Generalised Overlap Measures

Overview

• Background and motivation
• Assessment methods
  • overlap-based
  • model-based
• Experiments
  • validation
  • comparison of methods
• Conclusions

Non-rigid Registration (NRR)

• Alignment of image sets
  • dense correspondence
  • alignment of anatomical structures
• Alignment established by
  • image warping
  • comparison with other image(s)
  • maximising similarity
• Competing NRR algorithms produce different results

Motivation for Assessment

• Different methods for NRR
  • representation of warp (including regularisation)
  • similarity measure
  • optimisation
  • pair-wise vs group-wise
• Limitations of current methods of assessment
  • ground-truth deformations
  • binary overlap measures

Two New Approaches

• Generalised overlap
  • multiple labels
  • label interpolation
  • multiple images
• Model-based
  • NRR  combined appearance model
  • good registration  good model

Generalised Overlap

Overlap Measures

• Existing overlap measures
  • assume binary labels
  • evaluate one label at a time
  • cannot easily be applied to groupwise registration
• In practice
  • labels may be interpolated (pv) or fuzzy
  • there may be lots of labels
  • there may be lots of images
• Generalise existing overlap measures

Binary Overlap Measures

• Consider label regions A and B
• Tanimoto/Jacaard overlap
• Dice overlap

Alternate Form

• Binary value at each voxel Ai and Bi

Interpolated Label Images

• Result of applying NRR
• Label values in range [0,1]
• Fuzzy union and intersection

Generalised Overlap

• Fractional overlap
• Accumulated over labels and image pairs

Label Weighting

• Implicit volume weighting
• Equal weighting
• Inverse volume weighting
• Label complexity

Model-Based Assessment

Model-based Framework

• Registered image set  statistical appearance model
• Good registration  good model
  • generalises well to new examples
  • specific to class of images
• Registration quality  Model quality
  • problem transformed to defining model quality
  • ground-truth-free assessment of NRR

Building an Appearance Model

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Training and Synthetic Images

Model Quality

Measuring Inter-Image Distance

• Euclidean
  • simple and cheap
  • sensitive to small misalignments
• Shuffle distance
  • neighbourhood-based pixel differences
  • less sensitive to misalignment

Shuffle Distance

Varying Shuffle Radius

Experimental Evaluation

Experimental Design

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

Brain Data

• Eight labels per image
  • L/R white/grey matter
  • L/R lateral ventricle
  • L/R caudate nucleus

Perturbation Framework

• Alignment degraded by applying warps to data
• Clamped-plate splines (CPS) with 25 knot-points
• Random displacement (r, ) drawn from distribution

Examples of Perturbed Images

Results – Overlap

• Overlap decreases monotonically with misregistration

Results – Model-Based

• Measures increase monotonically with misregistration

Results – Comparison

• All three measures give similar results
  • overlap-based assessment requires ground truth (labels)
  • model-based approach does not need ground truth
• Compare sensitivity of methods
  • ability to detect small changes in registration

Results – Sensitivities

• Specificity most sensitive method

Conclusions

• Both approaches sensitive to subtle misregistration
• Overlap and model-based approaches ‘equivalent’
• Overlap provides ‘gold standard’
• Specificity is a good surrogate
  • monotonically related
  • no need for ground truth
  • more sensitive
  • only applies to groups (but any NRR method)

Acknowledgements

• Oscar Camara
  • Modelling, Understanding and Predicting Structural Brain Change (EPSRC GR/S48844/01)
• IBIM Project
  • Integrated Brain Image Modelling (EPSRC GR/S82503/01)
• David Kennedy
  • Centre for Morphometric Analysis, MGH: images and labels