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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.
Computational Radiology Laboratory. Slide 4
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
Computational Radiology Laboratory. Slide 5
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
Computational Radiology Laboratory. Slide 6
Existent segmentation data
• Manual segmentation performed by 4 independent experts
• low grade glioma
Expert 1 Expert 2 Expert 3 Expert 4
Original Image
Computational Radiology Laboratory. Slide 7
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
Computational Radiology Laboratory. Slide 8
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.
Computational Radiology Laboratory. Slide 9
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.
Computational Radiology Laboratory. Slide 11
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.
Computational Radiology Laboratory. Slide 12
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.
Computational Radiology Laboratory. Slide 13
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
Computational Radiology Laboratory. Slide 14
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
Computational Radiology Laboratory. Slide 15
Validation of a new algorithm
4 manual segmentations
1 automatic segmentation STAPLE
Output of a new segmentation algorithm
Performance assessment
+
Ground truth
Computational Radiology Laboratory. Slide 16
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.
Computational Radiology Laboratory. Slide 17
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
Computational Radiology Laboratory. Slide 18
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 )(
Computational Radiology Laboratory. Slide 19
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
Computational Radiology Laboratory. Slide 20
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
Computational Radiology Laboratory. Slide 21
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
Computational Radiology Laboratory. Slide 22
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.
Computational Radiology Laboratory. Slide 23
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