Progress Report

August 2nd, 2005

Progress Overview

• Further investigation of bending energy
• Experimentation with warps, knot-points, etc.
• Inspection of the number of modes accounted for in evaluation
• Perturbation of images and labels
• Initial analysis of perturbed datasets:
  • Numerical analysis
  • Visual appraisal

Synthetic Images, Modes and Sensitivity

• The number of modes (of an AM) used in evaluation affects sensitivity
• The graph in the next slide demonstrates this effect
• Error bars are not yet included
• Most mysterious is the curve which corresponds to 5 modes
• Typically, more modes lead to higher (better) sensitivity

Sensitivity and Modes

Sensitivity in evaluation for different number of modes

Bending Energy with Error Bars

• The standard deviation of mean bending energy is now incorporated
• Despite a MATLAB plotting bug, one can still spot the top of all error bars
• The error bars are very large despite the random nature and the many well-spread knot-points
• These error are expected to be unsteady indeed
• Two very close knot-points can significantly raise bending energy (a localised effect)

Bending Energy with Error Bars

Bending energy as function of number of random knot-points

Perturbation Framework

• Analysing images which have been subjected to warps
• Applying warps which are composed of a different number of knot-points
• Small deformations are merely visible to the eye
• With slight zooming, differences appear more clearly to a human assessor
• Difference images have been considered for display
• Ultimately, difference images were said to be unnecessary

Number of Knot-Points: The Selection

• Some example brains are shown in the next slide
• Composition of warped brain images, each with a varying number of knot-points
• More knot-points increase the chance of nasty bends
• Too few knot-points are not sufficient for greater overall (well-distributed) variation

Knot-Points Selection Visually

Click to enlarge

Choosing Number of Knot-Points

• 25 was the number of choice as it is "not too crinkly"
• On efficiency:
  • Generation of such warps is not a computationally expensive task
  • Warp generation complexity does not increase linearly when measured against number of knot-point
  • The relation between the number of knot-points and time required appears quadratic

Investigating 25 Knot-Point Transformations

• Use of some more specific figures
• These figures confirm that 25 knot-points was an acceptable choice
• Generation of about a dozen differerent perturbations to gain confidence
• Most values appear rather stable, but bending energy varies wildly
• Brains appear to be alterred similarly (in terms of deformation extent)

25 Knot-Points: A Survey

Click to enlarge

A Few Clarifications

• Older set (May/June) of registered images is used in the above experiments
• All investigations involved this old registration, which is somewhat questionable
• Due to delays in processing new labels along with the new images
• Final dataset, which exploits the most powerful algorithms, is now available
• Quality should not be much worse than the set currently available (in term of overlap measures)
• It was said that the new algorithm (warping to a reference) is not significantly better in practical terms

Image and Label Perturbation

• 20 different values of mean pixel displacement were chosen
• Only about 10 will be used in practice
• Use of ~8 points with denser distribution at the start
• For example, mean_pixel_displacement = 0, 0.01, 0.05, 0.2, 0.5, 1, 2, 4
• It will make it easier to 'stuff' point in the graph, if/when necessary

Image and Label Perturbation - Ctd.

• With the new set of images, displacement was increases by a constant plus a fixed increase at each stage
• As an example, consider the series warp_intensity = 10, 20, 40, 70, 110 where the numbers are be divided by thousands to account for mean pixel displacement
• Mean pixel displacement is not learned or derived from expectation
• Displacement is estimated by running many repeated experiments where the displacement gets recorded