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 Measuring Distance - Shuffle Distance  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

Visual Comparison 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