A Simulation Study of A Simulation Study of Segmentation Methods on Segmentation Methods on

the Soil Aggregate the Soil Aggregate Microtomographic ImagesMicrotomographic Images

Wei Wang, Alexandra N. Kravchenko, Kateryna Ananyeva,

Alvin J. M. Smucker, C.Y. Lim and Mark L. Rivers

Department of Crop & Soil Sciences, Department of Statistics & Department of Crop & Soil Sciences, Department of Statistics & Probability, MSUProbability, MSU

Advanced Photon Source, Argonne National LaboratoryAdvanced Photon Source, Argonne National Laboratory

Computed microtomographic Computed microtomographic images (CMT)images (CMT)

MotivationMotivation

Segmentation results will affect pore Segmentation results will affect pore network analysis, (e.g. pore connectivity, network analysis, (e.g. pore connectivity, tortuosity, medial axistortuosity, medial axis……) and therefore ) and therefore influence flow simulation (e.g. Lattice influence flow simulation (e.g. Lattice Boltzmann modeling ), pore-scale Boltzmann modeling ), pore-scale biological activity modeling.biological activity modeling.

Accurate pore/solid classification is very Accurate pore/solid classification is very important to understand pore structures important to understand pore structures in the intra-aggregate spaces.in the intra-aggregate spaces.

Difficulties in processing Difficulties in processing CMT imagesCMT images

Artifacts : partial volume effect Artifacts : partial volume effect (finite resolution effect), beam (finite resolution effect), beam hardening, ring artifactshardening, ring artifacts……

Complex composition of soil matrix Complex composition of soil matrix (large range of grey-scale values)(large range of grey-scale values)

Difficulties in processing Difficulties in processing CMT imagesCMT images

Lack of ground-truth information to Lack of ground-truth information to assess pore/solid classification assess pore/solid classification accuracyaccuracy

Identify criteria to select optimal Identify criteria to select optimal segmentation method for soil segmentation method for soil aggregate imagesaggregate images

ObjectivesObjectives

To evaluate criteria for selecting the To evaluate criteria for selecting the optimal segmentation method for optimal segmentation method for soil pore characterizationsoil pore characterization

To compare performance of several To compare performance of several commonly used segmentation commonly used segmentation methods in soil aggregate images methods in soil aggregate images with different porositieswith different porosities

Simulation approachSimulation approach

In order to overcome the absence of In order to overcome the absence of ground-truth information we proposed a ground-truth information we proposed a simulation approach including:simulation approach including:

● ● Simulate partial volume effect in the Simulate partial volume effect in the pore spacepore space

● ● Simulate different solid materialSimulate different solid material

● ● SimulateSimulate random noiserandom noise

Simulate partial volume Simulate partial volume effecteffect

Generate binary soil images at the scanned Generate binary soil images at the scanned resolution; resolution;

scanned pixel size

Ground-truth image

1 mm

Simulate partial volume Simulate partial volume effecteffect Generate 3 layers of pores at Generate 3 layers of pores at

smaller scales;smaller scales;

1/2 scanned pixel size

1 mm

1/8 scanned pixel size

1 mm

1/4 scanned pixel size

1 mm

Simulate partial volume Simulate partial volume effecteffect Combine all the layers of poresCombine all the layers of pores

1 mm

Simulate solid space and Simulate solid space and noisenoise Solid space simulation was done for all the Solid space simulation was done for all the ““whitewhite””

pixels using spatial simulation of LU decomposition pixels using spatial simulation of LU decomposition techniquetechnique

Gaussian random noise was added to the whole imageGaussian random noise was added to the whole image

Grey scale image Grey scale image simulationsimulation

Ground truth image Simulation in the pore space

Simulation in the solid space + noise simulation

Original image from the scan

Different porosity cases (1)Different porosity cases (1)Low Medium High High + flow pattern

Porosity = 4.8% Porosity = 7.8% Porosity = 16.5% Porosity = 22.8%

Different porosity cases (2)Different porosity cases (2)Low Medium High High + flow pattern

Porosity = 3.6% Porosity = 8.3% Porosity = 15.8% Porosity = 28.5%

Existing segmentation Existing segmentation methodsmethods

More than 40 different segmentation More than 40 different segmentation methods (Sezgin et al., 2004 )methods (Sezgin et al., 2004 )

They mainly can be classified into They mainly can be classified into several categories:several categories:

●● Manual thresholdingManual thresholding ●● Global thresholding methods Global thresholding methods ●● Local adaptive methodsLocal adaptive methods

Segmentation methodsSegmentation methods Global thresholding :Global thresholding : ●● Entropy Entropy method: Renyi method: Renyi’’s entropy (Sahoo et s entropy (Sahoo et

al., 1997) al., 1997)

● ● Iterative Iterative method: Riddler et al., 1978 method: Riddler et al., 1978

●● OtsuOtsu method: maximize between-class method: maximize between-class variance (Otsu, 1979)variance (Otsu, 1979)

Local adaptive method:Local adaptive method:

●● Indicator krigingIndicator kriging ( (IKIK) method: Oh and ) method: Oh and Lindquist, 1999 Lindquist, 1999

IK methodIK method Two steps : thresholding, krigingTwo steps : thresholding, kriging Thresholding step: the thresholds are determined by Thresholding step: the thresholds are determined by

fitting mixed Gaussian distributions to pore and solid fitting mixed Gaussian distributions to pore and solid spaces using Expectation-Maximization algorithm spaces using Expectation-Maximization algorithm (Dempster et al., 1977 ). (Dempster et al., 1977 ).

Histogram of simulated image

grey-scale value

Pro

b.

0 50 100 150 200 250

0.0

00

0.0

05

0.0

10

0.0

15

T1 T2

SolidPore

kriging step

?

Black

White

Segmentation performance Segmentation performance criterioncriterion Misclassification Error (ME): 0<ME<1 Misclassification Error (ME): 0<ME<1

(ground-truth image required)(ground-truth image required)

where where PP and and SS are the number of common are the number of common pore or solid pixels in both ground-truth pore or solid pixels in both ground-truth and segmented images.and segmented images.

T

SPME

1

Segmentation performance Segmentation performance criterioncriterion Region non-uniformity measure (NU): Region non-uniformity measure (NU):

0<NU<1 (ground-truth image not 0<NU<1 (ground-truth image not required)required)

Where Where PP and T are the numbers of pore and total and T are the numbers of pore and total number of pixels in the segmented image, and number of pixels in the segmented image, and are the variance of grey-scale values in the pore space are the variance of grey-scale values in the pore space and total variance in the simulated grayscale image. and total variance in the simulated grayscale image.

2P

2

2

P

T

PNU

2

Whether NU can be used as a criterion for

soil ?

How good is NU for soilHow good is NU for soil??

Pore morphological characteristics:Pore morphological characteristics:

PorosityPorosity Number of connected poresNumber of connected pores Number of pore boundary pixelsNumber of pore boundary pixels Number of pore skeleton pixelsNumber of pore skeleton pixels

Results (Low porosity)Results (Low porosity)

Ground truth image IK Entropy Iterative Otsu

Distinct segmentation error

Results (Medium Results (Medium porosity)porosity)

Ground truth image IK Entropy Iterative Otsu

Results (High porosity)Results (High porosity)Ground truth image IK Entropy Iterative Otsu

Results (High+flow Results (High+flow pattern)pattern)

Ground truth image IK Entropy Iterative Otsu

Comparisons of segmentation Comparisons of segmentation methods using ME and NUmethods using ME and NU

Overall ranking by ME : IK > Entropy > Iterative > Otsu

Overall ranking by NU : IK > Otsu > Iterative > Entropy

ME

0. 00

0. 01

0. 02

0. 03

0. 04

0. 05

0. 06

0. 07

0. 08

IK Iter

Otsu

Entropy

NU

0. 00

0. 02

0. 04

0. 06

0. 08

0. 10

0. 12

Entropy

IK Otsu

Iter

Indicator Kriging is the

best!

Indicator Kriging is the

best!

How good is NU for How good is NU for preserving pore preserving pore characteristicscharacteristics??

* Relative error = ( the pore characteristic value from the segmented image - * Relative error = ( the pore characteristic value from the segmented image - the pore characteristic ground-truth value)/ the ground-truth valuethe pore characteristic ground-truth value)/ the ground-truth value

0

20

40

60

80

100

Porosi ty Poreboundarypi xel s

Connectedpores

Poreskel etonpi xel s

Rel

ativ

e E

rror

, %

NU based Best accuracy could be achieved

SummarySummary

Soil aggregate CMT images were Soil aggregate CMT images were generated from the pore/solid binary generated from the pore/solid binary image by simulating partial volume image by simulating partial volume effect, different solid material and effect, different solid material and background noise. background noise.

No single method preserved pore No single method preserved pore characteristics in all cases. However, characteristics in all cases. However, Indicator KrigingIndicator Kriging method yielded method yielded segmented images most similar to the segmented images most similar to the ground-truth images in the majority of ground-truth images in the majority of cases studied. cases studied.

SummarySummary

We recommend using NU as a We recommend using NU as a criterion for choosing best criterion for choosing best segmentation approaches.segmentation approaches.

Segmentation assessment using NU Segmentation assessment using NU provides acceptable representation provides acceptable representation of pore characteristics in the of pore characteristics in the segmented images. segmented images.

USDA-CSREES National Research USDA-CSREES National Research Initiative: Initiative:

Project 2008-35102-04567Project 2008-35102-04567

NSF LTER Program at Kellogg Biological NSF LTER Program at Kellogg Biological Station and the Michigan Agricultural Station and the Michigan Agricultural Experiment StationExperiment Station

Advanced Photon Source, Argonne National Advanced Photon Source, Argonne National LabLab

AcknowledgementAcknowledgement

Thanks for your Thanks for your attention!attention!

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W. Oh, B. Lindquist. 1999. Image thesholding by indicator kriging. W. Oh, B. Lindquist. 1999. Image thesholding by indicator kriging. IEEE Transactions on Pattern Analysis and Machine Intelligence 21: IEEE Transactions on Pattern Analysis and Machine Intelligence 21: 590-602.590-602.

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Dempster, A.P., Laird, N.M. and Rubin, D.B., 1977. Maximum Dempster, A.P., Laird, N.M. and Rubin, D.B., 1977. Maximum likelihood from in- complete data via the em algorithm. Journal of the likelihood from in- complete data via the em algorithm. Journal of the Royal Statistical Society: Series B, 39(1): 1-38.Royal Statistical Society: Series B, 39(1): 1-38.