Progress Report

June 14th, 2005

Overview

• Perturbation method was established
• Data, labels and code were obtained
• Experimental plan
• Base text to accommodate the results of large experiments

Pending Experiments: Planning

• Experiments Planned (PDF)
• Quite detailed, but needs revising and perhaps expansion

Pending Experiments: Text

• Text and Figures (PDF)
• Both perspectives on the evaluation method are described, namely:
  • AAM evaluation
  • NRR assessment

Perturbation Framework: Foreword

• Implementing a way of visualising pixel displacements
• Running a series of random perturbations
• Aim is to see the distribution of the displacements
• Whiter shades indicating higher level of displacement

Visual Illustration #1

Grid is warped using the old implementation of perturbation

Visual Illustration #2

Old implementation: analysis of the deformations

Visual Illustration #3

Old implementation: averaging over several different perturbations to reveal locality of the warps. This behaviour is otherwise disguised.

Perturbation Framework: Aims and Further Details

• Attempting several different perturbations and calculating the mean displacements
• Aiming to have uniform colours in the image (implying a similar distribution)
• Not necessarily as uniform in the margins (buffer)
• Buffers in this case are 30 pixels wide

Derivation of Displacement Maps #1

Deviation from a smooth surface in x

Derivation of Displacement Maps #2

Deviation from a smooth surface in y

Derivation of Displacement Maps #3

Image displacements in x

Derivation of Displacement Maps #4

Image displacements in y

Derivation of Displacement Maps #5

Image displacements in both x and y (Pythagoras Theorem)

Improving the Perturbation Method

• By increasing:
  • size of the margins
  • the number of knot-points
  • the number of the perturbed sets (repeating the experiments with different random seeds)
• Can get valid statistics and talk about mean displacements that are uniform

Improving the Perturbation Method - Ctd.

• More uniform distributions mean that less random perturbations need to be generated for statistics
• As evaluation is very time-consuming, it is important that each perturbation affects wide regions of the image

Progressively Improving Perturbation #1

Perturbation of grid with multi-point clamped-plate splines and a large surrounding buffer

Progressively Improving Perturbation #2

Displacements map - brighter colours indicate greater spatial displacements

Progressively Improving Perturbation #3

25 knot-points, large buffer size

Progressively Improving Perturbation #4

25 knot-points, large buffer size - corresponding displacements

Evaluating Perturbation Quality

• Need for consistent perturbation
• Compute average and maximum displacement in perturbed images
• Expect values to be near the mean (small Sigma for the distribution)

Displacements Analysis

Larger Evaluation of Perturbation

• 81 Knot-points
• Added margins (100 pixels wide)
• First 3 random compositions of warps
• Affecting all image regions quite uniformly

Visual Example - Increasing Number of Knot-Points

81 knot-points, large buffer size

Visual Example - Ctd.

81 knot-points, large buffer size - corresponding displacements

Visual Example - Averaging over Repeated Perturbation Attempts

81 knot-points, large buffer size - average over 10 different experiments with different random seeds

Visual Example - Ctd.

81 knot-points, 10 experiments - corresponding displacements

Visual Example - Investigating Quality

81 knot-points, large buffer size

Visual Example - Ctd.

81 knot-points, large buffer size - corresponding displacements

Displacements Analysis

Seeing how maximum and average displacements vary as the magnitude of warps is increased

Displacements Analysis - Explanation

• Let us look at displacements against the warp magnitude factor
• There is a non-linear increase in terms of:
  • the mean displacement
  • the maximal displacement
• The ratio is unimportant, but it demonstrates a good relationship between the two values
• Maximal displacement increases linearly(ish) as function of the average and vice versa

Brain Warping #1

An example of a brain warp using the new framework with 81 knot-points and freedom near the image margins

Brain Warping #2

An example of a brain warp - corresponding warp magnitudes

Brain Warping #3

An example of radical warps

Brain Warping #4

An example of radical warps - corresponding warp magnitudes

Brain Warping #5

An example of the point where perturbation clearly breaks

Brain Warping #6

An example of the point where perturbation clearly breaks - corresponding warp magnitudes

Current Work - Possibilities

• Running some evaluations for average_displacement = 0..5 pixels
• Need to register the data better, going to the finer levels
• Repeat the experiments 10 times with different random perturbations
• Bill to carry out similar evaluation

Summary

• There have been 3 main points of progress:
  • planning experiments
  • establishing a reliable perturbation framework
  • better understanding (and quantification) of the framework

Present and Future

• Run large experiments with repetitions
• Obtain a new, broader benchmark involving model-based NRR evaluation and overlap measures
• Possibly modify and re-use experiments from the MICCAI submission