Stereological Techniques for Solid Textures

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Stereological Techniquesfor Solid Textures

• Rob Jagnow
• MIT

Julie Dorsey Yale University
Holly Rushmeier Yale University
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Objective
Given a 2D slice through an aggregate material,
create a 3D volume with a comparable appearance.
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Real-World Materials

• Concrete
• Asphalt
• Terrazzo
• Igneous
• minerals
• Porous
• materials

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Independently Recover

• Particle distribution
• Color
• Residual noise

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In Our Toolbox
The study of 3D properties based on 2D
observations.
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Prior Work Texture Synthesis

• 2D 2D
• 3D 3D

Efros Leung 99

• Procedural Textures

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Prior Work Texture Synthesis
Input
Heeger Bergen, 95
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Prior Work Stereology

• Saltikov 1967
• Particle size distributions from section
  measurements
• Underwood 1970
• Quantitative Stereology
• Howard and Reed 1998
• Unbiased Stereology
• Wojnar 2002
• Stereology from one of all the possible angles

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Recovering Sphere Distributions
Profile density (number of circles per unit
area)
Particle density (number of spheres per unit
volume)
Mean caliper particle diameter
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Recovering Sphere Distributions
Group profiles and particles into n
bins according to diameter
Particle densities
Profile densities
For the following examples, n 4
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Recovering Sphere Distributions
Note that the profile source is ambiguous
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Recovering Sphere Distributions
How many profiles of the largest size?

Probability that particle NV(j) exhibits
profile NA(i)
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Recovering Sphere Distributions
How many profiles of the smallest size?




Probability that particle NV(j) exhibits
profile NA(i)
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Recovering Sphere Distributions
Putting it all together

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Recovering Sphere Distributions
Some minor rearrangements

Maximum diameter
Normalize probabilities for each column j
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Recovering Sphere Distributions
K is upper-triangular and invertible
For spheres, we can solve for K analytically
for
otherwise
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Testing precision
Input distribution
Estimated distribution
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Other Particle Types
We cannot classify arbitrary particles by d/dmax
Instead, we choose to use
Approach Collect statistics for 2D profiles and
3D particles
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Profile Statistics
Segment input image to obtain profile densities
NA.
Input
Segmentation
Bin profiles according to their area,
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Particle Statistics
Look at thousands of random slices to obtain H
and K
Example probabilities of for simple
particles
probability
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Recovering Particle Distributions
Just like before,
Use NV to populate a synthetic volume.
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Recovering Color
Select mean particle colors from segmented
regions in the input image
Input
Mean Colors
Synthetic Volume
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Recovering Noise
How can we replicate the noisy appearance of the
input?
-

Input
Mean Colors
Residual
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Putting it all together
Input
Synthetic volume
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Prior Work Revisited
Input
Heeger Bergen 95
Our result
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Results Physical Data
Physical Model
Heeger Bergen 95
Our Method
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Results
Input
Result
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Results
Input
Result
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Summary

• Particle distribution
• Stereological techniques
• Color
• Mean colors of segmented profiles
• Residual noise
• Replicated using Heeger Bergen 95

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Future Work

• Automated particle construction
• Extend technique to other domains and anisotropic
  appearances
• Perceptual analysis of results

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Thanks to

• Maxwell Planck, undergraduate assistant
• Virginia Bernhardt
• Bob Sumner
• John Alex