stereological techniques for solid textures rob jagnow mit julie dorsey yale university holly...
Post on 21-Dec-2015
217 views
TRANSCRIPT
![Page 1: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/1.jpg)
Stereological Techniquesfor Solid Textures
Rob Jagnow
MIT
Julie Dorsey
Yale University
Holly Rushmeier
Yale University
![Page 2: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/2.jpg)
Given a 2D slice through an aggregate material, create a 3D volume with a comparable appearance.
ObjectiveObjective
![Page 3: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/3.jpg)
Real-World MaterialsReal-World Materials
• Concrete
• Asphalt
• Terrazzo
• Igneous
minerals
• Porous
materials
![Page 4: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/4.jpg)
Independently Recover…Independently Recover…
• Particle distribution
• Color
• Residual noise
![Page 5: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/5.jpg)
Stereology (ster'e-ol' -je)
e
The study of 3Dproperties based on2D observations.
In Our Toolbox…In Our Toolbox…
![Page 6: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/6.jpg)
Prior Work – Texture SynthesisPrior Work – Texture Synthesis
• 2D 2D
• 3D 3DEfros & Leung ’99
• 2D 3D– Heeger & Bergen 1995– Dischler et al. 1998– Wei 2003
Heeger & Bergen ’95
Wei 2003
• Procedural Textures
![Page 7: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/7.jpg)
Prior Work – Texture SynthesisPrior Work – Texture Synthesis
Input Heeger & Bergen, ’95
![Page 8: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/8.jpg)
Prior Work – StereologyPrior Work – Stereology
• Saltikov 1967Particle size distributions from section measurements
• Underwood 1970Quantitative Stereology
• Howard and Reed 1998Unbiased Stereology
• Wojnar 2002Stereology from one of all the possible angles
![Page 9: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/9.jpg)
Estimating 3D DistributionsEstimating 3D Distributions
• Macroscopic statistics of a 2D image are related to,but not equal to the statistics of a 3D volume
– Distributions of Spheres
– Distributions for Other Particles
– Managing Multiple Particle Types
![Page 10: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/10.jpg)
Distributions of SpheresDistributions of Spheres
• : maximum diameter
• Establish a relationship between– the size distribution of 2D circles
(as the number of circles per unit area)– the size distribution of 3D spheres
(as the number of spheres per unit volume)
maxd
![Page 11: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/11.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
AN
H
VN
= Profile density (number of circles per unit area)
= Mean caliper particle diameter
= Particle density (number of spheres per unit volume)
VA NHN
The fundamental relationshipof stereology:
![Page 12: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/12.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
Group profiles and particles into n binsaccording to diameter
}1{),( niiN A }1{),( niiNV
Particle densities =
Profile densities =
Densities , are related by the values ijKANVN
Relative probabilities :
- a sphere in the j th histogram bin with diameter - a profile in the i th histogram bin with diameter
ijK
n
id
n
i
)1(
n
j
![Page 13: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/13.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
Note that the profile source is ambiguous
For the following examples, n = 4
![Page 14: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/14.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
How many profiles of the largest size?
)4(AN )4(VN44K
=
ijK = Probability that particle NV(j) exhibits profile NA(i)
![Page 15: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/15.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
How many profiles of the smallest size?
)1(AN )4(VN11K
= + + +12K 13K 14K)3(VN)2(VN)1(VN
= Probability that particle NV(j) exhibits profile NA(i) ijK
![Page 16: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/16.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
Putting it all together…
AN VNK
=
![Page 17: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/17.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
Some minor rearrangements…
= maxd KAN VN
njKn
iij /
1
Normalize probabilities for each column j:
= Maximum diametermaxd
![Page 18: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/18.jpg)
Recovering Sphere DistributionsRecovering Sphere Distributions
VA KNdN max
For spheres, we can solve for K analytically:
0
)1(/1 2222 ijijnK ij
K is upper-triangular and invertible
for ij otherwise
AV NKdN 1
max
1 Solving for particle densities:
![Page 19: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/19.jpg)
Other Particle TypesOther Particle Types
We cannot classify arbitrary particles by d/dmax
Instead, we choose to use max/ AA
Approach: Collect statistics for 2D profiles and 3D particles
Algorithm inputs:
+
![Page 20: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/20.jpg)
Profile StatisticsProfile Statistics
Segment input image to obtain profile densities NA.
Bin profiles according to their area, max/ AA
Input Segmentation
![Page 21: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/21.jpg)
Particle StatisticsParticle Statistics
• Polygon mesh : random orientation
• Render
![Page 22: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/22.jpg)
Particle StatisticsParticle Statistics
Look at thousands of random slices to obtain H and K
Example probabilities of for simple particlesmax/ AA
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
spherecubelong ellipsoidflat ellipsoid
A/Amax
pro
ba
bili
ty
![Page 23: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/23.jpg)
Scale FactorScale Factor
• Scale factor s : to relate the size of particle P to the size of the particles in input image
– profile maximum area• : input image• : particle P
• Mean caliper diameter
Pmaximg /AAs
PmaxA
imgA
PHsH
![Page 24: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/24.jpg)
Recovering Particle DistributionsRecovering Particle Distributions
Just like before, VA KNHN
Use NV to populate a synthetic volume.
AV NKH
N 11
Solving for the particle densities,
![Page 25: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/25.jpg)
Managing Multiple Particle TypesManaging Multiple Particle Types
• particle type : i• mean caliper diameter :• representative matrix :• distribution :• probability that a particle
is type i : P( i )• total particle density :
iH
iK
ViN
i
ViiiA NKHN )(
i
ViiA NiPKHN ))((
ViV NN
Vi
ii NiPKH ))((
Ai
iiV NiPKHN1
))((
![Page 26: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/26.jpg)
Reconstructing the VolumeReconstructing the Volume
• Particle Positions
• Color
• Adding Fine Detail
![Page 27: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/27.jpg)
Particle Position - AnnealingParticle Position - Annealing
• Populate the volume with all of the particles, ignoring overlap
• Perform simulated annealing to resolve collision– Repeatedly searches for all collision
(in the x, y, z directions)– Relaxes particle positions to reduce
interpenetration
![Page 28: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/28.jpg)
Recovering ColorRecovering Color
Select mean particle colors fromsegmented regions in the input image
Input Mean ColorsSyntheticVolume
![Page 29: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/29.jpg)
Recovering NoiseRecovering NoiseHow can we replicate the noisy appearance of the input?
- =
Input Mean Colors Residual
The noise residual is less structured and responds well to
Heeger & Bergen’s method
Synthesized Residual
![Page 30: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/30.jpg)
without noise
Putting it all togetherPutting it all together
Input
Synthetic volume
![Page 31: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/31.jpg)
Prior Work – RevisitedPrior Work – Revisited
Input Heeger & Bergen ’95 Our result
![Page 32: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/32.jpg)
Results- Testing PrecisionResults- Testing Precision
Inputdistribution
Estimateddistribution
![Page 33: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/33.jpg)
Result- ComparisonResult- Comparison
![Page 34: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/34.jpg)
Collection of Particle ShapesCollection of Particle Shapes
• Can’t predict exact particle shapes
• Unable to count small profiles
• Limited to fewer profile observation
Calculations error
![Page 35: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/35.jpg)
Results – Physical DataResults – Physical Data
PhysicalModel
Heeger &Bergen ’95
Our Method
![Page 36: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/36.jpg)
ResultsResultsInput Result
![Page 37: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/37.jpg)
ResultsResults
Input Result
![Page 38: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/38.jpg)
SummarySummary
• Particle distribution– Stereological techniques
• Color– Mean colors of segmented profiles
• Residual noise– Replicated using Heeger & Bergen ’95
![Page 39: Stereological Techniques for Solid Textures Rob Jagnow MIT Julie Dorsey Yale University Holly Rushmeier Yale University](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d615503460f94a4347f/html5/thumbnails/39.jpg)
Future WorkFuture Work
• Automated particle construction
• Extend technique to other domains and anisotropic appearances
• Perceptual analysis of results