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Center For Applied and Computational Mathematics

Biomedical Image Registration

CT scan

Faculty: Nate Cahill

Summary:

Successfully aligning images from a single modality or from multiple modalities enables subsequent processing, analysis, and/or visualization that can aid in the screening, diagnosis, prognosis, treatment, and monitoring of disease. In the past two decades, a vast amount of research has been performed to develop various models and computational techniques for image registration across a wide spectrum of applications. Nonrigid image registration has received much attention in the medical imaging and computer vision research communities, because it enables a wide variety of applications. Feature tracking, segmentation, classification, temporal image differencing, tumour growth estimation, and pharmacokinetic modeling are examples of the many tasks that are enhanced by the use of aligned imagery.

Measures of Mutual Information for Multimodal Image Registration

Summary:

CT scan

Mutual information (MI) was introduced for use in multimodal image registration over a decade ago. The MI between two images is based on their marginal and joint/conditional entropies. The most common versions of entropy used to compute MI are the Shannon and differential entropies; however, many other definitions of entropy have been proposed as competitors. We show how to construct normalized versions of MI using any of these definitions of entropy. The resulting similarity measures are analogous to normalized mutual information (NMI), entropy correlation coefficient (ECC), and symmetric uncertainty (SU), which have all been shown to be superior to MI in a variety of situations. We use publicly available CT, PET, and MR brain images with known ground truth transformations to evaluate the performance of the normalized measures for rigid multimodal registration. Results show that for a number of different definitions of entropy, the proposed normalized versions of mutual information provide a statistically significant improvement in target registration error (TRE) over the non-normalized versions.

Publications:

  1. Normalized Measures of Mutual Information with General Definitions of Entropy for Multimodal Image Registration, N.D. Cahill, Proc. International Workshop on Biomedical Image Registration, LNCS 6204, pp. 258-268, July 2010.

Accounting for Changing Overlap in Variational Image Registration

Summary:

Any similarity measure used for image registration depends in some way on the region describing the overlap between the floating and reference images. In variational registration, where the Gateaux derivative of the similarity measure drives the registration, most literature implicitly assumes that the region remains constant. This assumption is valid if homogeneous Dirichlet or sliding boundary conditions are chosen for the displacement field; however, it is invalid if any other type of boundary conditions are chosen, or if the similarity measure is computed over some masked portion of the overlap region. We illustrate how these more general situations of different boundary conditions and/or masked regions can be accommodated in variational registration by explicitly accounting for the varying region in the Gateaux derivative of the similarity measure.

Publications:

  1. Accounting for Changing Overlap in Variational Image Registration, Cahill, N.D., J.A. Noble and D.J. Hawkes, Proc. International Symposium on Biomedical Imaging, pp. 384-387, April 2010.

A Demons Algorithm for Image Registration with Locally Adaptive Regularization

Summary:

Thirion's Demons is a popular algorithm for nonrigid image registration because of its linear computational complexity and ease of implementation. It approximately solves the diffusion registration problem by successively estimating force vectors that drive the deformation toward alignment and smoothing the force vectors by Gaussian convolution. We show how the Demons algorithm can be generalized to allow image-driven locally adaptive regularization in a manner that preserves both the linear complexity and ease of implementation of the original Demons algorithm. We show that the proposed algorithm exhibits lower target registration error and requires less computational effort than the original Demons algorithm on the registration of serial chest CT scans of patients with lung nodules.

Publications:

  1. A Demons Algorithm for Image Registration with Locally Adaptive Regularization, Cahill, N.D., J.A. Noble and D.J. Hawkes, Proc. Medical Image Computing and Computer Assisted Intervention, LNCS 5761, pp. 574-581, September 2009.

Incorporating Prior Knowledge on Class Probabilities into Intermodality Image Registration

Summary:

We present a methodology for incorporating prior knowledge on class probabilities into the registration process. By using knowledge from the imaging modality, pre-segmentations, and/or probabilistic atlases, we construct vectors of class probabilities for each image voxel. By defining new image similarity measures for distribution-valued images, we show how the class probability images can be nonrigidly registered in a variational framework. An experiment on nonrigid registration of MR and CT full-body scans illustrates that the proposed technique outperforms standard mutual information (MI) and normalized mutual information (NMI) based registration techniques when measured in terms of target registration error (TRE) of manually labeled fiducials.

Publications:

  1. Incorporating Prior Knowledge on Class Probabilities into Intermodality Image Registration, Hofmann, M., B. Scholkopf, I. Bezrukov and N.D. Cahill, Proc. MICCAI Workshop on Probabilistic Methods for Medical Image Analysis, pp. 220-231, September 2009.