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.

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.

Image registration by model criteria

ISBE

2004-10-18T04:54:12