Run-time correction of MRI Run-time correction of MRI inhomogeneities to inhomogeneities to

enhance warping accuracyenhance warping accuracy

Evan FletcherEvan Fletcher

Approaches to bias correctionApproaches to bias correction

1. 1. Non-template basedNon-template basedAdjust images to improve some quality measure Adjust images to improve some quality measure

(e.g. N3, bfc)(e.g. N3, bfc)Done in the absence of known true valuesDone in the absence of known true values

2. 2. Template basedTemplate basedDo comparisons between like tissue types of Do comparisons between like tissue types of

different images (Fox & Lewis, Colin different images (Fox & Lewis, Colin et al.et al.))With known lack of bias in template, this results in With known lack of bias in template, this results in

more certain correctionmore certain correction

Problems of bias correctionProblems of bias correction

Model 1Model 1

Cannot be sure of “ground truth:”Cannot be sure of “ground truth:”

Must adjust image closer to hypothetical Must adjust image closer to hypothetical qualitiesqualities

Model 2Model 2

Demands known similarity of tissue typesDemands known similarity of tissue types

Benefits to run-time correctionBenefits to run-time correction

Improve images more accurately Improve images more accurately than with non-template based than with non-template based correction modelscorrection models

Improve fidelity and stability of Improve fidelity and stability of Jacobians derived from warpsJacobians derived from warps

Method of run-time correctionMethod of run-time correction

1.1. Directly compare tissue intensities of 2 images Directly compare tissue intensities of 2 images at first stages of warping hierarchyat first stages of warping hierarchy

2.2. Rely on smoothing and warp hierarchy to Rely on smoothing and warp hierarchy to successively approximate matching of like successively approximate matching of like tissuestissues

3.3. Estimate bias correction field as inverse ratio Estimate bias correction field as inverse ratio of intensitiesof intensities

4.4. Apply latest correction field before each warp Apply latest correction field before each warp iterationiteration

Bias FieldsBias Fields

Bias field modelBias field model

Y = B * X + EY = B * X + E X is true voxel valueX is true voxel value Y is measured voxel Y is measured voxel

valuevalue B is local varying B is local varying

multiplicative biasmultiplicative bias E is Gaussian noiseE is Gaussian noise

Slice of sinusoidal bias field

Correction step 1Correction step 1templatetemplate subjectsubject

Sampling cube in template Warped image of sampling cube

Histograms of patchesHistograms of patchesDivide into sub rangesDivide into sub ranges

templatetemplate subjectsubject

Sampling local bias ratioSampling local bias ratio

Voxels in template warped into subject Voxels in template warped into subject Find common sub range with most shared Find common sub range with most shared

voxels voxels

This example Highest sub range has most shared voxels Highest sub range has most shared voxels

(1661)(1661) Ratio of means for this range is 1.32Ratio of means for this range is 1.32 Local bias correction estimate is 1/1.32 = 0.76Local bias correction estimate is 1/1.32 = 0.76

Creating smooth bias correction Creating smooth bias correction fieldsfields

1.1. Sample bias ratios at Sample bias ratios at grid points grid points

2.2. Use TP-Spline Use TP-Spline interpolation for interpolation for smooth correction fieldsmooth correction field

3.3. Apply multiplicatively Apply multiplicatively to subject image to subject image before next warp before next warp iterationiteration

4.4. Unbiased template Unbiased template absoluteabsolute bias bias correctioncorrection

Evolution of bias correction field:Evolution of bias correction field:Successive refinement & sampling of bias Successive refinement & sampling of bias

ratiosratios

24 mm 12 mm

7.2 mm 6mm

Image correction I: Image correction I: Experiment with phantom dataExperiment with phantom data

Use MNI Template Use MNI Template Create unbiased subject Create unbiased subject

by TP-Spline warpingby TP-Spline warping Impose known bias Impose known bias

fields & noise on subjectfields & noise on subject Warps from template to Warps from template to

biased subjectsbiased subjects Use correcting and non-Use correcting and non-

correcting warpscorrecting warps

Subject image MNI Template

Phantom data: Phantom data: bias fieldsbias fields

Impose bias field on Impose bias field on unbiased subject unbiased subject

Multiplicative field of Multiplicative field of magnitude magnitude 20 %20 %

Sinusoidal bias field

Biased image

Phantom data correction:Phantom data correction:measures of improvementmeasures of improvement

With phantom data, make direct With phantom data, make direct comparisons with known unbiased imagecomparisons with known unbiased image

Numerical comparisons use RNumerical comparisons use R22 measure of measure of image closeness and CV values of tissue image closeness and CV values of tissue variabilityvariability

Also make numerical RAlso make numerical R22 comparisons with comparisons with Jacobian images of unbiased warpsJacobian images of unbiased warps

Phantom data correction: Phantom data correction: before (top) & after (bottom)before (top) & after (bottom)

Bias correction field

Bias field to be corrected

Biased image

Corrected image

Phantom data correction:Phantom data correction:Comparison of image histogramsComparison of image histograms

Uncorrected biased image

Corrected biased image

Unbiased image

Phantom data correction:Phantom data correction:Jacobians 1Jacobians 1

Compare Jacobian images of correcting Compare Jacobian images of correcting and non-correcting warpsand non-correcting warps

Use “ground truth” of warps from unbiased Use “ground truth” of warps from unbiased imagesimages

Use numerical measures of accuracyUse numerical measures of accuracy

Phantom data correction:Phantom data correction:Jacobians 2Jacobians 2

ReferenceReference Correcting warpCorrecting warp Non-Non-correcting correcting

Phantom data correction:Phantom data correction:Distance measures to reference JacobianDistance measures to reference Jacobian

20 warps of template to biased images20 warps of template to biased images RR22 measure closeness of Jacobians to warps of measure closeness of Jacobians to warps of

unbiased images (max for Jacobians in practice ≈ 0.88)unbiased images (max for Jacobians in practice ≈ 0.88) Higher RHigher R22 is better! is better! Std dev shows reduced Jacobian variabilityStd dev shows reduced Jacobian variability

Non-correctingNon-correcting CorrectingCorrecting

Mean RMean R22 0.650.65 0.73

Std dev RStd dev R22 0.0390.039 0.018

Phantom data correction:Phantom data correction:Comparison with N3 Comparison with N3

Histograms Jacobian RHistograms Jacobian R22 values valuesNon-Non-Corr Corr WarpWarp

N3 + N3 + NC NC WarpWarp

Corr Corr WarpWarp

0.650.65 0.680.68 0.73

Top: N3 correction Bottom: warp correction

R2 measure of closeness to reference Jacobian is best for correcting warp

Image correction II: Image correction II: experiment with real dataexperiment with real data

Apply correction Apply correction during warping to real during warping to real image with severe image with severe biasbias

Use template derived Use template derived from real study groupfrom real study group

With real data, rely on With real data, rely on visual improvement of visual improvement of image, segmentation image, segmentation and histogramand histogram

Top: Template Bottom: subject

Real data correction:Real data correction:visual comparisonsvisual comparisons

Uncorrected: image & segmentation Warp-corrected

Real data correction:Real data correction:histogramshistograms

Uncorrected imageUncorrected image Corrected Image Corrected Image

SummarySummary

Phantom DataPhantom Data Numerical and visual comparisons with known Numerical and visual comparisons with known

images & Jacobiansimages & Jacobians Correcting warp is better than N3 and non-Correcting warp is better than N3 and non-

correctingcorrecting Jacobian variability decreased in corr. warpsJacobian variability decreased in corr. warpsReal DataReal Data Visual comparison between corrected and Visual comparison between corrected and

uncorrected images and histogramsuncorrected images and histograms Corrected images appear betterCorrected images appear better