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Computational Radiology Laboratory Harvard Medical School www.crl.med.harvard.edu
Children’s Hospital Department of Radiology Boston Massachusetts
Evaluation of Image Segmentation
Simon K. Warfield, Ph.D. Associate Professor of Radiology Harvard Medical School
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ComputationalRadiologyLaboratory. Slide 2
Segmentation • Segmentation
– Identification of structure in images. – Many different algorithms and a wide range
of principles upon which they are based. • Segmentation is used for:
– Quantitative image analysis – Image guided therapy – Visualization
• Evaluation : How to know when we have a good segmentation ?
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ComputationalRadiologyLaboratory. Slide 3
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.
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ComputationalRadiologyLaboratory. Slide 4
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.
MRI of brain phantom from Styner et al. IEEE TMI 2000
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ComputationalRadiologyLaboratory. Slide 5
Comparison To Higher Resolution
MRI Photograph MRI
Provided by Peter Ratiu and Florin Talos.
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ComputationalRadiologyLaboratory. Slide 6
Comparison To Higher Resolution
Photograph MRI Photograph Microscopy
Provided by Peter Ratiu and Florin Talos.
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ComputationalRadiologyLaboratory. Slide 7
Comparison to Autopsy Data • Neonate gyrification index
– Ratio of length of cortical boundary to length of smooth contour enclosing brain surface
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ComputationalRadiologyLaboratory. Slide 8
Staging
Stage 3 Stage 5
Stage 4 Stage 6
Stage 3: at 28 w GA shallow indentations of inf. frontal and sup. Temp. gyrus (1 infant at 30.6 w GA, normal range: 28.6 ± 0.5 w GA)
Stage 4: at 30 w GA 2 indentations divide front. lobe into 3 areas, sup. temp.gyrus clearly detectable (3 infants, 30.6 w GA ± 0.4 w, normal range: 29.9 ± 0.3 w GA)
Stage 5: at 32 w GA frontal lobe clearly divided into three parts: sup., middle and inf. Frontal gyrus (4 infants, 32.1 w GA ± 0.7 w, normal range: 31.6 ± 0.6 w GA)
Stage 6: at 34 w GA temporal lobe clearly divided into 3 parts: sup., middle and inf. temporal gyrus (8 infants, 33.5 w GA ± 0.5 w normal range: 33.8 ± 0.7 w GA)
“Assessment of cortical gyrus and sulcus formation using MR images in normal fetuses”, Abe S. et al., Prenatal Diagn 2003
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ComputationalRadiologyLaboratory. Slide 9
Neonate GI: MRI Vs Autopsy
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ComputationalRadiologyLaboratory. Slide 10
GI Increase Is Proportional to Change in Age.
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ComputationalRadiologyLaboratory. Slide 11
GI Versus Qualitative Staging
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ComputationalRadiologyLaboratory. Slide 12
Neonate Gyrification
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ComputationalRadiologyLaboratory. Slide 13
Validation of Image Segmentation
• STAPLE (Simultaneous Truth and Performance Level Estimation): – An algorithm for estimating performance
and ground truth from a collection of independent segmentations.
– Warfield, Zou, Wells, IEEE TMI 2004. – Warfield, Zou, Wells, PTRSA 2008. – Commowick and Warfield, IEEE TMI 2010.
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ComputationalRadiologyLaboratory. Slide 14
Validation of Image Segmentation • Comparison to expert performance; to other
algorithms. • Why compare to experts ?
– Experts are currently doing the segmentation tasks that we seek algorithms for:
• Surgical planning. • Neuroscience research. • Response to therapy assessment.
• What is the appropriate measure for such comparisons ?
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ComputationalRadiologyLaboratory. Slide 15
Measures of Expert Performance • Repeated measures of volume
– Intra-class correlation coefficient • Spatial overlap
– Jaccard: Area of intersection over union. – Dice: increased weight of intersection. – Vote counting: majority rule, etc.
• Boundary measures – Hausdorff, 95% Hausdorff.
• Bland-Altman methodology: – Requires a reference standard.
• Measures of correct classification rate: – Sensitivity, specificity ( Pr(D=1|T=1), Pr(D=0|T=0) ) – Positive predictive value and negative predictive value
(posterior probabilities Pr(T=1|D=1), Pr(T=0|D=0) )
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ComputationalRadiologyLaboratory. Slide 16
Measures of Expert Performance • 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.
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ComputationalRadiologyLaboratory. Slide 17
How to judge segmentations of the peripheral zone?
1.5T MR of prostate Peripheral zone and segmentations
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ComputationalRadiologyLaboratory. Slide 18
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):
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ComputationalRadiologyLaboratory. Slide 19
Expectation-Maximization • General procedure for estimation
problems that would be simplified if some missing data was available.
• Key requirements are specification of: – The complete data. – Conditional probability density of the hidden
data given the observed data. • Observable data D • Hidden data T, prob. density • Complete data (D,T)
f (T | D,θ̂)
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ComputationalRadiologyLaboratory. Slide 20
Expectation-Maximization • Solve the incomplete-data log likelihood
maximization problem
• E-step: estimate the conditional expectation of the complete-data log likelihood function.
• M-step: estimate parameter values Q(θ | θ̂) = E ln f (D,T |θ) |D,θ̂
€
argmaxθ Q θ | ˆ θ ( )
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ComputationalRadiologyLaboratory. Slide 21
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 the expectation.
– M-step: Estimate expert performance parameters by comparing D to the current estimate of T.
Q(θ | θ̂) = E ln f (D,T |θ) |D,θ̂
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ComputationalRadiologyLaboratory. Slide 22
STAPLE • Consider binary labels:
– foreground. – background.
• Spatial correlation of the unknown true segmentation can be modelled with a Markov Random Field.
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ComputationalRadiologyLaboratory. Slide 23
To Solve for Expert Parameters:
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ComputationalRadiologyLaboratory. Slide 24
True Segmentation Estimate
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ComputationalRadiologyLaboratory. Slide 25
Expert Performance Estimate Now we seek an expression for the conditional expectation of the complete-data log likelihood function that we can maximize.
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ComputationalRadiologyLaboratory. Slide 26
Expert Performance Estimate Now, consider each expert separately:
Differentiate this with respect to pj,qj and solve for zero.
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ComputationalRadiologyLaboratory. Slide 27
Expert Performance Estimate
p (sensitivity, true positive fraction) : ratio of expert identified class 1 to total class 1 in the image.
q (specificity, true negative fraction) : ratio of expert identified class 0 to total class 0 in the image.
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ComputationalRadiologyLaboratory. Slide 28
Extension to Several Tissue Labels
• Complete data density: • True segmentation Ti for each voxel i
– May be binary
– May be categorical
• Expert j makes segmentation decisions Dij
• Expert performance θs’s characterizes probability of deciding label s’ when true label is s.
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ComputationalRadiologyLaboratory. Slide 29
Probability Estimate of True Labels
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ComputationalRadiologyLaboratory. Slide 30
Expert Performance Estimate Now, consider each expert separately:
Note constraint on sum of parameters. Solve for maximum.
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ComputationalRadiologyLaboratory. Slide 31
Parameter Estimation Noting that
We can formulate the constrained optimization problem:
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ComputationalRadiologyLaboratory. Slide 32
Parameter Estimation Therefore
And noting that
We find that
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ComputationalRadiologyLaboratory. Slide 33
Results: Synthetic Experts • Several experiments with known ground truth
and known performance parameters. • Goal:
– Determine if STAPLE accurately identifies known ground truth.
– Determine if STAPLE accurately determines known expert performance parameters.
– Understand sensitivity of STAPLE with respect to changes in prior hyper-parameters; requirements for number of observations to enable good estimation; convergence characteristics.
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ComputationalRadiologyLaboratory. Slide 34
Synthetic Experts 10 observations of segmentation by expert with p=q=0.99
Four segmentations of ten shown. STAPLE ground truth.
STAPLE p,q estimates: mean p 0.990237 std. dev p 0.000616 mean q 0.990121 std. dev q 0.00071
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ComputationalRadiologyLaboratory. Slide 35
Synthetic Experts 10 segmentations by experts with p=0.95, q=0.90
Four segmentations of ten shown. STAPLE ground truth.
STAPLE p,q estimates: mean p 0.950104 std. dev p 0.001201 mean q 0.900035 std. dev q 0.001685
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ComputationalRadiologyLaboratory. Slide 36
Expert and Student Segmentations
Test image Expert consensus Student 1
Student 2 Student 3
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ComputationalRadiologyLaboratory. Slide 37
Phantom Segmentation
Image Expert Students Voting STAPLE
Image Expert segmentation
Student segmentations
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ComputationalRadiologyLaboratory. Slide 38
Prostate Peripheral Zone
Frequency of selection by experts. STAPLE truth estimate
1 2 3 4 5
pj .879 .991 .937 .918 .895
qj .998 .994 .999 .999 .999
Dice .913 .951 .967 .955 .944
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ComputationalRadiologyLaboratory. Slide 39
A Binary MRF Model for Spatial Homogeneity. Include a prior probability for the neighborhood configuration:
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ComputationalRadiologyLaboratory. Slide 40
MAP Estimation With MRF Prior
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ComputationalRadiologyLaboratory. Slide 41
Synthetic Experts Only three segmentations by different quality experts.
STAPLE ground truth.
STAPLE p,q estimates: p1, q1 0.9505,0.9494 p2, q2 0.9511,0.8987 p3, q3 0.9000,0.8987
p=0.95,q=0.95 p=0.95,q=0.90
p=0.90,q=0.90 With MRF prior
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ComputationalRadiologyLaboratory. Slide 42
Cryoablation of Kidney Tumor Segmentations before training session with radiologist:
Rater frequency. STAPLE with MRF. After training session:
Based on the STAPLE performance assessment, we found the training session created a statistically significant increase in performance of the raters.
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ComputationalRadiologyLaboratory. Slide 43
Newborn MRI Segmentation
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ComputationalRadiologyLaboratory. Slide 44
Newborn MRI Segmentation
Summary of segmentation quality (posterior probability Pr(T=t|D=t) ) for each tissue type for repeated manual segmentations.
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ComputationalRadiologyLaboratory. Slide 45
STAPLE Summary • Key advantages of STAPLE:
– Estimates ``true’’ segmentation. – Assesses expert performance.
• Principled mechanism which enables: – Comparison of different experts. – Comparison of algorithm and experts.
• Extensions for the future: – Can we learn image features that lead to
different levels of expert performance?
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ComputationalRadiologyLaboratory. Slide 46
Acknowledgements
• Neil Weisenfeld. • Andrea Mewes. • Petra Huppi. • Olivier Clatz. • William Wells. • Olivier Commowick.
This study was supported by: Center for the Integration of Medicine and Innovative Technology R01 RR021885, R01 GM074068 and R01 HD046855.
Colleagues contributing to this work: • Arne Hans. • Heidelise Als. • Lianne Woodward. • Frank Duffy. • Arne Hans. • Kelly Zou.