Shape From Texture

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Shape From Texture

• Nick Vallidis
• March 20, 2000
• COMP 290 Computer Vision

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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?

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Sometimes texture is all you need
Source Computer Analysis of Visual Textures by
Fumiaki Tomita and Saburo Tsuji
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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!

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Tell me more about textures!

• There are basically two kinds
• Deterministic
• Statistical
• Its pretty much man-made (deterministic) vs.
  natural (statistical)

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Deterministic Texture Examples
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Statistical Texture Examples
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Whats 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
• Well just pretend we can do the first two...

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Many things to many people

• There isnt one shape from texture algorithm.
• Textures are complex so there are many different
  aspects that can be taken advantage of.

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Comparison of a few approaches
Normalized Texture Property Map
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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

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What were calculating

• The tilt, ?, and slant, ?, of the plane

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Where do we get needles?

• Imagine straw covering a plane
• Use an edge detector and weve got needles! (this
  even gives us orientation!)

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Ok, so what do we do with them?

• The metric were working from is the needles
  angle with the X axis

?
X axis
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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!

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Calculate some statistics

• Find the center of mass of the vectors

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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)
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We can solve for the orientation!

• By converting C and S to polar coordinates, we
  get a simple form to solve for ? and ?

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Example!Original Texture/Needles
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Original vector distribution
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Rotated needles
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Rotated vector distribution
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Other texels
Source Computer Analysis of Visual Textures
Source Scale-Space Theory in Computer Vision by
Tony Lindeberg
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Other Texels II