1. Watermarking 3D Geometric Models Through Triangle Subdivision Mao et al. Proc. Of SPIE (2001)

2. Summary Object-space watermark for 3D geometric models Survive under affine transformation Embedding with little geometric distortion Details –Embedding procedures –Extraction procedures

3. Affine Transformations Mathematic details Translation, rotation, scale, … Key fact: –Linear combination is invariant under affine transformation

4. Assumptions Triangular mesh model with topology –Winged edge data structure with boundary edges

5. Embedding Steps (1/3) Preprocessing: tweak model so that collinear adjacent edges do not exist Randomly select a triangle to start embedding Generate two random numbers M1, M2 (with the input seed) to start dividing the edges, hence determine the ordering Start traversing until watermark has been embedded

6. Embedding the watermark (2/3) K-bit watermark –7-bit ASCII Normalize so that the ratio is between [0.0, 1.0], preferably around 0.5 7-bit ASCII

7. Embedding (3/3) Generate a random number M3 to register end of embedding Peel off the stego data

8. Extraction Algorithm Reconstruct the topology Identify stego model by edge collinearity Find M1 and M2 to start collecting watermarks (until M3)

9. Homework Watermarking 2D vector graphs Model consists of line lists Subdivide the line by watermarked subdivision Issues –Preprocessing: model contains no collinear adjacent edges –Model topology: linestrips –Starting/ending line of stego model: M1,M3 Implementation issues: –Subdivision/embedding procedure –Affine transformation code –Graphics code –Design examples

10. Affine Transformation Translate: Rotate: Scale:

11. Homework 2 Helper (Basic) float Embed (char key); –Input ascii, generate a ratio near 0.5. –A-Z (65-90); a-z (97-122) –Ref: examiner code Use ratio to split line segment –P1-P2: P1-Pm-P2 Rotate the line segment –Generate 3 new Pi’s Retrieve key from Pi’

12. Hw2 (Bonus) Design a stroke with n line segments (single line loop) Embedding –Preprocessing NO neighboring lines are collinear –Start with a random segment, embed a magic number M1 –Then embed your message to the following segments –Embed M2 at the last stroke –Produce the stego stroke Extraction (from the stego stroke) –Identify the starting stroke Collinear segments with M1 ratio –Extraction the ratio from the remaining stroke, until M2 appears –Reconstruct the message File I/O (single line loop) –should use binary files –Format: n(Z), x1,y1,x2,y2, x3,y3 (R) …