Summary

We have designed algorithms for a variety of image registration tasks (

Introduction

Registration refers to the process of bringing a source image (or volume) into correspondence with a reference one. There are various forms of registration that are needed for biomedical imaging; they differ in the type of transformation used ( e . g ., rigid body vs . elastic) and the criterion that is optimized ( e . g ., least squares vs . mutual information). The applications are numerous: noise reduction by correlation-averaging of high-resolution electron micrographs; 3D reconstruction from histological sections; motion compensation in MRI; multimodal imaging of the brain; creation of a mosaic of overlapping small image tiles. Registration is also becoming increasingly important in digital radiology, where it is of interest to compare images from the same patient acquired at different times ( e . g ., before, and after treatment).

Main Contribution

Over the years, we have designed a variety of image registration algorithms:

• Intramodal, rigid-body or affine: this basic algorithm is best suited for precise ( e . g ., sub-pixel) motion compensation.
• Intermodal, rigid-body or affine: this method uses "mutual information" and is designed to align images of the same patient obtained from different modalities ( e . g ., MRI, CT, PET).
• 2D-to-3D, rigid body: this method estimates the 3D pose of an object by matching a set of 2D projections (radiographs) to a reference 3D volume.
• Intramodal, elastic: the source image is geometrically transformed to best match the reference. The free-form deformation is represented in a B-spline basis.
• Intramodal, mosaicking: given a collection of partially overlapping tiles, we propose an efficient strategy to select which pairs to register in order to create a mosaic.

All approaches are parametric in the sense that the geometrical transformation is represented by a small number of parameters ( e . g ., translation vector and Euler angles for a rigid-body transformation, or a set of control points [or B-spline coefficients] for a free-form deformation). In all cases, we use a multiresolution optimization strategy that is particularly efficient with respect to both computation time and robustness. The clever use of spline functions result in precise registration; they play a role in the continuous representation of images, the Parzen-based estimation of joint histograms, and the parametrization of free-form deformations.

These methods require the development of special-purpose optimization algorithms that are capable of super-linear convergence when sufficiently close to the optimum. This is essential if one wants to take full advantage of a coarse-to-fine iteration strategy in which the current solution is propagated to the next finer scale.

We have also investigated the impact of the criterion that is used to drive the registration. We have proposed vector-spline regularization to combine an image-driven criterion with a landmark-driven one; the novelty of this contribution is that the resulting regularization fully takes into account the vectorial nature of the deformation, including cross terms. In the context of mutual information, we have proposed that the criterion be computed out of discrete data samples that follow a Halton distribution; when computed this way, mutual information exhibits a much lesser tendency to align the transformation with the grid of pixels than with methods based on regular sampling.