1. Northwestern University Polynomial Texture Maps Dan Hazen Based on the paper: Malzbender, T., Gelb, D., Wolters, H., “Polynomial Texture Maps”, Computer Graphics (SIGRAPH 01 PROCEEDINGS), August 2001. www.hpl.hp.com/ptm CS 395: Advanced Computer Graphics January 22, 2002

2. Northwestern University Introduction What are Polynomial Texture Maps (PTM’s)? Image based texture maps used for more accurate texturization of fine details. What are Polynomial Texture Maps (PTM’s)? Image based texture maps used for more accurate texturization of fine details. Why use PTM’s? More Realistic Textures! Why use PTM’s? More Realistic Textures!

3. Northwestern University Background Bi-directional Texture Function:

4. Northwestern University Background Bi-directional Texture Function (Cont.): Conventional BTF

5. Northwestern University Polynomial Texture Mapping Store coefficients at EACH TEXEL. Coefficients derived from series of photographs. L(u,v) = a 0 (u,v)l u 2 + a 1 (u,v)l v 2 + a 2 (u,v)l u l v + a 3 (u,v)l u + a 4 (u,v)l v + a 5 (u,v)

6. Northwestern University Polynomial Texture Mapping (Cont.) DEMO!

7. Northwestern University Polynomial Texture Mapping (Cont.) Capture images using devices to get the coefficients

8. Northwestern University Polynomial Texture Mapping (cont.) Storage Concerns: 1 Byte: Red 1 Byte: Blue 1 Byte: Green 6 Bytes: Coefficient a0-5 9 Bytes/Texel: Best Case:Worst Case: 1 Byte: Red 1 Byte: Blue 1 Byte: Green 6 Bytes: a0-5 Red 21 Bytes/Texel: 6 Bytes: a0-5 Blue 6 Bytes: a0-5 Green 500x500 Image: ~2.2 Megs500x500 Image: ~5.1 Megs

9. Northwestern University PTM Applications Specular Highlighting

10. Northwestern University PTM Applications (Cont.) Contrast Enhancement: Method 1 – Specular Highlights Original Photo Specular Highlight PTM Reconstruction PTM + Highlight

11. Northwestern University PTM Applications (Cont.) Contrast Enhancement: Method 2 – Diffuse Gain Original Photograph Diffuse Gain = 1.9 PTM Reconstruction

12. Northwestern University PTM Applications (Cont.) Contrast Enhancement: Method 3 – Light Extrapolation Original PhotographExtrapolated PTM Reconstruction

13. Northwestern University PTM Applications (Cont.) Video: http://www.hpl.hp.com/ptm/http://www.hpl.hp.com/ptm/

14. Northwestern University PTM Applications (Cont.)

15. Northwestern University PTM Applications (Cont.)

16. Northwestern University PTM Applications (Cont.)

17. Northwestern University PTM Applications (Cont.)

18. Northwestern University PTM Applications (Cont.)

19. Northwestern University PTM Applications (Cont.)

20. Northwestern University PTM Advantages and Issues Advantages 1. Only images needed to form the texture 2. Texture maps maintain roughness 3. Neat lighting and viewing tricks 4. Efficient enough for interactive speeds once coefficients are obtained Issues 1. Storage Costs 2. Using biquadratic polynomial: in some cases may not be precise enough

21. Northwestern University PTM Research Expansion Suggestions for research expansion: Use a higher order polynomial for better representation Use basis functions to reduce storage costs Get rid of fixed camera constraint to get a higher number of free dimensions Add modeling surface opacity to the list of features

22. Northwestern University Conclusions Polynomial Texture Maps (PTM’s) portray rough surfaces based on a set of input images Polynomial Texture Maps can be used for more than just interactively moving a light source around a texture; there are methods that improve image definition Easy to do in hardware but storage could be a problem QUESTIONS?