Projects:RegistrationDocumentation:RegEval Anisotropy

Effects of Voxel Anisotropy and Intensity-Inhomogeneity on Image-based 3D Registration

Dominik Meier, William Wells III, Andriy Fedorov, C.F. Westin, Ron Kikinis

Summary / Questions

This is a planned experiment & manuscript for results/models on how voxel-anisotropy and MR bias fields affect automated, intensity-based image registration, mostly in terms of precision and robustness. Given the complexity of interaction between cost function, optimizer & input data, much of the experiments will likely be empirical evidence, but other (theoretical/analytical) exploits would be welcome. Chief questions are:

• Anisotropy
  • at what point does voxel anisotropy seriously affect registration performance?
  • are individual DOF affected in different ways, i.e. how much more sensitive is rotation to this effect than other DOF?
  • what are the remedies & recommendations, e.g. images with voxel anisotropy ratios above X should be resampled or traverse DOF space in different ways (e.g. does isolate/constrain the most sensitive DOF help)?
  • strategies for non-rigid registration
• Intensity-Inhomogeneity
  • does bias field inhomogeneity in MRI images affect the quality of automated registration?
  • What is the relative sensitivity of different cost functions (MI vs. NormCorr)?
  • Is there a level where the bias field begins to compete with image content?
  • Should a bias-field correction be applied beforehand or after? Is bias correction affected by prior registration?
  • what is the effect of "differential bias"? for the purpose of subtraction and/or ratio images, is differential bias correction (Lewis et al. NeuroImage 2004) preferable to correcting each bias individually? Determined as residual in validation images of zero or predefined diff. -> moving out of scope a bit, because it is no longer pure registration but includes change detection via subtraction. On the other hand that is the common application and hence clarity on bias sources is needed. Most common applications for intra-subject intra-modality registration is are change detection, image guidance & image fusion.

Methods

The basic experiment proposed is to take reference images with high-resolution and isotropic voxel size; move them by a known amount, then filter & subsample to simulate anisotropy; and finally register & evaluate residual error. The self-validation format is there because having a ground truth is the easiest way to isolate the effects under study, but roughly any image pair with an acceptable gold-standard alignment is eligible. More detailed analyses of cost function behavior, capture range etc. are also possible.

• Test Data
  • isotropic resolution required, 1mm or small enough to allow subsampling by factors 2-3 and still remain in range of clinically relevant settings
  • organs: brain, kidney, breast,
  • modalities: MRI (incl. DTI, fMRI), CT
  • Brainweb
  • modalities where anisotropy is common AF: use case: anisotropy is common in diagnostic T2w prostate MRI, typical resolution is ~0.5x0.5x3 mm

• Anisotropy Experiment

1. take 1mm iso ref volume and move by known amount
2. filter (1-D avg filter) & subsample both image grids
3. register & evaluate residual error (evaluate RMS distance: distance of ICC points sent through R1*inv(R2)

• • we would like to isolate as best as possible the anisotropy effect from correlates such as overall resolution etc. Hence it seems appropriate to match the two image pairs being compared in voxel volume, e.g. the isotropic reference for a 1x1x3 mm image would be 1.44mm isotropic (3^.333), so that we can argue the two images contain (from a "volumetric" viewpoint) the same amount of information.

• BiasField Experiment:

1. take 1mm iso ref volume and move by known amount
2. apply bias field to both image grids
3. register & evaluate residual error

• Variational Parameters
  • voxel size factors: x 1 , 1.2 , 1.5 , 3 , 5, 10
  • bias field: derive from actual case, then amplify x 1 , 1.2 , 1.5
  • reference motion
  • registration sampling rate
  • to obtain Relevant Reference XForm: take 2 real-life scans of different protocols, e.g. FLAIR and T1, and perform BSpline registration, use that as reference + add additional translation & rotation

• Evaluation
  • registration error as RMS residual
  • cost function
  • ROC?

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Experiment 1: Anisotropy most strongly affects rotation axes perpendicular to the largest voxel dimension

• Rationale: we assume registration is more likely to fail for anisotropic voxels because 1) there is less edge information that is critical in matching accuracy, 2) the optimization landscape is less smooth, increasing the likelihood for the optimizer to get stuck in local minima
• method: for anisotropy ratios of x 1.2 , 1.5 , 3 , 5, 10, we build 2 image pairs each with the same misalignment/pose to be recovered; one image pair is anisotropic, the other isotropic of equivalent volume. Poses include rotations around each axis, with increasing amount until we reach a failure point. The failure point is our metric of interest

Literature

• Bias Correction + Registration (SPIE 2003)
• Evaluation of BSpline Registration Error(TMI 2009)
• Differential Bias Correction (NeuroImage 2004)
• Importance Sampling for Nonrigid Registr (TMI 2009)
• Automated Parameter Selection (TMI 2010)

Timeframe

• body of results by registration retreat in February 2011?
• manuscript submitssion around April 2011?