# Why Evaluate?

Because certain methods neglect available information

# Overview

• NRR and Models
• Evaluation method
• Validation of the method
• Evaluation of NRR
• Comparison between NRR algorithms
• Summary and conclusions

# Non-Rigid Registration

• Align images using
• spatial transformations
• similarity measures

# Non-Rigid Registration

• Align images using
• spatial transformations
• similarity measures

# Statistical Models

• Take a data set

• Find correspondences in set
• Learn how correspondences vary

# Statistical Models

• Take a data set
• Find correspondences in set

• Learn how correspondences vary

# Statistical Models

• Take a data set
• Find correspondences in set
• Learn how correspondences vary

# Finding Correspondences

• Need for an automatic approach

• Difficulties in 3-D
• Non-rigid registration to align data
• Produce deformation fields/grid

# Finding Correspondences

• Need for an automatic approach
• Difficulties in 3-D
 Where is a corresponding point in the volume? Picture from Johan Montagnat, INRIA

# Finding Correspondences

• Need for an automatic approach
• Difficulties in 3-D
• Non-rigid registration to align data

• Produce deformation fields/grid

# Finding Correspondences

• Need for an automatic approach
• Difficulties in 3-D
• Non-rigid registration to align data
• Produce deformation fields/grid

# Finding Correspondences - ctd.

• Grids of deformation encapsulate variation

• Perform statistical analysis on grids
• Use model of variation for synthesis

# Finding Correspondences - ctd.

• Grids of deformation encapsulate variation
• Perform statistical analysis on grids

• Use model of variation for synthesis

# Finding Correspondences - ctd.

• Grids of deformation encapsulate variation
• Perform statistical analysis on grids
• Use model of variation for synthesis

# Model Construction

 First variation mode Second variation mode

# Non-Rigid Registration «-» Modelling

• Each registration results in a model
• Better registration » better model
• A good model is:
• specific, i.e. instantiates only valid examples
• capable of generalising to new, unseen examples
• Specificity and Generalisation successfully exampled
• Optimal shape models (Davies et al. 2001)

0 to 5 CPS warps perturbing the correct solution.
Shown is the first mode of the model, ±2.5 SD

# Evaluation Method - Models

Model of the registered images and synthesis from the model

# Evaluation Method - Abstraction

A hyperspace representation where 'clouds' of images overlap

# Evaluation Method - Derivations

Calculating Specificity and Generalisation ability

# Measuring Distance

• Distance naturally assumed Euclidean
• Shuffle distance performs better

# Validation of the Method

As correspondences degrade, so does Generalisability (low values are good)

# Validation of the Method

As correspondences degrade, so does Specificity

# Validation of the Method

Investigate measures most sensitive to change

# Validation of the Method

Shuffle distances covering a large region are sensitive to differences

# Validation of the Method

The choice of shuffle distance radius becomes an efficiency vs. performance trade-off

# Evaluation of Registration

• Registration builds models automatically
• Model from group-wise registration presented below

• The evaluation requires no ground truth

# Registration Algorithms - Comparison

Group-wise methods surpass pair-wise regardless of the expressiveness of the model used

# Summary

• Each registration leads to a model
• Models can be evaluated
• Shuffle distance is used in evaluation
• Registration evaluated without ground truth

# Conclusions

• Model construction and NRR are analogous
• NRR can be evaluated using its resulting model
• Models can be evaluated using a sparse distance map
• Shuffle distance is more robust than Euclidean
• Group-wise registration surpasses pair-wise