Progress Report

June 28th, 2005

Overview

• Analysing the perturbation
• Implementation of bending energy
• Randomising knot-points placement
• Re-sampling of original, supposedly unwarped images and labels
• Preparation for experiments
• Awaiting re-registered data and validation to verify its quality

The Perturbation Framework: Progress

• Analysis of the perturbation has been augmented
• Reliability of the framework has improved
• Scripts are now in a working state, only awaiting data
• More on the issue of perturbation later on in this report

Random Warps

• The CPS-based warps used to be based on a rectagular grid
• A newly-added option caters for randomising of the warps
• Deciding whether the result is desirable
• The randomisation is not very simple to justify
• Values of the distribution are not very well scattered
• Perhaps this attribute of the distribution is a good one

Random Warps: Example

A random placement of knot-points in perturbation

Warping a Brain Image

The image being warped in some visual examples that follow

Computing Warp Intensity

The intensity (magnitude of displacement) of the warp in 2-D

Computing Warp Direction

• Colour coding chosen to represent directions of displacements
• The figures show that movement is not very complicated to track
• Movement always tends to be from the centre of the warp outwards, as expected
• Serious clean-up of code was involved in this implementation
• Aided the implementation of bending energy (soon to follow)

Computing Warp Direction - Example

81 knot-points, movement direction for the pixels being shifted

Analysing Warps Direction

For this given image and mean pixel displacements, the direction of the displacement at each point will now be shown

Analysing Warps Direction

An improved weighting on the colours to make the directions more prominent

A figure to show the mapping between directions and colours

Analysing Warps Direction

Explanation - Analysing Warps Direction

Yet another combined visualisation:
    displacements direction as colours (middle)
    next to the intensity (displacement magnitude) matrix on the left
    and the warped image on the right

Computing Warp Intensity along One Dimension

The intensity of warps along the X axis

Computing Warp Intensity along One Dimension

The intensity of warps along the Y axis

Computing the Second Derivative

2nd derivative of the intensity of the warps along the X axis

Computing the Second Derivative

2nd derivative of the intensity of the warps along the Y axis

Analysing Warps - Bending Energy

A more comprehensive overview where ending energy 'picks up' the nasty bends at the top-right and top-left corners

The Resampling Issue

Brain before (left) and after (right) a small warp where resampling has a relatively significant effect

Experiments - Revising the Plan

• Resampling of the images at the start to perhaps prevent the small 'dip'
• Also, a better initial registration might prevent the dip
• Experimental scripts set to warp at levels: ~1 (no warp, but resampled), 25, 50, 100, 200, 400, 800
• Around 5 pixels of average displacement at most
• The increase is linear (magnitude n results in roughly twice the displacement of n/2)

Experiments - Ctd.

• Evaluation with shuffle of radius: 0 (absolute difference), 1.5, 2.9, 3.7
• Approximately 7x7 window at most, but shape of mask differs
• 5-10 instantiations to smoothen the curve
• 37 images and labels which gave reasonable results in the past
• Subsets may result in less consistent results, so perhaps some risk is involved
• Moreover, use of entire set to get reasonable results implies robustness

VXL compilation

• Needed for a large number of experiments
• Problems with space or integrity of minimal builds
• Compilation efforts conceded yet again, for the third time

Initial Registration

• IBIM set of 37 brains (with labels) registered down to the finer levels
• Registration needs to be done by Vlad or Tim
• Everything set up including analysis of displacements direction and bending energy
• Need to apply it all to the data and carry out a comprehensive evaluation
• Possibly choosing subset due to some lower-quality images

Miscellany

• contacted authors of the Euclidean distance paper
• Liwei (first author) has not considered shuffle tramsform yet
• The paper might be of interest when wishing to compare more powerful or faster image distance measures

Overlap Measures in Registration

• Test registered set of images and labels first
• Check overlap to confirm registration (in terms of overlap) has improved
• KCL might pursue a submission without our involvement at first
• We can implement our own MI-based algorithms to evaluate ground truth using labels
• Open Source projects might provide the tools for this very generic problem

Overlap Measures in Registration - Ctd.

• Enquiry/advice on the use of labels for registration that is perfect in terms of overlap
  • have they considered using the labels to drive registration yet?
  • is there a way by which we can start with a good overlap?
  • if so, can we also have fairly decent similarity among the images?

28/6/2005 Afternoon Update

• Bill to implement the label measures to drive the registration
• No implementation yet
• Will take a bit of thought to implement properly
• Overlap measures-based registration accepted for MICCAI
• Not know whether as an oral or a poster

Summary

• Perturbation framework is ready
  • Several improvements made, e.g. re-sampling at the start
  • Scripts will make this job far less effort-consuming
• Tools to analyse the registration degradation
  • Warp directions
  • Bending energy

Present and Future

• Complete Experiments
• Compare with ground truth results
• Use feedback from previews reviews to target weaknesses, method validation in particular
• ISBI/ECCV/Journal paper incorporating the essence of our method