mage registration by model criteria

1
mage registration by model criteria

• R. S. Schestowitz, C. J. Twining,
• T. F. Cootes and C. J. Taylor

2
Overview

• Non-rigid registration (NRR)
• Registration and models
• Experiments
• Models as a similarity measure
• Toward automatic appearance model construction
• Results
• Conclusions

3
Non-rigid Image Registration

• Results in overlap of analogous structures.
• Transforming (warping) images.
• Evaluation using similarity measures.

4
NRR - Problems

• Results are arbitrary (not unique).
• Objective function defines goodness of a
  solution.
• Many sets of warps provide equally good
  solutions.
• The search method chosen affects the results.
• Suffers from limitations in certain cases
  
• Inter-subject registration with structural
  difference.
• Registration of sets of images.

5
Registration and Models

• Models of shape and appearance capture variation.
• NRR closely-related to building combined models.
• Given a registered image set
• Correspondences are known.
• A combined model can be built.
• Method for finding unique dense correspondence
• Find set of warps that lead to best model.
• Best model defined by Minimum Description Length.
• MDL approach developed for shapes.
• Can be extended for combined models.

6
Model Complexity

• We approximate MDL to gain speed.
• Infer from covariance matrix of model.
• We obtain .
• This approximates the determinant
  .
• avoids multiplication by 0.
• are the n Eigen-values of the
  covariance matrix whose magnitude is greatest.
• Log simplifies calculation.

7
Experiments - Data

• To demonstrate feasibility, we registered 1-D
  data.
• No difference in principle between 1- 2-, and
  3-D.
• We Investigated bumps (half-ellipses) that vary
  in
• Horizontal orientation
• Width
• Height
• The correct solution is known.
• Validation w.r.t. the correct solution.

8
Experiments - Optimisation

• Optimisation of the model-based objective
  function
• Carried out by applying clamped-plate splines.
• Localised, random warps are applied
• One image is transformed at a time.
• Objective function is optimised w.r.t. warp
  magnitude.

9
Results of Registration

• Before registration
• After registration
  Objective function
• Result approaches the solution defined by the
  model.

10
Resulting Models

• The combined model captures variability.
• Decomposes into 3 dimensions of variation.
• Before registration At
  correspondence After registration

11
A Subset Approach

• By stochastically choosing subsets
• Optimisation becomes more robust.
• Solution is reached more quickly.

12
Conclusions

• Modelling need not be independent of
  registration.
• Registration by models provides unique solutions.
• Correspondence in sets is identified in the
  process.
• Combined models are refined autonomously.
• The process benefits from treating subsets.