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This paper proposes to use the Laplace-Beltrami spectrum (LBS) as a global shape descriptor for medical shape analysis, allowing for shape comparisons using minimal shape preprocessing: no registration, mapping, or remeshing is necessary. The discriminatory power of the method is tested on a population of female caudate shapes of normal control subjects and of subjects with schizotypal personality disorder.

This paper introduces an outlier rejection and signal reconstruction method for high angular resolution diffusion weighted imaging. The approach is based on the thresholding of Laplacian measurements over the sphere of the apparent diffusion coefficient profiles defined for a given set of gradient directions. Exemplary results are presented.

Registration of images with pathologies is challenging due to tissue appearance changes and missing correspondences caused by the pathologies. Moreover, mass effects as observed for brain tumors may displace tissue, creating larger deformations over time than what is observed in a healthy brain. Deep learning models have successfully been applied to image registration to offer dramatic speed up and to use surrogate information (e.g., segmentations) during training. However, existing approaches focus on learning registration models using images from healthy patients. They are therefore not designed for the registration of images with strong pathologies for example in the context of brain tumors, and traumatic brain injuries. In this work, we explore a deep learning approach to register images with brain tumors to an atlas. Our model learns an appearance mapping from images with tumors to the atlas, while simultaneously predicting the transformation to atlas space. Using separate decoders, the network disentangles the tumor mass effect from the reconstruction of quasi-normal images. Results on both synthetic and real brain tumor scans show that our approach outperforms cost function masking for registration to the atlas and that reconstructed quasi-normal images can be used for better longitudinal registrations.

Deep learning (DL) approaches are state-of-the-art for many medical image segmentation tasks. They offer a number of advantages: they can be trained for specific tasks, computations are fast at test time, and segmentation quality is typically high. In contrast, previously popular multi-atlas segmentation (MAS) methods are relatively slow (as they rely on costly registrations) and even though sophisticated label fusion strategies have been proposed, DL approaches generally outperform MAS. In this work, we propose a DL-based label fusion strategy (VoteNet) which locally selects a set of reliable atlases whose labels are then fused via plurality voting. Experiments on 3D brain MRI data show that by selecting a good initial atlas set MAS with VoteNet significantly outperforms a number of other label fusion strategies as well as a direct DL segmentation approach. We also provide an experimental analysis of the upper performance bound achievable by our method. While unlikely achievable in practice, this bound suggests room for further performance improvements. Lastly, to address the runtime disadvantage of standard MAS, all our results make use of a fast DL registration approach.

Registering brain magnetic resonance imaging (MRI) scans containing pathologies is challenging primarily due to large deformations caused by the pathologies, leading to missing correspondences between scans. However, the registration task is important and directly related to personalized medicine, as registering between baseline pre-operative and post-recurrence scans may allow the evaluation of tumor infiltration and recurrence. While many registration methods exist, most of them do not specifically account for pathologies. Here, we propose a framework for the registration of longitudinal image-pairs of individual patients diagnosed with glioblastoma. Specifically, we present a combined image registration/reconstruction approach, which makes use of a patient-specific principal component analysis (PCA) model of image appearance to register baseline pre-operative and post-recurrence brain tumor scans. Our approach uses the post-recurrence scan to construct a patient-specific model, which then guides the registration of the pre-operative scan. Quantitative and qualitative evaluations of our framework on 10 patient image-pairs indicate that it provides excellent registration performance without requiring (1) any human intervention or (2) prior knowledge of tumor location, growth or appearance.

The plethora of data from neuroimaging studies provide a rich opportunity to discover effects and generate hypotheses through exploratory data analysis. Brain pathologies often manifest in changes in shape along with deterioration and alteration of brain matter, i.e., changes in mass. We propose a morphometry approach using unbalanced optimal transport that detects and localizes changes in mass and separates them from changes due to the location of mass. The approach generates images of mass allocation and mass transport cost for each subject in the population. Voxelwise correlations with clinical variables highlight regions of mass allocation or mass transfer related to the variables. We demonstrate the method on the white and gray matter segmentations from the OASIS brain MRI data set. The separation of white and gray matter ensures that optimal transport does not transfer mass between different tissues types and separates gray and white matter related changes. The OASIS data set includes subjects ranging from healthy to mild and moderate dementia, and the results corroborate known pathology changes related to dementia that are not discovered with traditional voxel-based morphometry. The transport-based morphometry increases the explanatory power of regression on clinical variables compared to traditional voxel-based morphometry, indicating that transport cost and mass allocation images capture a larger portion of pathology induced changes.

This paper proposes an approach to improve atlas-to-image registration accuracy with large pathologies. Instead of directly registering an atlas to a pathological image, the method learns a mapping from the pathological image to a quasi-normal image, for which more accurate registration is possible. Specifically, the method uses a deep variational convolutional encoder-decoder network to learn the mapping. Furthermore, the method estimates local mapping uncertainty through network inference statistics and uses those estimates to down-weight the image registration similarity measure in areas of high uncertainty. The performance of the method is quantified using synthetic brain tumor images and images from the brain tumor segmentation challenge (BRATS 2015).

In this paper we propose a new method for shape analysis based on the depth-ordering of shapes. We use this depth-ordering to non-parametrically define depth with respect to a normal control population. This allows us to quantify differences with respect to "normality". We combine this approach with a permutation test allowing it to test for localized shape differences. The method is evaluated on a synthetically generated striatum dataset as well as on a real caudate dataset.

This paper develops a method for splines on diffeomorphisms for image regression. In contrast to previously proposed methods to capture image changes over time, such as geodesic regression, the method can capture more complex spatio-temporal deformations. In particular, it is a first step towards capturing periodic motions for example of the heart or the lung. Starting from a variational formulation of splines the proposed approach allows for the use of temporal control points to control spline behavior. This necessitates the development of a shooting formulation for splines. Experimental results are shown for synthetic and real data. The performance of the method is compared to geodesic regression.

Fusion between an endoscopic movie and a CT can aid specifying the tumor target volume for radiotherapy. That requires a deformable pharyngeal surface registration between a 3D endoscope reconstruction and a CT segmentation. In this paper, we propose to use local geometric features for deriving a set of initial correspondences between two surfaces, with which an association graph can be constructed for registration by spectral graph matching. We also define a new similarity measurement to provide a meaningful way for computing inter-surface affinities in the association graph. Our registration method can deal with large non-rigid anatomical deformation, as well as missing data and topology change. We tested the robustness of our method with synthetic deformations and showed registration results on real data.

Low-rank image decomposition has the potential to address a broad range of challenges that routinely occur in clinical practice. Its novelty and utility in the context of atlas-based analysis stems from its ability to handle images containing large pathologies and large deformations. Potential applications include atlas-based tissue segmentation and unbiased atlas building from data containing pathologies. In this paper we present atlas-based tissue segmentation of MRI from patients with large pathologies. Specifically, a healthy brain atlas is registered with the low-rank components from the input MRIs, the low-rank components are then re-computed based on those registrations, and the process is then iteratively repeated. Preliminary evaluations are conducted using the brain tumor segmentation challenge data (BRATS '12).

We consider geodesic regression with parametric time-warps. This allows for example, to capture saturation effects as typically observed during brain development or degeneration. While highly-flexible models to analyze time-varying image and shape data based on generalizations of splines and polynomials have been proposed recently, they come at the cost of substantially more complex inference. Our focus in this paper is therefore to keep the model and its inference as simple as possible while allowing to capture expected biological variation. We demonstrate that by augmenting geodesic regression with parametric time-warp functions, we can achieve comparable flexibility to more complex models while retaining model simplicity. In addition, the time-warp parameters provide useful information of underlying anatomical changes as demonstrated for the analysis of corpora callosa and rat calvariae. We exemplify our strategy for shape regression on the Grassmann manifold, but note that the method is generally applicable for time-warped geodesic regression.

Magnetic resonance (MR) imaging has been demonstrated to be very useful for clinical diagnosis of Alzheimer's disease (AD). A common approach to using MR images for AD detection is to spatially normalize the images by non-rigid image registration, and then perform statistical analysis on the resulting deformation fields. Due to the high nonlinearity of the deformation field, recent studies suggest to use initial momentum instead as it lies in a linear space and fully encodes the deformation field. In this paper we explore the use of initial momentum for image classification by focusing on the problem of AD detection. Experiments on the public ADNI dataset show that the initial momentum, together with a simple sparse coding technique-locality-constrained linear coding (LLC)--can achieve a classification accuracy that is comparable to or even better than the state of the art. We also show that the performance of LLC can be greatly improved by introducing proper weights to the codebook.

Anatomical changes like brain atrophy or growth are usually not homogeneous in space and across spatial scales, since they map differently depending on the anatomical structures. Thus, the accurate analysis of volume changes from medical images requires to reliably localize and distinguish the spatial changes occurring at different scales, from voxel to regional level. We propose here a framework for the sparse probabilistic scale-space analysis of volume changes encoded by deformations. Our framework is based on the Helmoltz decomposition of vector fields. By scale-space analysis of the scalar pressure map associated to the irrotational component of the deformation, we robustly identify the areas of maximal volume changes, and we define a consistent sparse decomposition of the irrotational component. We show the effectiveness of our framework in the challenging problem of detecting the progression of tumor growth, and in the group-wise analysis of the longitudinal atrophy in Alzheimer's disease.

Atlas-building from population data is widely used in medical imaging. However, the emphasis of atlas-building approaches is typically to compute a mean / median shape or image based on population data. In this work, we focus on the statistical characterization of the population data, once spatial alignment has been achieved. We introduce and propose the use of the weighted functional boxplot. This allows the generalization of concepts such as the median, percentiles, or outliers to spaces where the data objects are functions, shapes, or images, and allows spatio-temporal atlas-building based on kernel regression. In our experiments, we demonstrate the utility of the approach to construct statistical atlases for pediatric upper airways and corpora callosa revealing their growth patterns. Furthermore, we show how such atlas information can be used to assess the effect of airway surgery in children.

An approach to study population differences in cerebral vasculature is proposed. This is done by (1) extending the concept of encoding cerebral blood vessel networks as spatial graphs and (2) quantifying graph similarity in a kernel-based discriminant classifier setup. We argue that augmenting graph vertices with information about their proximity to selected brain structures adds discriminative information and consequently leads to a more expressive encoding. Using graph-kernels then allows us to quantify graph similarity in a principled way. To demonstrate our approach, we assess the hypothesis that gender differences manifest as variations in the architecture of cerebral blood vessels, an observation that previously had only been tested and confirmed for the Circle of Willis. Our results strongly support this hypothesis, i.e, we can demonstrate non-trivial, statistically significant deviations from random gender classification in a cross-validation setup on 40 healthy patients.

We propose a robust multimodal dictionary learning method for multimodal images. Joint dictionary learning for both modalities may be impaired by lack of correspondence between image modalities in training data, for example due to areas of low quality in one of the modalities. Dictionaries learned with such non-corresponding data will induce uncertainty about image representation. In this paper, we propose a probabilistic model that accounts for image areas that are poorly corresponding between the image modalities. We cast the problem of learning a dictionary in presence of problematic image patches as a likelihood maximization problem and solve it with a variant of the EM algorithm. Our algorithm iterates identification of poorly corresponding patches and refinements of the dictionary. We tested our method on synthetic and real data. We show improvements in image prediction quality and alignment accuracy when using the method for multimodal image registration.

We seek to compute a diffeomorphic map between a pair of diffusion-weighted images under large deformation. Unlike existing techniques, our method allows any diffusion model to be fitted after registration for subsequent multifaceted analysis. This is achieved by directly aligning the diffusion-weighted images using a large deformation diffeomorphic registration framework formulated from an optimal control perspective. Our algorithm seeks the optimal coordinate mapping by simultaneously considering structural alignment, local fiber reorientation, and deformation regularization. Our algorithm also incorporates a multi-kernel strategy to concurrently register anatomical structures of different scales. We demonstrate the efficacy of our approach using in vivo data and report on detailed qualitative and quantitative results in comparison with several different registration strategies.

We propose a metamorphic geodesic regression approach approximating spatial transformations for image time-series while simultaneously accounting for intensity changes. Such changes occur for example in magnetic resonance imaging (MRI) studies of the developing brain due to myelination. To simplify computations we propose an approximate metamorphic geodesic regression formulation that only requires pairwise computations of image metamorphoses. The approximated solution is an appropriately weighted average of initial momenta. To obtain initial momenta reliably, we develop a shooting method for image metamorphosis.

Registration of Diffusion-weighted imaging (DWI) data emerges as an important topic in magnetic resonance (MR) image analysis. As existing methods are often designed for specific diffusion models, it is difficult to fit to the registered data different models other than the one used for registration. In this paper we describe a diffeomorphic registration algorithm for DWI data in a large deformation setting. Our method generates spatially normalized DWI data and it is thus possible to fit various diffusion models after registration for comparison purposes. Our algorithm includes (1) a reorientation component, where each diffusion profile (DWI signal as a function on a unit sphere) is decomposed, reoriented and recomposed to form the orientation-corrected DWI profile, and (2) a large deformation diffeomorphic registration component to ensure one-to-one mapping in a large-structural-variation scenario. In addition our algorithm uses a geodesic shooting mechanism to avoid the huge computational resources that are needed to register high-dimensional vector-valued data. We also incorporate into our algorithm a multi-kernel strategy where anatomical structures at different scales are considered simultaneously during registration. We demonstrate the efficacy of our method using in vivo data.

Longitudinal imaging studies are frequently used to investigate temporal changes in brain morphology. Image intensity may also change over time, for example when studying brain maturation. However, such intensity changes are not accounted for in image similarity measures for standard image registration methods. Hence, (i) local similarity measures, (ii) methods estimating intensity transformations between images, and (iii) metamorphosis approaches have been developed to either achieve robustness with respect to intensity changes or to simultaneously capture spatial and intensity changes. For these methods, longitudinal intensity changes are not explicitly modeled and images are treated as independent static samples. Here, we propose a model-based image similarity measure for longitudinal image registration in the presence of spatially non-uniform intensity change.

Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

This paper presents a method for automatic color and intensity normalization of digitized histology slides stained with two different agents. In comparison to previous approaches, prior information on the stain vectors is used in the estimation process, resulting in improved stability of the estimates. Due to the prevalence of hematoxylin and eosin staining for histology slides, the proposed method has significant practical utility. In particular, it can be used as a first step to standardize appearances across slides, that is very effective at countering effects due to differing stain amounts and protocols, and to slide fading. The approach is validated using synthetic experiments and 13 real datasets.

We present a continuous and convex formulation for Finsler active contours using seed regions or utilizing a regional bias term. The utilization of general Finsler metrics instead of Riemannian metrics allows the segmentation boundary to favor appropriate locations (e.g. with strong image discontinuities) and suitable directions (e.g. aligned with dark to bright image gradients). Strong edges are not required everywhere along the desired segmentation boundary due to incorporation of a regional bias. The resulting optimization procedure is simple and efficient, and leads to binary segmentation results regardless of the underlying continuous formulation. We demonstrate the proposed method in several examples.

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

In this paper, we present a novel approach for the segmentation of white matter tracts based on Finsler active contours. This technique provides an optimal measure of connectivity, explicitly segments the connecting fiber bundle, and is equipped with a metric which is able to utilize the directional information of high angular resolution data. We demonstrate the effectiveness of the algorithm for segmenting the cingulum bundle.

Individual white matter fibers cannot be resolved by current magnetic resonance (MR) technology. Many fibers of a fiber bundle will pass through an individual volume element (voxel). Individual visualized fiber tracts are thus the result of interpolation on a relatively coarse voxel grid, and an infinite number of them may be generated in a given volume by interpolation. This paper aims at creating a level set representation of a fiber bundle to describe this apparent continuum of fibers. It further introduces a coordinate system warped to the fiber bundle geometry, allowing for the definition of geometrically meaningful fiber bundle measures.