Deformable image registration (DIR), aiming to find spatial correspondence between images, is one of the most critical problems in the domain of medical image analysis. In this paper, we present a novel, generic, and accurate diffeomorphic image registration framework that utilizes neural ordinary differential equations (NODEs). We model each voxel as a moving particle and consider the set of all voxels in a 3D image as a high-dimensional dynamical system whose trajectory determines the targeted deformation field. Our method leverages deep neural networks for their expressive power in modeling dynamical systems, and simultaneously optimizes for a dynamical system between the image pairs and the corresponding transformation. Our formulation allows various constraints to be imposed along the transformation to maintain desired regularities. Our experiment results show that our method outperforms the benchmarks under various metrics. Additionally, we demonstrate the feasibility to expand our framework to register multiple image sets using a unified form of transformation, which could possibly serve a wider range of applications.

Automatic Non-rigid Histological Image Registration (ANHIR) challenge was organized to compare the performance of image registration algorithms on several kinds of microscopy histology images in a fair and independent manner. We have assembled 8 datasets, containing 355 images with 18 different stains, resulting in 481 image pairs to be registered. Registration accuracy was evaluated using manually placed landmarks. In total, 256 teams registered for the challenge, 10 submitted the results, and 6 participated in the workshop. Here, we present the results of 7 well-performing methods from the challenge together with 6 well-known existing methods. The best methods used coarse but robust initial alignment, followed by non-rigid registration, used multiresolution, and were carefully tuned for the data at hand. They outperformed off-the-shelf methods, mostly by being more robust. The best methods could successfully register over 98% of all landmarks and their mean landmark registration accuracy (TRE) was 0.44% of the image diagonal. The challenge remains open to submissions and all images are available for download.

Multi-atlas segmentation is an effective approach for automatically labeling objects of interest in biomedical images. In this approach, multiple expert-segmented example images, called atlases, are registered to a target image, and deformed atlas segmentations are combined using label fusion. Among the proposed label fusion strategies, weighted voting with spatially varying weight distributions derived from atlas-target intensity similarity have been particularly successful. However, one limitation of these strategies is that the weights are computed independently for each atlas, without taking into account the fact that different atlases may produce similar label errors. To address this limitation, we propose a new solution for the label fusion problem in which weighted voting is formulated in terms of minimizing the total expectation of labeling error and in which pairwise dependency between atlases is explicitly modeled as the joint probability of two atlases making a segmentation error at a voxel. This probability is approximated using intensity similarity between a pair of atlases and the target image in the neighborhood of each voxel. We validate our method in two medical image segmentation problems: hippocampus segmentation and hippocampus subfield segmentation in magnetic resonance (MR) images. For both problems, we show consistent and significant improvement over label fusion strategies that assign atlas weights independently.

Multi-atlas segmentation has been widely applied in medical image analysis. With deformable registration, this technique realizes label transfer from pre-labeled atlases to unknown images. When deformable registration produces error, label fusion that combines results produced by multiple atlases is an effective way for reducing segmentation errors. Among the existing label fusion strategies, similarity-weighted voting strategies with spatially varying weight distributions have been particularly successful. We show that, weighted voting based label fusion produces a spatial bias that under-segments structures with convex shapes. The bias can be approximated as applying spatial convolution to the ground truth spatial label probability maps, where the convolution kernel combines the distribution of residual registration errors and the function producing similarity-based voting weights. To reduce this bias, we apply a standard spatial deconvolution to the spatial probability maps obtained from weighted voting. In a brain image segmentation experiment, we demonstrate the spatial bias and show that our technique substantially reduces this spatial bias.

Label fusion strategies are used in multi-atlas image segmentation approaches to compute a consensus segmentation of an image, given a set of candidate segmentations produced by registering the image to a set of atlases [19, 11, 8]. Effective label fusion strategies, such as local similarity-weighted voting [1, 13] substantially reduce segmentation errors compared to single-atlas segmentation. This paper extends the label fusion idea to the problem of finding correspondences across a set of images. Instead of computing a consensus segmentation, weighted voting is used to estimate a consensus coordinate map between a target image and a reference space. Two variants of the problem are considered: (1) where correspondences between a set of atlases are known and are propagated to the target image; (2) where correspondences are estimated across a set of images without prior knowledge. Evaluation in synthetic data shows that correspondences recovered by fusion methods are more accurate than those based on registration to a population template. In a 2D example in real MRI data, fusion methods result in more consistent mappings between manual segmentations of the hippocampus.

Most image segmentation algorithms are designed to estimate a single segmentation for each image, where the gold standard segmentation is often labeled by a human expert. However, it is common that multiple manual segmentations are available for some images, e.g. independently labeled by different experts. For efficient usages of manual segmentations, we propose to simultaneously produce automatic estimations for each expert. The key advantage of this proposal is that it allows to incorporate the correlations between different experts to improve the accuracy of automatic segmentation. In a brain image segmentation problem, where for each image six manual segmentations are available, we show that jointly estimating several manual segmentations produces significant improvement over independently estimating each of them.

Automatic segmentation using multi-atlas label fusion has been widely applied in medical image analysis. To simplify the label fusion problem, most methods implicitly make a strong assumption that the segmentation errors produced by different atlases are uncorrelated. We show that violating this assumption significantly reduces the efficiency of multi-atlas segmentation. To address this problem, we propose a regression-based approach for label fusion. Our experiments on segmenting the hippocampus in magnetic resonance images (MRI) show significant improvement over previous label fusion techniques.

A variant of the popular nonparametric nonuniform intensity normalization (N3) algorithm is proposed for bias field correction. Given the superb performance of N3 and its public availability, it has been the subject of several evaluation studies. These studies have demonstrated the importance of certain parameters associated with the B-spline least-squares fitting. We propose the substitution of a recently developed fast and robust B-spline approximation routine and a modified hierarchical optimization scheme for improved bias field correction over the original N3 algorithm. Similar to the N3 algorithm, we also make the source code, testing, and technical documentation of our contribution, which we denote as "N4ITK," available to the public through the Insight Toolkit of the National Institutes of Health. Performance assessment is demonstrated using simulated data from the publicly available Brainweb database, hyperpolarized (3)He lung image data, and 9.4T postmortem hippocampus data.

This paper describes a new statistical analysis framework for diffusion-based white matter studies. The framework is based on a recent unbiased normalization algorithm for diffusion tensor images. Taking advantage of the fact that most human white matter tracts are thin sheet-like structures, this framework uses deformable medial models to represent six of the major tracts in a white matter atlas derived for a given set of images. The medial representation allows one to average tensor-based features along directions perpendicular to the tracts, thus reducing data dimensionality and accounting for errors in normalization. Unlike earlier work in the area of tract-based spatial statistics (Smith et al, 2006), this framework enables the analysis of individual white matter structures, and provides a range of possibilities for computing statistics and visualizing differences between cohorts. The framework is demonstrated in a study of white matter differences in pediatric chromosome 22q deletion syndrome.

Large scale gene expression studies in the mammalian brain offer the promise of understanding the topology, networks and ultimately the function of its complex anatomy, opening previously unexplored avenues in neuroscience. High-throughput methods permit genome-wide searches to discover genes that are uniquely expressed in brain circuits and regions that control behavior. Previous gene expression mapping studies in model organisms have employed situ hybridization (ISH), a technique that uses labeled nucleic acid probes to bind to specific mRNA transcripts in tissue sections. A key requirement for this effort is the development of fast and robust algorithms for anatomically mapping and quantifying gene expression for ISH. We describe a neuroinformatics pipeline for automatically mapping expression profiles of ISH data and its use to produce the first genomic scale 3-D mapping of gene expression in a mammalian brain. The pipeline is fully automated and adaptable to other organisms and tissues. Our automated study of over 20,000 genes indicates that at least 78.8 percent are expressed at some level in the adult C56BL/6J mouse brain. In addition to providing a platform for genomic scale search, high-resolution images and visualization tools for expression analysis are available at the Allen Brain Atlas web site (http://www.brain-map.org).

The continuous medial representation (cm-rep) is an approach that makes it possible to model, normalize, and analyze anatomical structures on the basis of medial geometry. Having recently presented a partial differential equation (PDE)-based approach for 3-D cm-rep modeling [1], here we present an equivalent 2-D approach that involves solving an ordinary differential equation. This paper derives a closed form solution of this equation and shows how Pythagorean hodograph curves can be used to express the solution as a piecewise polynomial function, allowing efficient and robust medial modeling. The utility of the approach in medical image analysis is demonstrated by applying it to the problem of shape-based normalization of the midsagittal section of the corpus callosum. Using diffusion tensor tractography, we show that shape-based normalization aligns subregions of the corpus callosum, defined by connectivity, more accurately than normalization based on volumetric registration. Furthermore, shape-based normalization helps increase the statistical power of group analysis in an experiment where features derived from diffusion tensor tractography are compared between two cohorts. These results suggest that cm-rep is an appropriate tool for normalizing the corpus callosum in white matter studies.

Spatial normalization of diffusion tensor images plays a key role in voxel-based analysis of white matter (WM) group differences. Currently, it has been achieved using low-dimensional registration methods in the large majority of clinical studies. This paper aims to motivate the use of high-dimensional normalization approaches by generating evidence of their impact on the findings of such studies. Using an ongoing amyotrophic lateral sclerosis (ALS) study, we evaluated three normalization methods representing the current range of available approaches: low-dimensional normalization using the fractional anisotropy (FA), high-dimensional normalization using the FA, and high-dimensional normalization using full tensor information. Each method was assessed in terms of its ability to detect significant differences between ALS patients and controls. Our findings suggest that inadequate normalization with low-dimensional approaches can result in insufficient removal of shape differences which in turn can confound FA differences in a complex manner, and that utilizing high-dimensional normalization can both significantly minimize the confounding effect of shape differences to FA differences and provide a more complete description of WM differences in terms of both size and tissue architecture differences. We also found that high-dimensional approaches, by leveraging full tensor features instead of tensor-derived indices, can further improve the alignment of WM tracts.

The m-rep approach pioneered by Pizer et al. (2003) is a powerful morphological tool that makes it possible to employ features derived from medial loci (skeletons) in shape analysis. This paper extends the medial representation paradigm into the continuous realm, modeling skeletons and boundaries of three-dimensional objects as continuous parametric manifolds, while also maintaining the proper geometric relationship between these manifolds. The parametric representation of the boundary-medial relationship makes it possible to fit shape-based coordinate systems to the interiors of objects, providing a framework for combined statistical analysis of shape and appearance. Our approach leverages the idea of inverse skeletonization, where the skeleton of an object is defined first and the object's boundary is derived analytically from the skeleton. This paper derives a set of sufficient conditions ensuring that inverse skeletonization is well-posed for single-manifold skeletons and formulates a partial differential equation whose solutions satisfy the sufficient conditions. An efficient variational algorithm for deformable template modeling using the continuous medial representation is described and used to fit a template to the hippocampus in 87 subjects from a schizophrenia study with sub-voxel accuracy and 95% mean overlap.

This paper presents a multiscale framework based on a medial representation for the segmentation and shape characterization of anatomical objects in medical imagery. The segmentation procedure is based on a Bayesian deformable templates methodology in which the prior information about the geometry and shape of anatomical objects is incorporated via the construction of exemplary templates. The anatomical variability is accommodated in the Bayesian framework by defining probabilistic transformations on these templates. The transformations, thus, defined are parameterized directly in terms of natural shape operations, such as growth and bending, and their locations. A preliminary validation study of the segmentation procedure is presented. We also present a novel statistical shape analysis approach based on the medial descriptions that examines shape via separate intuitive categories, such as global variability at the coarse scale and localized variability at the fine scale. We show that the method can be used to statistically describe shape variability in intuitive terms such as growing and bending.

A model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives. Metrics are described that compute an object representation's prior probability of local geometry by reflecting variabilities in the net's node and link parameter values, and that compute a likelihood function measuring the degree of match of an image to that object representation. A paradigm for image analysis of deforming such a model to optimize a posteriori probability is described, and this paradigm is shown to be usable as a uniform approach for object definition, object-based registration between images of the same or different imaging modalities, and measurement of shape variation of an abnormal anatomical object, compared with a normal anatomical object. Examples of applications of these methods in radiotherapy, surgery, and psychiatry are given.