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

[NOTE: GIF animations omitted]
[NOTE: Click here for a version with animations]

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
• Transforming entire set instead
• Solution is unique, not dependent on reference

Experiments: A Different Approach

• Commonly a reference is chosen
  
       
• Images transformed to fit the reference
• Transforming entire set instead
• Solution is unique, not dependent on reference

Experiments: A Different Approach

• Commonly a reference is chosen
• Images transformed to fit the reference
• Transforming entire set instead
  
      
• Solution is unique, not dependent on reference

Experiments: A Different Approach

• Commonly a reference is chosen
• Images transformed to fit the reference
• Transforming entire set instead
  
      
• 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