Roy Schestowitz, Bill Crum, Vlad Petrovic, Carole Twining, Tim Cootes, Chris Taylor
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