Perturbation Method

Notes for discussion

Problems Identified: Locality

Problems Identified: Re-sampling

Note: Warp fields aggregation will resolve this issue

Problems Identified: Diffeomorphism

Diffeomorphism breaks with multi knot-point splines

Required Perturbation Properties: #1

Range of scales

• Images are subjected to warps of varying intensity
• Perturbation framework to allow intensity (magnitude) to increase by a fixed amount
• Flexible in terms of the scales supported or else obscenely large deformations cannot be investigated.
• To investigate: at which point does the amount of perturbation become difficult to detect and quantify?

The effect of small warps

Required Perturbation Properties: #2

Diffeomorphism

• No folding and tearing

Required Perturbation Properties: #3

Large number of perturbation 'sources'

• To make the effects of perturbation less local and more global
• Large number of random processes, e.g. warps
• Spread around the image boundaries

Required Perturbation Properties: #4

No pixel condensation at images edges and corners

• 'Stuffing' of pixels
• Tends to happen when there is not sufficient freedom for pixels to be moved outside the image boundaries

Required Perturbation Properties: #5

Stochastic

• Perturbation needs to have a stochastic nature
• Points needs to be displaced by a random unit
• Displacement drawn from a normal distribution

Required Perturbation Properties: #6

Predictable

• For any given point, the distribution of its displacements needs to be well-understood

Required Perturbation Properties: #7

Similar distributions across the entire image

• Displacements affect all parts of the image similarly
• May be difficult to assure

Required Perturbation Properties: #8

No re-sampling error

• Images are warped (transformed), interpolated and re-sampled
• Loss of detail, visible in the form of blurring
• Good perturbation will have small errors
• Errors add noise to the final results

Alternative Approach

• Add buffers to images
• Apply smaller localised warps
• Single-point CPS