Current volumetric biomedical foundation models struggle to generalize as public 3D datasets are small and do not cover the broad diversity of medical procedures, conditions, anatomical regions, and imaging protocols. We address this by creating a representation learning method that instead anticipates strong domain shifts at training time itself. We first propose a data engine that synthesizes highly variable training samples that would enable generalization to new biomedical contexts. To then train a single 3D network for any voxel-level task, we develop a contrastive learning method that pretrains the network to be stable against nuisance imaging variation simulated by the data engine, a key inductive bias for generalization. This network's features can be used as robust representations of input images for downstream tasks and its weights provide a strong, _dataset-agnostic_ initialization for finetuning on new datasets. As a result, we set new standards across _both_ multimodality registration and few-shot segmentation, a first for any 3D biomedical vision model, all without (pre-)training on any existing dataset of real images.

We present a novel approach to calibrating linguistic expressions of certainty, e.g., "Maybe" and "Likely". Unlike prior work that assigns a single score to each certainty phrase, we model uncertainty as distributions over the simplex to capture their semantics more accurately. To accommodate this new representation of certainty, we generalize existing measures of miscalibration and introduce a novel post-hoc calibration method. Leveraging these tools, we analyze the calibration of both humans (e.g., radiologists) and computational models (e.g., language models) and provide interpretable suggestions to improve their calibration.

Mutual Information (MI) is a fundamental measure of statistical dependence widely used in representation learning. While direct optimization of MI via its definition as a Kullback-Leibler divergence (KLD) is often intractable, many recent methods have instead maximized alternative dependence measures, most notably, the Jensen-Shannon divergence (JSD) between joint and product of marginal distributions via discriminative losses. However, the connection between these surrogate objectives and MI remains poorly understood. In this work, we bridge this gap by deriving a new, tight, and tractable lower bound on KLD as a function of JSD in the general case. By specializing this bound to joint and marginal distributions, we demonstrate that maximizing the JSD-based information increases a guaranteed lower bound on mutual information. Furthermore, we revisit the practical implementation of JSD-based objectives and observe that minimizing the cross-entropy loss of a binary classifier trained to distinguish joint from marginal pairs recovers a known variational lower bound on the JSD. Extensive experiments demonstrate that our lower bound is tight when applied to MI estimation. We compared our lower bound to state-of-the-art neural estimators of variational lower bound across a range of established reference scenarios. Our lower bound estimator consistently provides a stable, low-variance estimate of a tight lower bound on MI. We also demonstrate its practical usefulness in the context of the Information Bottleneck framework. Taken together, our results provide new theoretical justifications and strong empirical evidence for using discriminative learning in MI-based representation learning.

Determining the 3D pose of a patient from a limited set of 2D X-ray images is a critical task in interventional settings. While preoperative volumetric imaging (e.g., CT and MRI) provides precise 3D localization and visualization of anatomical targets, these modalities cannot be acquired during procedures, where fast 2D imaging (X-ray) is used instead. To integrate volumetric guidance into intraoperative procedures, we present PolyPose, a simple and robust method for deformable 2D/3D registration. PolyPose parameterizes complex 3D deformation fields as a composition of rigid transforms, leveraging the biological constraint that individual bones do not bend in typical motion. Unlike existing methods that either assume no inter-joint movement or fail outright in this under-determined setting, our polyrigid formulation enforces anatomically plausible priors that respect the piecewise-rigid nature of human movement. This approach eliminates the need for expensive deformation regularizers that require patient- and procedure-specific hyperparameter optimization. Across extensive experiments on diverse datasets from orthopedic surgery and radiotherapy, we show that this strong inductive bias enables PolyPose to successfully align the patient's preoperative volume to as few as two X-rays, thereby providing crucial 3D guidance in challenging sparse-view and limited-angle settings where current registration methods fail. Additional visualizations, tutorials, and code are available at https://polypose.csail.mit.edu.

Learning-based image reconstruction models, such as those based on the U-Net, require a large set of labeled images if good generalization is to be guaranteed. In some imaging domains, however, labeled data with pixel- or voxel-level label accuracy are scarce due to the cost of acquiring them. This problem is exacerbated further in domains like medical imaging, where there is no single ground truth label, resulting in large amounts of repeat variability in the labels. Therefore, training reconstruction networks to generalize better by learning from both labeled and unlabeled examples (called semi-supervised learning) is problem of practical and theoretical interest. However, traditional semi-supervised learning methods for image reconstruction often necessitate handcrafting a differentiable regularizer specific to some given imaging problem, which can be extremely time-consuming. In this work, we propose "supervision by denoising" (SUD), a framework to supervise reconstruction models using their own denoised output as labels. SUD unifies stochastic averaging and spatial denoising techniques under a spatio-temporal denoising framework and alternates denoising and model weight update steps in an optimization framework for semi-supervision. As example applications, we apply SUD to two problems from biomedical imaging-anatomical brain reconstruction (3D) and cortical parcellation (2D)-to demonstrate a significant improvement in reconstruction over supervised-only and ensembling baselines.

Surgical decisions are informed by aligning rapid portable 2D intraoperative images (e.g. X-rays) to a high-fidelity 3D preoperative reference scan (e.g. CT). However, 2D/3D registration can often fail in practice: conventional optimization methods are prohibitively slow and suscepti-ble to local minima, while neural networks trained on small datasets fail on new patients or require impractical land-mark supervision. We present DiffPose, a self-supervised approach that leverages patient-specific simulation and differentiable physics-based rendering to achieve accurate 2D/3D registration without relying on manually labeled data. Preoperatively, a CNN is trained to regress the pose of a randomly oriented synthetic X-ray rendered from the pre-operative CT. The CNN then initializes rapid intraoperative test-time optimization that uses the differentiable X-ray ren-derer to refine the solution. Our work further proposes several geometrically principled methods for sampling camera poses from SE (3), for sparse differentiable rendering, and for driving registration in the tangent space sc(3) with geodesic and multiscale locality-sensitive losses. DiffPose achieves sub-millimeter accuracy across surgical datasets at intraoperative speeds, improving upon existing unsupervised methods by an order of magnitude and even outperforming supervised baselines. Our implementation is at https://github.com/eigenvivek/DiffPose.

In magnetic resonance imaging (MRI), slice-to-volume reconstruction (SVR) refers to computational reconstruction of an unknown 3D magnetic resonance volume from stacks of 2D slices corrupted by motion. While promising, current SVR methods require multiple slice stacks for accurate 3D reconstruction, leading to long scans and limiting their use in time-sensitive applications such as fetal fMRI. Here, we propose a SVR method that overcomes the shortcomings of previous work and produces state-of-the-art reconstructions in the presence of extreme inter-slice motion. Inspired by the recent success of single-view depth estimation methods, we formulate SVR as a single-stack motion estimation task and train a fully convolutional network to predict a motion stack for a given slice stack, producing a 3D reconstruction as a byproduct of the predicted motion. Extensive experiments on the SVR of adult and fetal brains demonstrate that our fully convolutional method is twice as accurate as previous SVR methods. Our code is available at github.com/seannz/svr.

The idea of representing a signal as the weights of a neural network, called *Implicit Neural Representations* (INRs), has led to exciting implications for compression, view synthesis and 3D volumetric data understanding. One problem in this setting pertains to the use of INRs for downstream processing tasks. Despite some conceptual results, this remains challenging because the INR for a given image/signal often exists in isolation. What does the neighborhood around a given INR correspond to? Based on this question, we offer an operator theoretic reformulation of the INR model, which we call Operator INR (or O-INR). At a high level, instead of mapping positional encodings to a signal, O-INR maps one function space to another function space. A practical form of this general casting is obtained by appealing to Integral Transforms. The resultant model does not need multi-layer perceptrons (MLPs), used in most existing INR models -- we show that convolutions are sufficient and offer benefits including numerically stable behavior. We show that O-INR can easily handle most problem settings in the literature, and offers a similar performance profile as baselines. These benefits come with minimal, if any, compromise. Our code is available at https://github.com/vsingh-group/oinr.

Star-convex shapes arise across bio-microscopy and radiology in the form of nuclei, nodules, metastases, and other units. Existing instance segmentation networks for such structures train on densely labeled instances for each dataset, which requires substantial and often impractical manual annotation effort. Further, significant reengineering or finetuning is needed when presented with new datasets and imaging modalities due to changes in contrast, shape, orientation, resolution, and density. We present AnyStar, a domain-randomized generative model that simulates synthetic training data of blob-like objects with randomized appearance, environments, and imaging physics to train general-purpose star-convex instance segmentation networks. As a result, networks trained using our generative model do not require annotated images from un-seen datasets. A single network trained on our synthesized data accurately 3D segments C. elegans and P. dumerilii nuclei in fluorescence microscopy, mouse cortical nuclei in μCT, zebrafish brain nuclei in EM, and placental cotyledons in human fetal MRI, all without any retraining, finetuning, transfer learning, or domain adaptation. Code is available at https://github.com/neel-dey/AnyStar.

Rigid motion tracking is paramount in many medical imaging applications where movements need to be detected, corrected, or accounted for. Modern strategies rely on convolutional neural networks (CNN) and pose this problem as rigid registration. Yet, CNNs do not exploit natural symmetries in this task, as they are equivariant to translations (their outputs shift with their inputs) but not to rotations. Here we propose EquiTrack, the first method that uses recent steerable SE(3)-equivariant CNNs (E-CNN) for motion tracking. While steerable E-CNNs can extract corresponding features across different poses, testing them on noisy medical images reveals that they do not have enough learning capacity to learn noise invariance. Thus, we introduce a hybrid architecture that pairs a denoiser with an E-CNN to decouple the processing of anatomically irrelevant intensity features from the extraction of equivariant spatial features. Rigid transforms are then estimated in closed-form. EquiTrack outperforms state-of-the-art learning and optimisation methods for motion tracking in adult brain MRI and fetal MRI time series. Our code is available at https://github.com/BBillot/EquiTrack.

Image-to-image translation has seen major advances in computer vision but can be difficult to apply to medical images, where imaging artifacts and data scarcity degrade the performance of conditional generative adversarial networks. We develop the spatial-intensity transform (SIT) to improve output image quality while closely matching the target domain. SIT constrains the generator to a smooth spatial transform (diffeomorphism) composed with sparse intensity changes. SIT is a lightweight, modular network component that is effective on various architectures and training schemes. Relative to unconstrained baselines, this technique significantly improves image fidelity, and our models generalize robustly to different scanners. Additionally, SIT provides a disentangled view of anatomical and textural changes for each translation, making it easier to interpret the model's predictions in terms of physiological phenomena. We demonstrate SIT on two tasks: predicting longitudinal brain MRIs in patients with various stages of neurodegeneration, and visualizing changes with age and stroke severity in clinical brain scans of stroke patients. On the first task, our model accurately forecasts brain aging trajectories without supervised training on paired scans. On the second task, it captures associations between ventricle expansion and aging, as well as between white matter hyperintensities and stroke severity. As conditional generative models become increasingly versatile tools for visualization and forecasting, our approach demonstrates a simple and powerful technique for improving robustness, which is critical for translation to clinical settings. Source code is available at github.com/clintonjwang/spatial-intensity-transforms.

Reconstructing 3D MR volumes from multiple motion-corrupted stacks of 2D slices has shown promise in imaging of moving subjects, e. g., fetal MRI. However, existing slice-to-volume reconstruction methods are time-consuming, especially when a high-resolution volume is desired. Moreover, they are still vulnerable to severe subject motion and when image artifacts are present in acquired slices. In this work, we present NeSVoR, a resolution-agnostic slice-to-volume reconstruction method, which models the underlying volume as a continuous function of spatial coordinates with implicit neural representation. To improve robustness to subject motion and other image artifacts, we adopt a continuous and comprehensive slice acquisition model that takes into account rigid inter-slice motion, point spread function, and bias fields. NeSVoR also estimates pixel-wise and slice-wise variances of image noise and enables removal of outliers during reconstruction and visualization of uncertainty. Extensive experiments are performed on both simulated and in vivo data to evaluate the proposed method. Results show that NeSVoR achieves state-of-the-art reconstruction quality while providing two to ten-fold acceleration in reconstruction times over the state-of-the-art algorithms.

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence—a natural extension relevant to shapes extracted from simulation, medical imaging, and volume rendering—presents unique challenges that do not appear in the two-dimensional case. In this work, we propose a method for mapping between volumes represented as tetrahedral meshes. Our formulation minimizes a distortion energy designed to extract maps symmetrically, i.e., without dependence on the ordering of the source and target domains. We accompany our method with theoretical discussion describing the consequences of this symmetry assumption, leading us to select a symmetrized ARAP energy that favors isometric correspondences. Our final formulation optimizes for near-isometry while matching the boundary. We demonstrate our method on a diverse geometric dataset, producing low-distortion matchings that align closely to the boundary.

We present a volumetric mesh-based algorithm for parameterizing the placenta to a flattened template to enable effective visualization of local anatomy and function. MRI shows potential as a research tool as it provides signals directly related to placental function. However, due to the curved and highly variable in vivo shape of the placenta, interpreting and visualizing these images is difficult. We address interpretation challenges by mapping the placenta so that it resembles the familiar ex vivo shape. We formulate the parameterization as an optimization problem for mapping the placental shape represented by a volumetric mesh to a flattened template. We employ the symmetric Dirichlet energy to control local distortion throughout the volume. Local injectivity in the mapping is enforced by a constrained line search during the gradient descent optimization. We validate our method using a research study of 111 placental shapes extracted from BOLD MRI images. Our mapping achieves sub-voxel accuracy in matching the template while maintaining low distortion throughout the volume. We demonstrate how the resulting flattening of the placenta improves visualization of anatomy and function. Our code is freely available at https://github.com/mabulnaga/placenta-flattening.

We propose and demonstrate a representation learning approach by maximizing the mutual information between local features of images and text. The goal of this approach is to learn useful image representations by taking advantage of the rich information contained in the free text that describes the findings in the image. Our method trains image and text encoders by encouraging the resulting representations to exhibit high local mutual information. We make use of recent advances in mutual information estimation with neural network discriminators. We argue that the sum of local mutual information is typically a lower bound on the global mutual information. Our experimental results in the downstream image classification tasks demonstrate the advantages of using local features for image-text representation learning.

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of parameter values as random perturbations of the optimal parameter set from training by a Gaussian with a single variance parameter. The variance is chosen to maximize the log-likelihood of the ensemble average (𝕃) on the validation data set. Empirically, and perhaps surprisingly, 𝕃 has a well-defined maximum as the variance grows from zero (which corresponds to the baseline model). Conveniently, calibration level of predictions also tends to grow favorably until the peak of 𝕃 is reached. In most experiments, PEP provides a small improvement in performance, and, in some cases, a substantial improvement in empirical calibration. We show that this "PEP effect'' (the gain in log-likelihood) is related to the mean curvature of the likelihood function and the empirical Fisher information. Experiments on ImageNet pre-trained networks including ResNet, DenseNet, and Inception showed improved calibration and likelihood. We further observed a mild improvement in classification accuracy on these networks. Experiments on classification benchmarks such as MNIST and CIFAR-10 showed improved calibration and likelihood, as well as the relationship between the PEP effect and overfitting; this demonstrates that PEP can be used to probe the level of overfitting that occurred during training. In general, no special training procedure or network architecture is needed, and in the case of pre-trained networks, no additional training is needed.

We introduce an approach for image segmentation based on sparse correspondences between keypoints in testing and training images. Keypoints represent automatically identified distinctive image locations, where each keypoint correspondence suggests a transformation between images. We use these correspondences to transfer the label maps of entire organs from the training images to the test image. The keypoint transfer algorithm includes three steps: 1) keypoint matching; 2) voting-based keypoint labeling; and 3) keypoint-based probabilistic transfer of organ segmentations. We report segmentation results for abdominal organs in whole-body CT and MRI, as well as in contrast-enhanced CT and MRI. Our method offers a speed-up of about three orders of magnitude in comparison with common multi-atlas segmentation while achieving an accuracy that compares favorably. Moreover, keypoint transfer does not require the registration to an atlas or a training phase. Finally, the method allows for the segmentation of scans with a highly variable field-of-view.

We present an algorithm for creating high resolution anatomically plausible images consistent with acquired clinical brain MRI scans with large inter-slice spacing. Although large data sets of clinical images contain a wealth of information, time constraints during acquisition result in sparse scans that fail to capture much of the anatomy. These characteristics often render computational analysis impractical as many image analysis algorithms tend to fail when applied to such images. Highly specialized algorithms that explicitly handle sparse slice spacing do not generalize well across problem domains. In contrast, we aim to enable application of existing algorithms that were originally developed for high resolution research scans to significantly undersampled scans. We introduce a generative model that captures fine-scale anatomical structure across subjects in clinical image collections and derive an algorithm for filling in the missing data in scans with large inter-slice spacing. Our experimental results demonstrate that the resulting method outperforms state-of-the-art upsampling super-resolution techniques, and promises to facilitate subsequent analysis not previously possible with scans of this quality. Our implementation is freely available at https://github.com/adalca/papago.

We present a robust method to correct for motion and deformations in in-utero volumetric MRI time series. Spatio-temporal analysis of dynamic MRI requires robust alignment across time in the presence of substantial and unpredictable motion. We make a Markov assumption on the nature of deformations to take advantage of the temporal structure in the image data. Forward message passing in the corresponding hidden Markov model (HMM) yields an estimation algorithm that only has to account for relatively small motion between consecutive frames. We demonstrate the utility of the temporal model by showing that its use improves the accuracy of the segmentation propagation through temporal registration. Our results suggest that the proposed model captures accurately the temporal dynamics of deformations in in-utero MRI time series.

Using image-based descriptors to investigate clinical hypotheses and therapeutic implications is challenging due to the notorious "curse of dimensionality" coupled with a small sample size. In this paper, we present a low-dimensional analysis of anatomical shape variability in the space of diffeomorphisms and demonstrate its benefits for clinical studies. To combat the high dimensionality of the deformation descriptors, we develop a probabilistic model of principal geodesic analysis in a bandlimited low-dimensional space that still captures the underlying variability of image data. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than models based on the high-dimensional state-of-the-art approaches such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA).

We introduce a generative probabilistic model for segmentation of brain lesions in multi-dimensional images that generalizes the EM segmenter, a common approach for modelling brain images using Gaussian mixtures and a probabilistic tissue atlas that employs expectation-maximization (EM), to estimate the label map for a new image. Our model augments the probabilistic atlas of the healthy tissues with a latent atlas of the lesion. We derive an estimation algorithm with closed-form EM update equations. The method extracts a latent atlas prior distribution and the lesion posterior distributions jointly from the image data. It delineates lesion areas individually in each channel, allowing for differences in lesion appearance across modalities, an important feature of many brain tumor imaging sequences. We also propose discriminative model extensions to map the output of the generative model to arbitrary labels with semantic and biological meaning, such as "tumor core" or "fluid-filled structure", but without a one-to-one correspondence to the hypo- or hyper-intense lesion areas identified by the generative model. We test the approach in two image sets: the publicly available BRATS set of glioma patient scans, and multimodal brain images of patients with acute and subacute ischemic stroke. We find the generative model that has been designed for tumor lesions to generalize well to stroke images, and the extended discriminative -discriminative model to be one of the top ranking methods in the BRATS evaluation.

In this paper we report the set-up and results of the Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) organized in conjunction with the MICCAI 2012 and 2013 conferences. Twenty state-of-the-art tumor segmentation algorithms were applied to a set of 65 multi-contrast MR scans of low- and high-grade glioma patients-manually annotated by up to four raters-and to 65 comparable scans generated using tumor image simulation software. Quantitative evaluations revealed considerable disagreement between the human raters in segmenting various tumor sub-regions (Dice scores in the range 74%-85%), illustrating the difficulty of this task. We found that different algorithms worked best for different sub-regions (reaching performance comparable to human inter-rater variability), but that no single algorithm ranked in the top for all sub-regions simultaneously. Fusing several good algorithms using a hierarchical majority vote yielded segmentations that consistently ranked above all individual algorithms, indicating remaining opportunities for further methodological improvements. The BRATS image data and manual annotations continue to be publicly available through an online evaluation system as an ongoing benchmarking resource.

We propose a novel approach to identify the foci of a neurological disorder based on anatomical and functional connectivity information. Specifically, we formulate a generative model that characterizes the network of abnormal functional connectivity emanating from the affected foci. This allows us to aggregate pairwise connectivity changes into a region-based representation of the disease. We employ the variational expectation-maximization algorithm to fit the model and subsequently identify both the afflicted regions and the differences in connectivity induced by the disorder. We demonstrate our method on a population study of schizophrenia.

We propose a novel probabilistic framework to merge information from diffusion weighted imaging tractography and resting-state functional magnetic resonance imaging correlations to identify connectivity patterns in the brain. In particular, we model the interaction between latent anatomical and functional connectivity and present an intuitive extension to population studies. We employ the EM algorithm to estimate the model parameters by maximizing the data likelihood. The method simultaneously infers the templates of latent connectivity for each population and the differences in connectivity between the groups. We demonstrate our method on a schizophrenia study. Our model identifies significant increases in functional connectivity between the parietal/posterior cingulate region and the frontal lobe and reduced functional connectivity between the parietal/posterior cingulate region and the temporal lobe in schizophrenia. We further establish that our model learns predictive differences between the control and clinical populations, and that combining the two modalities yields better results than considering each one in isolation.

Our goal is to model anatomical variability across individuals, which presents substantial challenges in clinical population studies and in building atlases for segmentation. Based on a mixture model for a population, we derive an efficient algorithm that clusters a set of images while co-registering them into a common coordinate frame. The output of the algorithm is a small number of template images that represent different modes of a population. This is in contrast to traditional computational anatomy methods that assume a single template for population modeling. The experimental results demonstrate the promise of our approach for statistical analysis in clinical studies of anatomy.

Matching functional brain regions across individuals is a challenging task, largely due to the variability in their location and extent. It is particularly difficult, but highly relevant, for patients with pathologies such as brain tumors, which can cause substantial reorganization of functional systems. In such cases spatial registration based on anatomical data is only of limited value if the goal is to establish correspondences of functional areas among different individuals, or to localize potentially displaced active regions. Rather than rely on spatial alignment, we propose to perform registration in an alternative space whose geometry is governed by the functional interaction patterns in the brain. We first embed each brain into a functional map that reflects connectivity patterns during a fMRI experiment. The resulting functional maps are then registered, and the obtained correspondences are propagated back to the two brains. In application to a language fMRI experiment, our preliminary results suggest that the proposed method yields improved functional correspondences across subjects. This advantage is pronounced for subjects with tumors that affect the language areas and thus cause spatial reorganization of the functional regions.

We present a model that describes the structure in the responses of different brain areas to a set of stimuli in terms of stimulus categories" (clusters of stimuli) and "functional units" (clusters of voxels). We assume that voxels within a unit respond similarly to all stimuli from the same category, and design a nonparametric hierarchical model to capture inter-subject variability among the units. The model explicitly captures the relationship between brain activations and fMRI time courses. A variational inference algorithm derived based on the model can learn categories, units, and a set of unit-category activation probabilities from data. When applied to data from an fMRI study of object recognition, the method finds meaningful and consistent clusterings of stimuli into categories and voxels into units."

We propose a nonparametric, probabilistic model for the automatic segmentation of medical images, given a training set of images and corresponding label maps. The resulting inference algorithms rely on pairwise registrations between the test image and individual training images. The training labels are then transferred to the test image and fused to compute the final segmentation of the test subject. Such label fusion methods have been shown to yield accurate segmentation, since the use of multiple registrations captures greater inter-subject anatomical variability and improves robustness against occasional registration failures. To the best of our knowledge, this manuscript presents the first comprehensive probabilistic framework that rigorously motivates label fusion as a segmentation approach. The proposed framework allows us to compare different label fusion algorithms theoretically and practically. In particular, recent label fusion or multiatlas segmentation algorithms are interpreted as special cases of our framework. We conduct two sets of experiments to validate the proposed methods. In the first set of experiments, we use 39 brain MRI scans-with manually segmented white matter, cerebral cortex, ventricles and subcortical structures-to compare different label fusion algorithms and the widely-used FreeSurfer whole-brain segmentation tool. Our results indicate that the proposed framework yields more accurate segmentation than FreeSurfer and previous label fusion algorithms. In a second experiment, we use brain MRI scans of 282 subjects to demonstrate that the proposed segmentation tool is sufficiently sensitive to robustly detect hippocampal volume changes in a study of aging and Alzheimer's Disease.

We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a Xeon 3.2 GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1) parcellation of in vivo cortical surfaces and 2) Brodmann area localization in ex vivo cortical surfaces.

Image registration is typically formulated as an optimization problem with multiple tunable, manually set parameters. We present a principled framework for learning thousands of parameters of registration cost functions, such as a spatially-varying tradeoff between the image dissimilarity and regularization terms. Our approach belongs to the classic machine learning framework of model selection by optimization of cross-validation error. This second layer of optimization of cross-validation error over and above registration selects parameters in the registration cost function that result in good registration as measured by the performance of the specific application in a training data set. Much research effort has been devoted to developing generic registration algorithms, which are then specialized to particular imaging modalities, particular imaging targets and particular postregistration analyses. Our framework allows for a systematic adaptation of generic registration cost functions to specific applications by learning the "free" parameters in the cost functions. Here, we consider the application of localizing underlying cytoarchitecture and functional regions in the cerebral cortex by alignment of cortical folding. Most previous work assumes that perfectly registering the macro-anatomy also perfectly aligns the underlying cortical function even though macro-anatomy does not completely predict brain function. In contrast, we learn 1) optimal weights on different cortical folds or 2) optimal cortical folding template in the generic weighted sum of squared differences dissimilarity measure for the localization task. We demonstrate state-of-the-art localization results in both histological and functional magnetic resonance imaging data sets.

In this paper we investigate the use of data driven clustering methods for functional connectivity analysis in fMRI. In particular, we consider the k-means and spectral clustering algorithms as alternatives to the commonly used seed-based analysis. To enable clustering of the entire brain volume, we use the Nystrom Method to approximate the necessary spectral decompositions. We apply k-means, spectral clustering and seed-based analysis to resting-state fMRI data collected from 45 healthy young adults. Without placing any a priori constraints, both clustering methods yield partitions that are associated with brain systems previously identified via seed-based analysis. Our empirical results suggest that clustering provides a valuable tool for functional connectivity analysis.

A natural requirement in pairwise image registration is that the resulting deformation is independent of the order of the images. This constraint is typically achieved via a symmetric cost function and has been shown to reduce the effects of local optima. Consequently, symmetric registration has been successfully applied to pairwise image registration as well as the spatial alignment of individual images with a template. However, recent work has shown that the relationship between an image and a template is fundamentally asymmetric. In this paper, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.

We present iCluster, a fast and efficient algorithm that clusters a set of images while co-registering them using a parameterized, nonlinear transformation model. The output of the algorithm is a small number of template images that represent different modes in a population. This is in contrast with traditional, hypothesis-driven computational anatomy approaches that assume a single template to construct an atlas. We derive the algorithm based on a generative model of an image population as a mixture of deformable template images. We validate and explore our method in four experiments. In the first experiment, we use synthetic data to explore the behavior of the algorithm and inform a design choice on parameter settings. In the second experiment, we demonstrate the utility of having multiple atlases for the application of localizing temporal lobe brain structures in a pool of subjects that contains healthy controls and schizophrenia patients. Next, we employ iCluster to partition a data set of 415 whole brain MR volumes of subjects aged 18 through 96 years into three anatomical subgroups. Our analysis suggests that these subgroups mainly correspond to age groups. The templates reveal significant structural differences across these age groups that confirm previous findings in aging research. In the final experiment, we run iCluster on a group of 15 patients with dementia and 15 age-matched healthy controls. The algorithm produces two modes, one of which contains dementia patients only. These results suggest that the algorithm can be used to discover subpopulations that correspond to interesting structural or functional "modes."

In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.

We present iCluster, a fast and efficient algorithm that clusters a set of images while co-registering them using a parameterized, nonlinear transformation model. The output is a small number of template images that represent different modes in a population. This is in contrast with traditional approaches that assume a single template to construct atlases. We validate and explore the algorithm in two experiments. First, we employ iCluster to partition a data set of 416 whole brain MR volumes of subjects aged 18-96 years into three sub-groups, which mainly correspond to age groups. The templates reveal significant structural differences across these age groups that confirm previous findings in aging research. In the second experiment, we run iCluster on a group of 30 patients with dementia and 30 age-matched healthy controls. The algorithm produced three modes that mainly corresponded to a sub-population of healthy controls, a sub-population of patients with dementia and a mixture group that contained both types. These results suggest that the algorithm can be used to discover sub-populations that correspond to interesting structural or functional "modes".

BACKGROUND: Image-based screens can produce hundreds of measured features for each of hundreds of millions of individual cells in a single experiment. RESULTS: Here, we describe CellProfiler Analyst, open-source software for the interactive exploration and analysis of multidimensional data, particularly data from high-throughput, image-based experiments. CONCLUSION: The system enables interactive data exploration for image-based screens and automated scoring of complex phenotypes that require combinations of multiple measured features per cell.

The theories of signal sampling, filter banks, wavelets, and "overcomplete wavelets" are well established for the Euclidean spaces and are widely used in the processing and analysis of images. While recent advances have extended some filtering methods to spherical images, many key challenges remain. In this paper, we develop theoretical conditions for the invertibility of filter banks under continuous spherical convolution. Furthermore, we present an analogue of the Papoulis generalized sampling theorem on the 2-Sphere. We use the theoretical results to establish a general framework for the design of invertible filter banks on the sphere and demonstrate the approach with examples of self-invertible spherical wavelets and steerable pyramids. We conclude by examining the use of a self-invertible spherical steerable pyramid in a denoising experiment and discussing the computational complexity of the filtering framework.

We argue that registration should be thought of as a means to an end, and not as a goal by itself. In particular, we consider the problem of predicting the locations of hidden labels of a test image using observable features, given a training set with both the hidden labels and observable features. For example, the hidden labels could be segmentation labels or activation regions in fMRI, while the observable features could be sulcal geometry or MR intensity. We analyze a probabilistic framework for computing an optimal atlas, and the subsequent registration of a new subject using only the observable features to optimize the hidden label alignment to the training set. We compare two approaches for co-registering training images for the atlas construction: the traditional approach of only using observable features and a novel approach of only using hidden labels. We argue that the alternative approach is superior particularly when the relationship between the hidden labels and observable features is complex and unknown. As an application, we consider the task of registering cortical folds to optimize Brodmann area localization. We show that the alignment of the Brodmann areas improves by up to 25% when using the alternative atlas compared with the traditional atlas. To the best of our knowledge, these are the most accurate Brodmann area localization results (achieved via cortical fold registration) reported to date.

We introduce the use of over-complete spherical wavelets for shape analysis of 2D closed surfaces. Bi-orthogonal spherical wavelets have been shown to be powerful tools in the segmentation and shape analysis of 2D closed surfaces, but unfortunately they suffer from aliasing problems and are therefore not invariant under rotations of the underlying surface parameterization. In this paper, we demonstrate the theoretical advantage of over-complete wavelets over bi-orthogonal wavelets and illustrate their utility on both synthetic and real data. In particular, we show that over-complete spherical wavelets allow us to build more stable cortical folding development models, and detect a wider array of regions of folding development in a newborn dataset.

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a significant challenge in clustering large data sets into many clusters. In this paper, we present a dif- ferent approach to approximate mixture fitting for clustering. We introduce an exemplar-based likelihood function that approximates the exact likelihood. This formulation leads to a convex minimization problem and an efficient algorithm with guaranteed convergence to the globally optimal solution. The resulting clus- tering can be thought of as a probabilistic mapping of the data points to the set of exemplars that minimizes the average distance and the information-theoretic cost of mapping. We present experimental results illustrating the performance of our algorithm and its comparison with the conventional approach to mixture model clustering.

The thirteen articles in this special issue are devoted to mathematical analysis of biomedical imaging processes and systems.

In vivo quantification of neuroanatomical shape variations is possible due to recent advances in medical imaging and has proven useful in the study of neuropathology and neurodevelopment. In this paper, we apply a spherical wavelet transformation to extract shape features of cortical surfaces reconstructed from magnetic resonance images (MRIs) of a set of subjects. The spherical wavelet transformation can characterize the underlying functions in a local fashion in both space and frequency, in contrast to spherical harmonics that have a global basis set. We perform principal component analysis (PCA) on these wavelet shape features to study patterns of shape variation within normal population from coarse to fine resolution. In addition, we study the development of cortical folding in newborns using the Gompertz model in the wavelet domain, which allows us to characterize the order of development of large-scale and finer folding patterns independently. Given a limited amount of training data, we use a regularization framework to estimate the parameters of the Gompertz model to improve the prediction performance on new data. We develop an efficient method to estimate this regularized Gompertz model based on the Broyden-Fletcher-Goldfarb-Shannon (BFGS) approximation. Promising results are presented using both PCA and the folding development model in the wavelet domain. The cortical folding development model provides quantitative anatomic information regarding macroscopic cortical folding development and may be of potential use as a biomarker for early diagnosis of neurologic deficits in newborns.

Multiscale filtering methods, such as wavelets and steerable pyramids, are widely used in processing and analysis of planar images and promise similar benefits in application to spherical images. While recent advances have extended some filtering methods to the sphere, many key challenges remain. In this paper, we develop conditions for the invertibility of spherical filter banks for both continuous and discrete convolution and illustrate how such conditions can be incorporated into the design of self-invertible axis-symmetric wavelets. Self-invertibility is particularly desirable when modifying images in the wavelet domain.

In many scientific and engineering applications, detecting and under- standing differences between two groups of examples can be reduced to a classical problem of training a classifier for labeling new examples while making as few mistakes as possible. In the traditional classifi- cation setting, the resulting classifier is rarely analyzed in terms of the properties of the input data captured by the discriminative model. How- ever, such analysis is crucial if we want to understand and visualize the detected differences. We propose an approach to interpretation of the sta- tistical model in the original feature space that allows us to argue about the model in terms of the relevant changes to the input vectors. For each point in the input space, we define a discriminative direction to be the direction that moves the point towards the other class while introducing as little irrelevant change as possible with respect to the classifier func- tion. We derive the discriminative direction for kernel-based classifiers, demonstrate the technique on several examples and briefly discuss its use in the statistical shape analysis, an application that originally motivated this work. 1 Introduction Once a classifier is estimated from the training data, it can be used to label new examples, and in many application domains, such as character recognition, text classification and oth- ers, this constitutes the final goal of the learning stage. The statistical learning algorithms are also used in scientific studies to detect and analyze differences between the two classes when the ``correct answer'' is unknown, and the information we have on the differences is represented implicitly by the training set. Example applications include morphologi- cal analysis of anatomical organs (comparing organ shape in patients vs. normal controls), molecular design (identifying complex molecules that satisfy certain requirements), etc. In such applications, interpretation of the resulting classifier in terms of the original feature vectors can provide an insight into the nature of the differences detected by the learning algorithm and is therefore a crucial step in the analysis. Furthermore, we would argue that studying the spatial structure of the data captured by the classification function is important in any application, as it leads to a better understanding of the data and can potentially help in improving the technique. This paper addresses the problem of translating a classifier into a different representation that allows us to visualize and study the differences between the classes. We introduce and derive a so called discriminative direction at every point in the original feature space with respect to a given classifier. Informally speaking, the discriminative direction tells us how to change any input example to make it look more like an example from another class without introducing any irrelevant changes that possibly make it more similar to other examples from the same class. It allows us to characterize differences captured by the classifier and to express them as changes in the original input examples. This paper is organized as follows. We start with a brief background section on kernel- based classification, stating without proof the main facts on kernel-based SVMs necessary for derivation of the discriminative direction. We follow the notation used in [3, 8, 9]. In Section 3, we provide a formal definition of the discriminative direction and explain how it can be estimated from the classification function. We then present some special cases, in which the computation can be simplified significantly due to a particular structure of the kernel. Section 4 demonstrates the discriminative direction for different kernels, followed by an example from the problem of statistical analysis of shape differences that originally motivated this work.

In this paper, we present a novel approach to robust skeleton extraction. We use undirected graphs to model connectivity of the skeleton points. The graph topology remains unchanged throughout the skeleton computation, which greatly reduces sensitivity of the skeleton to noise in the shape outline. Furthermore, this representation naturally defines an ordering of the points along the skeleton. The process of skeleton extraction can be formulated as energy minimization in this framework. We provide an iterative, snake-like algorithm for the skeleton estimation using distance transform. Fixed topology skeletons are useful if the global shape of the object is known ahead of time, such as for people silhouettes, hand outlines, medical structures, images of letters and digits. Small changes in the object outline should be either ignored, or detected and analyzed, but they do not change the general structure of the underlying skeleton. Example applications include tracking, object recognition and shape analysis.

This paper formulates and solves a new variant of the stereo correspondence problem: simultaneously recovering the disparities, true colors, and opacities of visible surface elements. This problem arises in newer applications of stereo reconstruction, such as view interpolation and the layering of real imagery with synthetic graphics for special effects and virtual studio applications. While this problem is intrinsically more difficult than traditional stereo correspondence, where only the disparities are being recovered, it provides a principled way of dealing with commonly occurring problems such as occlusions and the handling of mixed (foreground/background) pixels near depth discontinuities. It also provides a novel means for separating foreground and background objects (matting), without the use of a special blue screen. We formulate the problem as the recovery of colors and opacities in a generalized 3-D (x, y, d) disparity space, and solve the problem using a combination of initial evidence aggregation followed by iterative energy minimization.