- Given
*n*images (or volumes) - Obtain the following
- Warps that define correspondence
- Model that faithfully describes the variation

- Several methods exist to solve the former task
- Weak solutions to the latter (e.g. SDM's)

- Registration:
- Introduction of methods for obtaining correspondence
- Comparison of methods
- Proposal of alternatives

- Model building:
- Explanation of the process
- Relation to registration
- Framework for model construction

- Introduction
- Goals
- Flaws, gaps and problems

- What is needed:
- Set of warps for each image (or volume)
- The warps lead to overlap
- Warps can be aggregated to form a single composite grid
- Can use a list of warps to be applied in a sequence

- All warps are expected to have a
*pattern* - This implies a small and controlled distribution

- Warp; then measure similarity
- Warping involves
- Setting up a grid, e.g. equally-spaced grid
- Change (transform) grid
- Resample data to fit deformed grid

- Similarity involves
- Computing a number
- The number decreases/increases as function of similarity

- Cannot guarantee correct structures are aligned
- Infinite number of ways to align data
- Noisy/corrupted data - need robustness

- Approach in
*selection*- Picking image pairs
- Fixed reference
- Changing reference
- Mean/Median
- Handling entire set
- Handling subsets

- Solution depends on selection

- Transformation
*types*- Rigid
- Affine
- Non-rigid

- Transformation
*functions/mechanisms*- B-splines
- Clamped-plate splines
- Cosine-based or bi-linear grid-based

- Any function will do, but needs to be
- (Easily) Invertible
- Quick to compute
- Diffeomorphism

- Measure similarity more analytically, e.g.
- MDL-based
- Model-based

- Compute similarity in different frame of reference
- Interlace data

- Registration can be solved in many ways
- The ground truth is based on the anatomy
- Cannot place infinite number of markers in subject
- Hence registration can only ever approximate
- Problems when structures appear/disappear

- A means of
- Capturing variation in data
- Interpreting data
- Synthesising data

- Models require correspondence to be known
- Both entities involve transformation/deformation
- Models
*deform*to fit/synthesise data - Registration applies
*deformations*to data

- Take data set
- Identify correspondences
- Vectorise
- Apply PCA
- Use the model
- For fitting
- For interpretation
- More...

- Registration treated by different (yet related) methods/strands:
- Carole - Minimum description length
- Myself - Appearance model (similar idea to MDL)
- Tim - All conventional methods and the ones above
- Vlad - Works with Tim
- Kola - Towards building of compartmentalised brain models

- Unifying registration and model construction
- Showing the powers of group-wise registration
- Devising a principled similarity measure
- Discovering faster registration methodologies, e.g.
- Multi-resolution
- Cunning point selection for triangulation
- Localising warps

- Piece-wise affine representation of deformation fields
- In 2-D: triangulation of RoI
- In 3-D: e.g. tetrahedra of volume
- Position of nodes control deformation
- Heavily-based on existing algorithms

- Advantages
- Easy to invert
- Efficiency in moving from frame to frame
- Freedom in placement of nodes in image/volume

- Disadvantages
- Derivatives of mapping are non-continuous
- Triangulation might fold

- Need annotated data
- Larger set size needed for group-wise optimisation
- Reduce load on memory at any given time
- Values for registration parameters are unknown

- Must care to warp to a sensible 'target'
- Reference image is an arbitrary choice
- Group-wise method should 'treat' all images equally
- Group-wise aspires to become a data-driven method
- Registration is dependent on the
*whole*data

- Group-wise versus pair-wise
- Similarity, for example, can be calculated in different frames of reference
- Can warp the reference to fit target
- Or warp target to fit reference

- Also possible to make multiple warps
- Transform one target to fit another target
- Requires 'going through' reference
- Warp is cheaper to compute than its inverse
- Hence 'pull-back' is expensive

- Similarity, for example, can be calculated in different frames of reference

- Registration:
- Warping methods
- Similarity measures
- Group-wise/pair-wise

- Models:
- Require correspondence
- Related to registration

- Use deformation fields for model construction
- Fast transformations are essential
- Test and validate results