Overview

• Motivation
• Assessment methods
  • overlap-based
  • model-based
• Validation experiments
• Results
  • methods validity
  • comparison of methods
• Conclusions

Non-rigid Registration (NRR)

• Concerned with alignment of image sets
• Identifying corresponding structures (e.g. anatomical)
• Alignment established by
  • transforming an image
  • comparing it against another image in the set (pair-wise)
  • comparing it against the remainder of the image set (group-wise)
  • transformation aspires to make images similar
• Competing NRR algorithms produce different results

Motivation for Asssessment

• Different methods for NRR
  • objective function (transformation, similarity measures)
  • optimisation, regularisation
  • multiple pair-wise vs. Group-wise
• Need for objective measures of performance
  • ground-truth deformations
  • overlap measures
  • model-based measures
• Comparison of different measures

The Two Approaches

• Overlap
  • multiple label images
  • registration to standard frame
  • accumulation of overlap fractions
• Model-based
  • NRR implies a combined appearance model
  • good registration  good model

Overlap Measures – Premise

• Existing overlap measures
  • assume binary labels
  • evaluate 1 label pair at a time
  • do not accumulate over multiple images and labels
  • cannot easily be applied to groupwise registration
• But in registration experiments
  • labels may be interpolated (pv) or fuzzy
  • there may be lots of labels
  • there may be lots of image pairs
• We address these problems to obtain figures of merit which summarise large studies.

Binary Overlap Measures

Binary Overlap - Alternate Form

Binary Overlap - Ctd.

Overlap-based Assessment

• Approximation of overlap among brain structures
• Weighting of different anatomical labels:
  • Implicit volume weighting (i.e. large labels contribute more)
  • inverse volume weighting
  • inverse label volume squared
  • label complexity (voxel intensity gradient)

Model-based Assessment Framework

• Take a set of registered images
• Train an appearance model from these images
• Generate images from the model
• Compare each image in the model-generated set against each image in the training (registered) set

Clouds Overlap in Hyperspace

Generalisation and Specificity

• Derive Generalisation and Specificity from distances
• Short distances impy better model, thus better registartion

Shuffle Distance

• Robust alternative for Euclidean distance
  • compare each pixel in one image against a corresponding neibourhood of pixels in another
  • match to most similar pixel in that neibourhood
• Shown below: left: one image, Right: another image, Centre, from left to right: contribution to shuffle distance for neighbourhood of 1 (abs. diff.), 9, 25, and 49 pixels.

Shuffle Distance – Example

Validaton Experiments

• MGH dataset (37 brains)
• Selected 2D slice
• Initial ‘correct’ NRR
• Progressive perturbation of registration
• 10 random instantiations for unbiased results
• Comparison of the two different measures
  • overlap (UCL)
  • model-based (Manchester)

Brain Data

• 37 images with 8 corresponding labels for each
• Images non-rigidly registered using a minimum description length-based algorithm

Perturbation Framework

• Data initially brought into alignment
• Alignment degraded by applying warps to data
• Warps based on composition of biharmonic clamped-plate splines with 25 knot-points

Results – Overlap

• Overlap decreases as function of misregistartion
  • Monotonic response
  • Consistent across different methods of label accumulation

Results – Model-Based

• Models degraded as function of misregistration
  • lower Generalisation and Specificity imply better models
  • shuffle distance supersedes Euclidean distance (proven later)

Results – Comparison

• Methods are closely-correlated
  • overlap-based assessment requires ground truth (labels)
  • model-based approach need not have ground truth
• Need criterion to compare the methods

Sensitivity

• Measure to indicate the ability to detect fine degradations
• Defined as the amount of change in the measure
  • proportional to extent of misregistartion
  • divided by the size of the error (ability to discern changes reliably)

Results – Sensitivities

• Generalisation - least sensitive assessment method
  • large error bars due to small training set (37 images)
• Model Specificity - most sensitive

Conclusions

• Registration can be assessed either with or without ground-turth
• Two assessement approaches are correlated
• Generic approaches: can be used to assess any kind of registration
• Both approaches can detect subtle misregistration
• Overlap of manual labelling is the practical ‘gold standard’
• Specificity is a good surrogate
  • monotonically related
  • no need for ground truth
  • more sensitive

Acknowledgements

• Oscar Camara and his funding source: Modelling, Understanding and Predicting Structural Brain Change (EPSRC GR/S48844/01)
• Integrated Brain Image Modelling (EPSRC GR/S82503/01)
• David Kennedy of the Centre for Morphometric Analysis at MGH: for the 37-image data set used in this work