mage registration by model criteria

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

Overview

• Non-rigid registration (NRR) • Registration and models• Experiments

– Models as a similarity measure – Toward automatic appearance model construction

• Results• Conclusions

Non-rigid Image Registration

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

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.

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.

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.

n

ii

1

)log(

ni1

n

ii

1

)(

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.

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.

Results of Registration

Before registration

After registration Objective function

• Result approaches the solution defined by the model.

Resulting Models

• The combined model captures variability.• Decomposes into 3 dimensions of variation.

Before registration At correspondence After registration

A Subset Approach

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

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.