (10,4) (3,0) (7,3) (3,2)
(1,2) C3 C1
(5,1) C2
(10,0)
(0,0)

13. Ordering cluster (degree, bits, greatest angle)
(4,5)
(8,5)
(1,4)
(5,4)
(10,4)
(3,0)
(7,3)
(3,2)
r (5.25,2.5)
(1,2) C3 C1 C2
(5,1)
(10,0)
(0,0)
Order: C2>

14. Ordering cluster (degree, bits, greatest angle)
(4,5)
(8,5)
(1,4)
(5,4)
(10,4)
(3,0)
(7,3)
(3,2)
r (5.25,2.5)
(1,2) C3 C1 C2
(5,1)
(10,0)
(0,0)
Order: C2>C3>C1

15. Ordering vertex (number of vertex,distance)
(4,5)
(8,5) V6 V3
(1,4) V1
(5,4)
(10,4) V4
(3,0)
(7,3) V2
(3,2)
r (5.25,2.5)
(1,2) V5
(5,1) V7
(10,0)
(0,0)
V1=V2
V5 <V4 <V3
V6<V7

16. Ordering vertex (number of vertex,distance)
(4,5)
(8,5) V6 V3
(1,4) V1
(5,4)
(10,4) V4
(3,0)
(7,3) V2
(3,2)
r (5.25,2.5)
(1,2) V5
V1=V2
(5,1) V7
(10,0)
(0,0)
Order: V1 =V2 < V6 < V7< V5 <V4 < V3

17. Sequence Tracing Step (4,5) (8,5) (1,4) (5,4) (10,4) 0011 C3 (3,0)
(7,3)
(3,2) C2
(1,2) C1
(5,1)
(10,0)
(0,0)
Coding Sequence C2
0011

18. Sequence Tracing Step (4,5) (8,5) (1,4) (5,4) (10,4) C3 0011 (3,0)
(7,3)
(3,2) C2
(1,2) C1
1100
(5,1)
(10,0)
(0,0)
Coding Sequence C2

19. Sequence Tracing Step (4,5) (8,5) 1101 (1,4) (5,4) (10,4) C3 0011
(3,0)
(7,3)
(3,2) C2
(1,2) C1
1100
(5,1)
(10,0)
(0,0)
Coding Sequence C2

20. Sequence Tracing Step (4,5) 1111 (8,5) 1101 (1,4) (5,4) (10,4) C3 0011
(3,0)
(7,3)
(3,2) C2
(1,2) C1
1100
(5,1)
(10,0)
(0,0)
Coding Sequence C2 C3

21. Sequence Tracing Step (4,5) 1111 (8,5) 1101 (1,4) (5,4) (10,4) C3 0011
(3,0)
(7,3)
(3,2) C2
(1,2) C1
1100
(5,1)
(10,0)
(0,0)
0010
Coding Sequence C2 C3

22. Sequence Tracing Step (4,5) 1111 (8,5) 1101 (1,4) (5,4) (10,4) C3 0011
(3,0)
(7,3)
0000
(3,2) C2
(1,2) C1
1100
(5,1)
(10,0)
(0,0)
0010
Coding Sequence C2 C3 C1

23. Sequence Tracing Step (4,5) 1111 (8,5) 1101 (1,4) 0001 (5,4) (10,4) C3
0011
(3,0)
(7,3)
0000
(3,2) C2
(1,2) C1
1100
(5,1)
(10,0)
(0,0)
0010
Order: V1 =V2 < V6 < V7< V5 <V4 < V3
Coding Sequence C2 C3 C1

24. Conclusion
The author describes a scheme to enhance the robustness of any watermarking algorithm against compression and decompression.
The author identify vertives that can be used to encode watermarks robust against progressive mesh compression.
Since the watermarks are used for authenticaion, we had to customize the scheme for the same 3D model. 24