Computational Radiology Laboratory Harvard Medical School Brigham and Women’s Hospital Children’s Hospital Boston Massachusetts

Computational Radiology LaboratoryHarvard Medical Schoolwww.crl.med.harvard.edu

Brigham and Women’s Hospital Children’s Hospital Boston Massachusetts

A validation framework for brain tumor segmentation

Neculai Archip, Ph.D.

Harvard Medical School

Computational Radiology Laboratory. Slide 2

Outline

• Brain image database;

• Existent segmentation data;

• STAPLE;

• How to validate a new algorithm;

• Performance study.


Motivation of Brain Tumor Segmentation: Augmented Visualization in Image Guided Neurosurgery

• Acquire MRI, DT-MRI, fMRI preoperatively– Plan intervention– Enhance tumor

visualization– Better perceive critical

healthy structures

• Align preoperative data with intra-operative configuration of patient


Brain Image database

• Acquisition information: – 10 SPGR T1

– POST GAD resolution: 256x256x124

– pixel size: 0.9375 x 0.9375 mm

– slice thickness: 1.5 mm

– slice gap: 0.0 mm

– acquisition order: LR

case tumor location slice 1 meningioma left frontal 44 2 meningioma left parasellar 58 3 meningioma right parietal 784 low grade glioma left frontal 35 5 astrocytoma right frontal 92 6 low grade glioma right frontal 81 7 astrocytoma right frontal 92 8 astrocytoma left temporal 39 9 astrocytoma left frontotemporal 31 10 low grade glioma left temporal 35


Existent segmentation data

• Manual segmentation performed by 4 independent experts

• low grade glioma

Expert 1 Expert 2 Expert 3 Expert 4

Original Image


One automatic segmentation algorithm

• Kaus et al. – “Adaptive Template Moderated Brain Tumor Segmentation in MRI”, Radiology. 2001;218:586-591

Segmented images

Registration

Statistical Classification

Template Distance Transforms

Brain atlas

Grey value images

Original tumor image

Tumor segmentation performed by Kaus’

method


Validation of Image Segmentation• Spectrum of accuracy versus realism in

reference standard.• Digital phantoms.

– Ground truth known accurately.– Not so realistic.

• Acquisitions and careful segmentation.– Some uncertainty in ground truth.– More realistic.

• Autopsy/histopathology.– Addresses pathology directly; resolution.

• Clinical data ?– Hard to know ground truth.– Most realistic model.


Validation of Image Segmentation

• Comparison to digital and physical phantoms:– Excellent for testing the anatomy, noise and

artifact which is modeled.– Typically lacks range of normal or

pathological variability encountered in practice.


Validation of Image Segmentation

• Comparison to expert performance; to other algorithms:

• What is the appropriate measure for such comparisons ?

• Our new approach:• Simultaneous estimation of hidden ``ground

truth’’ and expert performance.• Enables comparison between and to experts.• Can be easily applied to clinical data exhibiting

range of normal and pathological variability.


STAPLE

• STAPLE (Simultaneous Truth and Performance Level Estimation):– An algorithm for estimating performance

and ground truth from a collection of independent segmentations.

– Warfield, Zou, Wells MICCAI 2002.– Warfield, Zou, Wells, IEEE TMI 2004.


Estimation Problem

• Complete data density:• Binary ground truth Ti for each voxel i.

• Expert j makes segmentation decisions Dij.

• Expert performance characterized by sensitivity p and specificity q.

– We observe expert decisions D. If we knew ground truth T, we could construct maximum likelihood estimates for each expert’s sensitivity (true positive fraction) and specificity (true negative fraction):

)|( qp,TD,f

)|,(lnmaxargˆ,ˆ qp,TDqpqp,

f


Expectation-Maximization• Since we don’t know ground truth T, treat T as a

random variable, and solve for the expert performance parameters that maximize:

• Parameter values θj=[pj qj]T that maximize the conditional expectation of the log-likelihood function are found by iterating two steps:– E-step: Estimate probability of hidden ground truth T

given a previous estimate of the expert quality parameters, and take expectation.

– M-step: Estimate expert performance parameters by comparing D to the current estimate of T.

ˆ ˆ( | ) ln ( | ) |Q E f

θ θ D,T θ D,θ


Validation of a new algorithm

4 manual segmentations

1 automatic segmentation STAPLE

Output of a new segmentation algorithm

Performance assessment

+

Ground truth


A new algorithm• Spectral clustering algorithms:

– Shi and Malik 2000 • NCUT criterion

– Ng, Jordan and Weiss 2002 • Supervised clustering using k eigenvectors

– Miela and Shi 2002• Supervised clustering – connection with Markov Chains

– Fowlkes, Belongie, Chung, Malik 2004 • Nyström method – spine segmentation from MRI

• Fiedler eigenvector based segmentation:– Archip et al. 2005.

• Related approached used in seriation and the consecutive ones problems.


Segmentation as weighted graph partitioning

Pixels i I = vertices of graph GEdges ij = pixel pairs with Sij > 0

Similarity matrix S = [ Sij ]

Given a partition (A,B) of the vertex set V

rjXiX

X

jXiX

I eotherwise

jFiF

ij es2||)()(||,

2

22||)()(||

2

22

,0

)||()(||

),(

),(

),(

),(),(

VBassoc

BAcut

VAassoc

BAcutBANcut


Optimize NCUT

• an approximation is obtained by solving the

generalized eigenvalue problem

for the second smallest generalized eigenvector.

Dyy

ySDyGMinNcut

t

t

y

)(min)(

DyySD )(


The algorithm• P = D-S • P sparse• Py= λy• Lanczos used for efficiency• λ1, λ2 first 2 eigenvalues

– λ1 =1; use λ2 instead

• y1,y2 first 2 eigenvectors– y2 – Fiedler eigenvector


Use Fiedler eigenvector to segment the image

• Sort Fiedler eigenvector with the permutation

• Apply to the image pixels vector

• The new image vector

• Split into compact blocks s.t. components similarity• Complete segmentation – interactively select the cluster

of interest.

),...,( 21 Nii

),...,( 21 NIII

),...,(21 N

ii III

I


Tumor Segmentation Evaluation

1 2 3 4 KausFiedlerbased

pj 0.867 0.978 0.971 0.908 0.978 0.956

qj 0.999 1.000 0.998 0.999 1.000 0.998

Tumor region Experts STAPLEKaus Fiedler based


Conclusions

• Framework for the validation of brain tumor segmentation: image + software.

• STAPLE public available.

• Image and segmentation data will be made public available.

• Existent data to be added to the image database.


Acknowledgements

• Simon K. Warfield.• Peter M. Black.• Alexandra Golby.• Ferenc A. Jolesz.• Ron Kikinis.• Lawrence Panych.• Kelly H. Zou.• Steve Haker.• Vicente Grau-Colomer.• Olivier Clatz• Herve Delingette

• Herve Delingette• Nicholas Ayache• Martha Shenton.• Clare Tempany.• Carl Winalski.• Michael Kaus.• William M. Wells.• Andrea Mewes.• Heidelise Als.• Petra Huppi.• Terrie Inder.

Contributors to this research:

www.crl.med.harvard.edu

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Computational Radiology Laboratory Harvard Medical School Brigham and Women’s Hospital Children’s Hospital Boston Massachusetts