# Non-Rigid Registration and Automatic Model Building

### Roy Schestowitz

Special thanks to Eric Meyer for creating this presentation CSS and JavaScript

# Overview

• Non-Rigid Registration
• Statistical Models
• Automatic Model Building
• Experiments and Results

# 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

# Experiments: Method

• Transformation using clamped-plate splines
• Similarity measure is model determinant, where
• Model encapsulates entire data set
• Determinant approximates minimum description length
• This approach was shown to work in shape models

# Experiments: Method

• Transformation using clamped-plate splines
• Similarity measure is model determinant, where
• Model encapsulates entire data set
• Determinant approximates minimum description length
• This approach was shown to work in shape models

# Experiments: Method

• Transformation using clamped-plate splines
• Similarity measure is model determinant, where
• Model encapsulates entire data set
• Determinant approximates minimum description length

• This approach was shown to work in shape models

# Experiments: Method

• Transformation using clamped-plate splines
• Similarity measure is model determinant, where
• Model encapsulates entire data set
• Determinant approximates minimum description length
• This approach was shown to work in shape models

Kotcheff and Taylor (1998), Davies (2002)

# Experiments: A Different Approach

• Commonly a reference is chosen

• Images transformed to fit the reference
• Solution is unique, not dependent on reference

# Experiments: A Different Approach

• Commonly a reference is chosen

• Images transformed to fit the reference
• Solution is unique, not dependent on reference

# Experiments: A Different Approach

• Commonly a reference is chosen
• Images transformed to fit the reference

• Solution is unique, not dependent on reference

# Experiments: A Different Approach

• Commonly a reference is chosen
• Images transformed to fit the reference

• Solution is unique, not dependent on reference

# Experiments: Implementation

• Concepts are applied to 1-D data

• Extends to 2-D and 3-D in principle
• Placement of localised warps
• Optimisation over warp magnitude
• Experiments performed under MATLAB

# Experiments: Implementation

• Concepts are applied to 1-D data

• Extends to 2-D and 3-D in principle
• Placement of localised warps
• Optimisation over warp magnitude
• Experiments performed under MATLAB

# Experiments: Implementation

• Concepts are applied to 1-D data
• Extends to 2-D and 3-D in principle
• Placement of localised warps

• Optimisation over warp magnitude
• Experiments performed under MATLAB

# Experiments: Implementation

• Concepts are applied to 1-D data
• Extends to 2-D and 3-D in principle
• Placement of localised warps

• Optimisation over warp magnitude
• Experiments performed under MATLAB

# Experiments: Implementation

• Concepts are applied to 1-D data
• Extends to 2-D and 3-D in principle
• Placement of localised warps
• Optimisation over warp magnitude
• Experiments performed under MATLAB

Project URI: http://schestowitz.com/AART

# Results

• Registration is approached

# Results

• Registration is approached

# Results

• Registration is approached
•  Model construction: correct model model obtained

# Results

• Registration is approached
•  Model construction: correct model model obtained: at start

# Results

• Registration is approached
•  Model construction: correct model model obtained: at end

# Group-wise Registration (VXL)

• Looking at registration in 3-D
• Emphasis on a group-wise approach
• Learning the effects of registration parameters

# Group-wise Registration (VXL)

• Looking at registration in 3-D
• Emphasis on a group-wise approach
• Learning the effects of registration parameters

# Group-wise Registration (VXL)

• Looking at registration in 3-D
• Emphasis on a group-wise approach
• Learning the effects of registration parameters

# Experiments: Group-wise Registration

• Comparing different approaches:
• Pair-wise methods
• Group-wise methods

# Experiments: Group-wise Registration

• Comparing different approaches:
• Pair-wise methods
• Group-wise methods

# Experiments: Group-wise Registration

• Comparing different approaches:
• Pair-wise methods (left)
• Group-wise methods (right)

# Experiments: Group-wise Registration

• Comparing different similarity measures:
• SSD-related measures
• Information-theoretic measures

# Experiments: Group-wise Registration

• Comparing different similarity measures:
• SSD-related measures
• Information-theoretic measures

# Experiments: Group-wise Registration

• Comparing different similarity measures:
• SSD-related measures (left)
• Information-theoretic measures (right)

# Experiments: Group-wise Registration

• Different optimisation methods

# Summary

• Registration can be
• solved for groups of data simultaneously
• posed as model optimisation problem
• Registration benefits from evaluation using models
• Models can be constructed using registration
• Group-wise registration is robust