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

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?

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

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!

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)

3/20/2000Shape From Texture6 Deterministic Texture Examples

3/20/2000Shape From Texture7 Statistical Texture Examples

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...

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.

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

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

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

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!)

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 

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!

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

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…)

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)

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

3/20/2000Shape From Texture20 Original vector distribution

3/20/2000Shape From Texture21 Rotated needles

3/20/2000Shape From Texture22 Rotated vector distribution

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

3/20/2000Shape From Texture24 Other Texels II