Nathan D. Cahill

Learning similarity measure for multi-modal 3D image registration

Multi-modal image registration is a challenging problem in medical imaging. The goal is to align anatomically identical structures; however, their appearance in images acquired with different imaging devices, such as CT or MR, may be very different. Registration algorithms generally deform one image, the floating image, such that it matches with a second, the reference image, by maximizing some similarity score between the deformed and the reference image. Instead of using a universal, but a priori fixed similarity criterion such as mutual information, we propose learning a similarity measure in a discriminative manner such that the reference and correctly deformed floating images receive high similarity scores. To this end, we develop an algorithm derived from max-margin structured output learning, and employ the learned similarity measure within a standard rigid registration algorithm. Compared to other approaches, our method adapts to the specific registration problem at hand and exploits correlations between neighboring pixels in the reference and the floating image. Empirical evaluation on CT-MR/PET-MR rigid registration tasks demonstrates that our approach yields robust performance and outperforms the state of the art methods for multi-modal medical image registration.

A Demons Algorithm for Image Registration with Locally Adaptive Regularization

Thirions 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. In this article, 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.

ICA-fNORM: Spatial Normalization of fMRI Data Using Intrinsic Group-ICA Networks

A common pre-processing challenge associated with group level fMRI analysis is spatial registration of multiple subjects to a standard space. Spatial normalization, using a reference image such as the Montreal Neurological Institute brain template, is the most common technique currently in use to achieve spatial congruence across multiple subjects. This method corrects for global shape differences preserving regional asymmetries, but does not account for functional differences. We propose a novel approach to co-register task-based fMRI data using resting state group-ICA networks. We posit that these intrinsic networks (INs) can provide to the spatial normalization process with important information about how each individual’s brain is organized functionally. The algorithm is initiated by the extraction of single subject representations of INs using group level independent component analysis (ICA) on resting state fMRI data. In this proof-of-concept work two of the robust, commonly identified, networks are chosen as functional templates. As an estimation step, the relevant INs are utilized to derive a set of normalization parameters for each subject. Finally, the normalization parameters are applied individually to a different set of fMRI data acquired while the subjects performed an auditory oddball task. These normalization parameters, although derived using rest data, generalize successfully to data obtained with a cognitive paradigm for each subject. The improvement in results is verified using two widely applied fMRI analysis methods: the general linear model and ICA. Resulting activation patterns from each analysis method show significant improvements in terms of detection sensitivity and statistical significance at the group level. The results presented in this article provide initial evidence to show that common functional domains from the resting state brain may be used to improve the group statistics of task-fMRI data.

Normalized measures of mutual information with general definitions of entropy for multimodal image registration

Mutual information (MI) was introduced for use in multimodal image registration over a decade ago [1,2,3,4]. 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. In this article, 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 images1 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.

Demons algorithms for fluid and curvature registration

As the number of clinical applications requiring nonrigid image registration continues to grow, it is important to design registration algorithms that not only build on the best available theory, but also are computationally efficient. Thirions Demons algorithm [1] estimates nonrigid deformations by successively estimating force vectors that drive the deformation toward alignment, and then smoothing the force vectors by convolution with a Gaussian kernel. It essentially approximates a deformation under diffusion regularization [2], and it is a popular choice of algorithm for nonrigid registration because of its linear computational complexity and ease of implementation. In this article, we show how the Demons algorithm can be generalized to handle other common regularizers, yielding O(n) algorithms that employ Gaussian convolution for elastic, fluid, and curvature registration. We compare the speed of the proposed algorithms with algorithms based on Fourier methods [3] for registering serial chest CT studies.

Schroedinger Eigenmaps with nondiagonal potentials for spatial-spectral clustering of hyperspectral imagery

Schroedinger Eigenmaps (SE) has recently emerged as a powerful graph-based technique for semi-supervised manifold learning and recovery. By extending the Laplacian of a graph constructed from hyperspectral imagery to incorporate barrier or cluster potentials, SE enables machine learning techniques that employ expert/labeled information provided at a subset of pixels. In this paper, we show how different types of nondiagonal potentials can be used within the SE framework in a way that allows for the integration of spatial and spectral information in unsupervised manifold learning and recovery. The nondiagonal potentials encode spatial proximity, which when combined with the spectral proximity information in the original graph, yields a framework that is competitive with state-of-the-art spectral/spatial fusion approaches for clustering and subsequent classification of hyperspectral image data.

Revisiting overlap invariance in medical image alignment

In Studholme et al. introduced normalized mutual information (NMI) as an overlap invariant generalization of mutual information (MI). Even though Studholme showed how NMI could be used effectively in multimodal medical image alignment, the overlap invariance was only established empirically on a few simple examples. In this paper, we illustrate a simple example in which NMI fails to be invariant to changes in overlap size, as do other standard similarity measures including MI, cross correlation (CCorr), correlation coefficient (CCoeff), correlation ratio (CR), and entropy correlation coefficient (ECC). We then derive modified forms of all of these similarity measures that are proven to be invariant to changes in overlap size. This is done by making certain assumptions about background statistics. Experiments on multimodal rigid registration of brain images show that 1) most of the modified similarity measures outperform their standard forms, and 2) the modified version of MI exhibits superior performance over any of the other similarity measures for both CT/MR and PET/MR registration.

Spatial Variance in Resting fMRI Networks of Schizophrenia Patients: An Independent Vector Analysis

Spatial variability in resting functional MRI (fMRI) brain networks has not been well studied in schizophrenia, a disease known for both neurodevelopmental and widespread anatomic changes. Motivated by abundant evidence of neuroanatomical variability from previous studies of schizophrenia, we draw upon a relatively new approach called independent vector analysis (IVA) to assess this variability in resting fMRI networks. IVA is a blind-source separation algorithm, which segregates fMRI data into temporally coherent but spatially independent networks and has been shown to be especially good at capturing spatial variability among subjects in the extracted networks. We introduce several new ways to quantify differences in variability of IVA-derived networks between schizophrenia patients (SZs = 82) and healthy controls (HCs = 89). Voxelwise amplitude analyses showed significant group differences in the spatial maps of auditory cortex, the basal ganglia, the sensorimotor network, and visual cortex. Tests for differences (HC-SZ) in the spatial variability maps suggest, that at rest, SZs exhibit more activity within externally focused sensory and integrative network and less activity in the default mode network thought to be related to internal reflection. Additionally, tests for difference of variance between groups further emphasize that SZs exhibit greater network variability. These results, consistent with our prediction of increased spatial variability within SZs, enhance our understanding of the disease and suggest that it is not just the amplitude of connectivity that is different in schizophrenia, but also the consistency in spatial connectivity patterns across subjects.

Semi-Supervised Normalized Cuts for Image Segmentation

Since its introduction as a powerful graph-based method for image segmentation, the Normalized Cuts (NCuts) algorithm has been generalized to incorporate expert knowledge about how certain pixels or regions should be grouped, or how the resulting segmentation should be biased to be correlated with priors. Previous approaches incorporate hard must-link constraints on how certain pixels should be grouped as well as hard cannot-link constraints on how other pixels should be separated into different groups. In this paper, we reformulate NCuts to allow both sets of constraints to be handled in a soft manner, enabling the user to tune the degree to which the constraints are satisfied. An approximate spectral solution to the reformulated problem exists without requiring explicit construction of a large, dense matrix, hence, computation time is comparable to that of unconstrained NCuts. Using synthetic data and real imagery, we show that soft handling of constraints yields better results than unconstrained NCuts and enables more robust clustering and segmentation than is possible when the constraints are strictly enforced.

SLIC superpixels for efficient graph-based dimensionality reduction of hyperspectral imagery

Nonlinear graph-based dimensionality reduction algorithms such as Laplacian Eigenmaps (LE) and Schroedinger Eigenmaps (SE) have been shown to be very effective at yielding low-dimensional representations of hyperspectral image data. However, the steps of graph construction and eigenvector computation required by LE and SE can be prohibitively costly as the number of image pixels grows. In this paper, we propose pre-clustering the hyperspectral image into Simple Linear Iterative Clustering (SLIC) superpixels and then performing LE- or SE-based dimensionality reduction with the superpixels as input. We then investigate how different superpixel size and regularity choices yield trade-offs between improvements in computational efficiency and accuracy of subsequent classification using the low-dimensional representations.