Keeping Track of Displacements

• Does the current implementation only trace points of choice?
• Does it give a displacement magnitude range?
• It turns out that Euclidean distance is used
• Distance between the original and warped position is calculated
• Mean, minimum and maximum are derived from a distance matrix
• However, distribution is not uniform
• Other issues: Centre affected more than edges, blurring, etc.

Problems with Current Framework

• More problems observed:
  • Multi-point perturbation (as applied to IBIM data and its evaluation) breaks diffeomorphism
  • This was already demonstrated in experiments last year (registration using model complexity minimisation)
  • More warps lead to higher resampling error
  • How to quantify displacement when many warps are aggregated?
• Some of the issues to be addressed are closely correlated

Current (Alternative) Approach:

• add buffers to the image margins
• Consider use of single-point CPS warps
• Use small warps and apply them to sub-regions, handling one small section of the image at a time
• apply perturbation within a series of windows so that the displacements are more homogeneous (in progress)

Problems Visualised #1

Problems Visualised #2

Problems Visualised #3

Diffeomorphism breaks with multi knot-point splines

Alternative Approach Visualised

How to Quantify Composite Displacements

• Trace points through the sequence of warps
  • might be hard
  • probably the sensible approach to tackling the problem

Alternative for Displacement Quantification

• Colour tracing
  • assign colours to image regions
  • for each pixel, find distance to nearest pixel with the same colour
  • this traces the movement of a given pixel
  • for each pixel this generates a matrix
  • matrix can be visualised as a map of distances
  • from this, one can hope/expect to have uniform distribution of values, having applied enough warps

Issues with Colour Tracing

• Resampling error is problematic
  • blur
  • change in colours
• Discrete number of colours

Issues with Colour Tracing - Ctd.

• Solution: Handle smaller squares (chunks) with colours, where similar colours do not intersect
• Another pitfall: the method does not handle large deformations well
• Yet another issue: image dimensions
  • Need to make some colour image available for different sizes or generate it on the fly
  • It is then treated in conjunction with the real image so that displacements can be learned
  • The same warps are applied to the real and synthetic (colour) image

Issues with Colour Tracing - Ctd.

• Further issues:
  • Efficiency: finding the closest colour means scanning all neighbours for the best (colour match) and closest (READ: nearest) match
  • Subjectivity: because of interpolation, there is a best match/shortest distance trade-off

Pending Experiments: Planning

• Text and experiments in preparation (see PDF)
• Both perspectives on the evaluation method are described
  • AAM evaluation
  • NRR assessment

Experiments Planned

• Part 1: Validation of Evaluation
  • needs reliable (trustworthy) perturbation framework
  • comparing Euclidean, shuffles
  • symmetric (shuffle distance in both directions)
  • plotting sensitivity
  • both brain and face data (indicates that the method has wide-range applicability)

Experiments Planned

• Part 2: Comparison with Overlap measure
  • based on ground-truth
  • needed as further proof (validation)

Experiments Planned

• Part 3: Evaluating registration algorithms
  • pair-wise, group-wise, and others
  • model-building framework can/will be explained separately
  • possibly involve ITK (Imperial College) registration algorithms

Summary and Ways Forward

• Currently perturbation suffers from:
  • localisation problem
  • consistency
  • predictability of displacement
• Need to discuss possible framework/s tomorrow
  • understanding the flaws of existing methods
  • proposing improvements
• More experiments yet to be performed with careful attention