1. Shape From Texture Nick Vallidis March 20, 2000 COMP 290 Computer Vision

2. 3/20/2000Shape From Texture2 Why Shape from Texture? Texture provides our visual systems with a huge amount of information Computers should gain lots of information from it too then, right?

3. 3/20/2000Shape From Texture3 Sometimes texture is all you need Source: Computer Analysis of Visual Textures by Fumiaki Tomita and Saburo Tsuji

4. 3/20/2000Shape From Texture4 So what is texture? One very restrictive definition: “Repeating patterns of local variations in image intensity which are too fine to be distinguished as separate objects” The patterns that repeat are sometimes referred to as texels –NOTE: not the same as a graphics texel as it is made of more than one pixel!

5. 3/20/2000Shape From Texture5 Tell me more about textures! There are basically two kinds: –Deterministic –Statistical It’s pretty much man-made (deterministic) vs. natural (statistical)

6. 3/20/2000Shape From Texture6 Deterministic Texture Examples

7. 3/20/2000Shape From Texture7 Statistical Texture Examples

8. 3/20/2000Shape From Texture8 What’s the general approach? Texture segmentation –hard! This is still a big research area. Texture classification –There are many methods to do this. Shape from texture –We’ll just pretend we can do the first two...

9. 3/20/2000Shape From Texture9 Many things to many people There isn’t “one” shape from texture algorithm. Textures are complex so there are many different aspects that can be taken advantage of.

10. 3/20/2000Shape From Texture10 Comparison of a few approaches *Normalized Texture Property Map

11. 3/20/2000Shape From Texture11 Surface Orientation from Texture Statistical texture method Assumptions: –Texels are small line segments: “needles” –Needles distributed uniformly (in both angle and position) –Only one, approximately-planar surface –Orthographic projection

12. 3/20/2000Shape From Texture12 What we’re calculating The tilt, , and slant, , of the plane:

13. 3/20/2000Shape From Texture13 Where do we get needles? Imagine straw covering a plane Use an edge detector and we’ve got needles! (this even gives us orientation!)

14. 3/20/2000Shape From Texture14 Ok, so what do we do with them? The metric we’re working from is the needle’s angle with the X axis: X axis 

15. 3/20/2000Shape From Texture15 Define some random quantities For every needle, define a vector: [cos(2  ), sin(2  )] So we can tell the angle of the plane by the distribution of these vectors on the unit circle!

16. 3/20/2000Shape From Texture16 Calculate some statistics Find the center of mass of the vectors:

17. 3/20/2000Shape From Texture17 Calculate some statistics But C and S can be put in terms of  and  : (only holds for orthographic projection) (Sorry, no proof on this one…)

18. 3/20/2000Shape From Texture18 We can solve for the orientation! By converting C and S to polar coordinates, we get a simple form to solve for  and  : (where and)

19. 3/20/2000Shape From Texture19 Example! Original Texture/Needles

20. 3/20/2000Shape From Texture20 Original vector distribution

21. 3/20/2000Shape From Texture21 Rotated needles

22. 3/20/2000Shape From Texture22 Rotated vector distribution

23. 3/20/2000Shape From Texture23 Other texels Source: Computer Analysis of Visual Textures Source: Scale-Space Theory in Computer Vision by Tony Lindeberg

24. 3/20/2000Shape From Texture24 Other Texels II