Parameterization-invariant shape comparisons of anatomical surfaces

Structural or/and functional MRI-based machine learning techniques for attention-deficit/hyperactivity disorder diagnosis: A systematic review and meta-analysis

BACKGROUND

The aim of this study was to investigate the diagnostic value of ML techniques based on sMRI or/and fMRI for ADHD.

METHODS

We conducted a comprehensive search (from database creation date to March 2024) for relevant English articles on sMRI or/and fMRI-based ML techniques for diagnosing ADHD. The pooled sensitivity, specificity, positive likelihood ratio (LR+), negative likelihood ratio (LR-), summary receiver operating characteristic (SROC) curve and area under the curve (AUC) were calculated to assess the diagnostic value of sMRI or/and fMRI-based ML techniques. The I2 test was used to assess heterogeneity and the source of heterogeneity was investigated by performing a meta-regression analysis. Publication bias was assessed using the Deeks funnel plot asymmetry test.

RESULTS

Forty-three studies were included in the systematic review, 27 of which were included in our meta-analysis. The pooled sensitivity and specificity of sMRI or/and fMRI-based ML techniques for the diagnosis of ADHD were 0.74 (95 % CI 0.65-0.81) and 0.75 (95 % CI 0.67-0.81), respectively. SROC curve showed that AUC was 0.81 (95 % CI 0.77-0.84). Based on these findings, the sMRI or/and fMRI-based ML techniques have relatively good diagnostic value for ADHD.

LIMITATIONS

Our meta-analysis specifically focused on ML techniques based on sMRI or/and fMRI studies. Since EEG-based ML techniques are also used for diagnosing ADHD, further systematic analyses are necessary to explore ML methods based on multimodal medical data.

CONCLUSION

sMRI or/and fMRI-based ML technique is a promising objective diagnostic method for ADHD.

4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered. Also, different deforming objects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus they need to be temporally aligned. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemannian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the [Formula: see text] metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates; (2) the computation of geodesics between 4D surfaces; (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces; and (4) the synthesis of random 4D surfaces. We demonstrate the performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

Classifying organisms and artefacts by their outline shapes

We often wish to classify objects by their shapes. Indeed, the study of shapes is an important part of many scientific fields, such as evolutionary biology, structural biology, image processing and archaeology. However, mathematical shape spaces are rather complicated and nonlinear. The most widely used methods of shape analysis, geometric morphometrics, treat the shapes as sets of points. Diffeomorphic methods consider the underlying curve rather than points, but have rarely been applied to real-world problems. Using a machine classifier, we tested the ability of several of these methods to describe and classify the shapes of a variety of organic and man-made objects. We find that one method, based on square-root velocity functions (SRVFs), outperforms all others, including a standard geometric morphometric method (eigenshapes), and that it is also superior to human experts using shape alone. When the SRVF approach is constrained to take account of homologous landmarks it can accurately classify objects of very different shapes. The SRVF method identifies a shortest path between shapes, and we show that this can be used to estimate the shapes of intermediate steps in evolutionary series. Diffeomorphic shape analysis methods, we conclude, now provide practical and effective solutions to many shape description and classification problems in the natural and human sciences.

LESA: Longitudinal Elastic Shape Analysis of Brain Subcortical Structures

Over the past 30 years, magnetic resonance imaging has become a ubiquitous tool for accurately visualizing the change and development of the brain's subcortical structures (e.g., hippocampus). Although subcortical structures act as information hubs of the nervous system, their quantification is still in its infancy due to many challenges in shape extraction, representation, and modeling. Here, we develop a simple and efficient framework of longitudinal elastic shape analysis (LESA) for subcortical structures. Integrating ideas from elastic shape analysis of static surfaces and statistical modeling of sparse longitudinal data, LESA provides a set of tools for systematically quantifying changes of longitudinal subcortical surface shapes from raw structure MRI data. The key novelties of LESA include: (i) it can efficiently represent complex subcortical structures using a small number of basis functions and (ii) it can accurately delineate the spatiotemporal shape changes of the human subcortical structures. We applied LESA to analyze three longitudinal neuroimaging data sets and showcase its wide applications in estimating continuous shape trajectories, building life-span growth patterns, and comparing shape differences among different groups. In particular, with the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, we found that the Alzheimer's Disease (AD) can significantly speed the shape change of ventricle and hippocampus from 60 to 75 years old compared with normal aging.

Elastic shape analysis of brain structures for predictive modeling of PTSD

It is well-known that morphological features in the brain undergo changes due to traumatic events and associated disorders such as post-traumatic stress disorder (PTSD). However, existing approaches typically offer group-level comparisons, and there are limited predictive approaches for modeling behavioral outcomes based on brain shape features that can account for heterogeneity in PTSD, which is of paramount interest. We propose a comprehensive shape analysis framework representing brain sub-structures, such as the hippocampus, amygdala, and putamen, as parameterized surfaces and quantifying their shape differences using an elastic shape metric. Under this metric, we compute shape summaries (mean, covariance, PCA) of brain sub-structures and represent individual brain shapes by their principal scores under a shape-PCA basis. These representations are rich enough to allow visualizations of full 3D structures and help understand localized changes. In order to validate the elastic shape analysis, we use the principal components (PCs) to reconstruct the brain structures and perform further evaluation by performing a regression analysis to model PTSD and trauma severity using the brain shapes represented via PCs and in conjunction with auxiliary exposure variables. We apply our method to data from the Grady Trauma Project (GTP), where the goal is to predict clinical measures of PTSD. The framework seamlessly integrates accurate morphological features and other clinical covariates to yield superior predictive performance when modeling PTSD outcomes. Compared to vertex-wise analysis and other widely applied shape analysis methods, the elastic shape analysis approach results in considerably higher reconstruction accuracy for the brain shape and reveals significantly greater predictive power. It also helps identify local deformations in brain shapes associated with PTSD severity.

Surface-Based Connectivity Integration: An atlas-free approach to jointly study functional and structural connectivity

There has been increasing interest in jointly studying structural connectivity (SC) and functional connectivity (FC) derived from diffusion and functional MRI. Previous connectome integration studies almost exclusively required predefined atlases. However, there are many potential atlases to choose from and this choice heavily affects all subsequent analyses. To avoid such an arbitrary choice, we propose a novel atlas-free approach, named Surface-Based Connectivity Integration (SBCI), to more accurately study the relationships between SC and FC throughout the intra-cortical gray matter. SBCI represents both SC and FC in a continuous manner on the white surface, avoiding the need for prespecified atlases. The continuous SC is represented as a probability density function and is smoothed for better facilitation of its integration with FC. To infer the relationship between SC and FC, three novel sets of SC-FC coupling (SFC) measures are derived. Using data from the Human Connectome Project, we introduce the high-quality SFC measures produced by SBCI and demonstrate the use of these measures to study sex differences in a cohort of young adults. Compared with atlas-based methods, this atlas-free framework produces more reproducible SFC features and shows greater predictive power in distinguishing biological sex. This opens promising new directions for all connectomics studies.

Computing Univariate Neurodegenerative Biomarkers with Volumetric Optimal Transportation: A Pilot Study

Changes in cognitive performance due to neurodegenerative diseases such as Alzheimer's disease (AD) are closely correlated to the brain structure alteration. A univariate and personalized neurodegenerative biomarker with strong statistical power based on magnetic resonance imaging (MRI) will benefit clinical diagnosis and prognosis of neurodegenerative diseases. However, few biomarkers of this type have been developed, especially those that are robust to image noise and applicable to clinical analyses. In this paper, we introduce a variational framework to compute optimal transportation (OT) on brain structural MRI volumes and develop a univariate neuroimaging index based on OT to quantify neurodegenerative alterations. Specifically, we compute the OT from each image to a template and measure the Wasserstein distance between them. The obtained Wasserstein distance, Wasserstein Index (WI) for short to specify the distance to a template, is concise, informative and robust to random noise. Comparing to the popular linear programming-based OT computation method, our framework makes use of Newton's method, which makes it possible to compute WI in large-scale datasets. Experimental results, on 314 subjects (140 Aβ + AD and 174 Aβ- normal controls) from the Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset, provide preliminary evidence that the proposed WI is correlated with a clinical cognitive measure (the Mini-Mental State Examination (MMSE) score), and it is able to identify group difference and achieve a good classification accuracy, outperforming two other popular univariate indices including hippocampal volume and entorhinal cortex thickness. The current pilot work suggests the application of WI as a potential univariate neurodegenerative biomarker.

Analysis of shape data: From landmarks to elastic curves

Proliferation of high-resolution imaging data in recent years has led to sub-stantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves. We provide an expository account of elastic shape analysis of parametric planar curves representing shapes of two-dimensional (2D) objects by discussing its differences, and its commonalities, to the landmark-based approach. Particular attention is accorded to the role of reparameterization of a curve, which in addition to rotation, scaling and translation, represents an important shape-preserving transformation of a curve. The transition to the curve-based approach moves the mathematical setting of shape analysis from finite-dimensional non-Euclidean spaces to infinite-dimensional ones. We discuss some of the challenges associated with the infinite-dimensionality of the shape space, and illustrate the use of geometry-based methods in the computation of intrinsic statistical summaries and in the definition of statistical models on a 2D imaging dataset consisting of mouse vertebrae. We conclude with an overview of the current state-of-the-art in the field.

Classification Accuracy of Neuroimaging Biomarkers in Attention-Deficit/Hyperactivity Disorder: Effects of Sample Size and Circular Analysis

BACKGROUND

Motivated by an inconsistency between reports of high diagnosis-classification accuracies and known heterogeneity in attention-deficit/hyperactivity disorder (ADHD), this study assessed classification accuracy in studies of ADHD as a function of methodological factors that can bias results. We hypothesized that high classification results in ADHD diagnosis are inflated by methodological factors.

METHODS

We reviewed 69 studies (of 95 studies identified) that used neuroimaging features to predict ADHD diagnosis. Based on reported methods, we assessed the prevalence of circular analysis, which inflates classification accuracy, and evaluated the relationship between sample size and accuracy to test if small-sample models tend to report higher classification accuracy, also an indicator of bias.

RESULTS

Circular analysis was detected in 15.9% of ADHD classification studies, lack of independent test set was noted in 13%, and insufficient methodological detail to establish its presence was noted in another 11.6%. Accuracy of classification ranged from 60% to 80% in the 59.4% of reviewed studies that met criteria for independence of feature selection, model construction, and test datasets. Moreover, there was a negative relationship between accuracy and sample size, implying additional bias contributing to reported accuracies at lower sample sizes.

CONCLUSIONS

High classification accuracies in neuroimaging studies of ADHD appear to be inflated by circular analysis and small sample size. Accuracies on independent datasets were consistent with known heterogeneity of the disorder. Steps to resolve these issues, and a shift toward accounting for sample heterogeneity and prediction of future outcomes, will be crucial in future classification studies in ADHD.

Mixture of Probabilistic Principal Component Analyzers for Shapes from Point Sets

Inferring a probability density function (pdf) for shape from a population of point sets is a challenging problem. The lack of point-to-point correspondences and the non-linearity of the shape spaces undermine the linear models. Methods based on manifolds model the shape variations naturally, however, statistics are often limited to a single geodesic mean and an arbitrary number of variation modes. We relax the manifold assumption and consider a piece-wise linear form, implementing a mixture of distinctive shape classes. The pdf for point sets is defined hierarchically, modeling a mixture of Probabilistic Principal Component Analyzers (PPCA) in higher dimension. A Variational Bayesian approach is designed for unsupervised learning of the posteriors of point set labels, local variation modes, and point correspondences. By maximizing the model evidence, the numbers of clusters, modes of variations, and points on the mean models are automatically selected. Using the predictive distribution, we project a test shape to the spaces spanned by the local PPCA's. The method is applied to point sets from: i) synthetic data, ii) healthy versus pathological heart morphologies, and iii) lumbar vertebrae. The proposed method selects models with expected numbers of clusters and variation modes, achieving lower generalization-specificity errors compared to state-of-the-art.

Numerical Inversion of SRNF Maps for Elastic Shape Analysis of Genus-Zero Surfaces

Recent developments in elastic shape analysis (ESA) are motivated by the fact that it provides a comprehensive framework for simultaneous registration, deformation, and comparison of shapes. These methods achieve computational efficiency using certain square-root representations that transform invariant elastic metrics into euclidean metrics, allowing for the application of standard algorithms and statistical tools. For analyzing shapes of embeddings of in , Jermyn et al. [1] introduced square-root normal fields (SRNFs), which transform an elastic metric, with desirable invariant properties, into the metric. These SRNFs are essentially surface normals scaled by square-roots of infinitesimal area elements. A critical need in shape analysis is a method for inverting solutions (deformations, averages, modes of variations, etc.) computed in SRNF space, back to the original surface space for visualizations and inferences. Due to the lack of theory for understanding SRNF maps and their inverses, we take a numerical approach, and derive an efficient multiresolution algorithm, based on solving an optimization problem in the surface space, that estimates surfaces corresponding to given SRNFs. This solution is found to be effective even for complex shapes that undergo significant deformations including bending and stretching, e.g., human bodies and animals. We use this inversion for computing elastic shape deformations, transferring deformations, summarizing shapes, and for finding modes of variability in a given collection, while simultaneously registering the surfaces. We demonstrate the proposed algorithms using a statistical analysis of human body shapes, classification of generic surfaces, and analysis of brain structures.

Shape Analysis with Hyperbolic Wasserstein Distance

Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise. Thus it has the potential for the 3D shape indexing and classification research. While the algorithms for computing Wasserstein distance have been extensively studied, most of them only work for genus-0 surfaces. This paper proposes a novel framework to compute Wasserstein distance between general topological surfaces with hyperbolic metric. The computational algorithms are based on Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram and the method is general and robust. We apply our method to study human facial expression, longitudinal brain cortical morphometry with normal aging, and cortical shape classification in Alzheimer's disease (AD). Experimental results demonstrate that our method may be used as an effective shape index, which outperforms some other standard shape measures in our AD versus healthy control classification study.

Conformal invariants for multiply connected surfaces: Application to landmark curve-based brain morphometry analysis

Landmark curves were widely adopted in neuroimaging research for surface correspondence computation and quantified morphometry analysis. However, most of the landmark based morphometry studies only focused on landmark curve shape difference. Here we propose to compute a set of conformal invariant-based shape indices, which are associated with the landmark curve induced boundary lengths in the hyperbolic parameter domain. Such shape indices may be used to identify which surfaces are conformally equivalent and further quantitatively measure surface deformation. With the surface Ricci flow method, we can conformally map a multiply connected surface to the Poincaré disk. Our algorithm provides a stable method to compute the shape index values in the 2D (Poincaré Disk) parameter domain. The proposed shape indices are succinct, intrinsic and informative. Experimental results with synthetic data and 3D MRI data demonstrate that our method is invariant under isometric transformations and able to detect brain surface abnormalities. We also applied the new shape indices to analyze brain morphometry abnormalities associated with Alzheimer' s disease (AD). We studied the baseline MRI scans of a set of healthy control and AD patients from the Alzheimer' s Disease Neuroimaging Initiative (ADNI: 30 healthy control subjects vs. 30 AD patients). Although the lengths of the landmarks in Euclidean space, cortical surface area, and volume features did not differ between the two groups, our conformal invariant based shape indices revealed significant differences by Hotelling' s T² test. The novel conformal invariant shape indices may offer a new sensitive biomarker and enrich our brain imaging analysis toolset for studying diagnosis and prognosis of AD.

A Bayesian framework for joint morphometry of surface and curve meshes in multi-object complexes

We present a Bayesian framework for atlas construction of multi-object shape complexes comprised of both surface and curve meshes. It is general and can be applied to any parametric deformation framework and to all shape models with which it is possible to define probability density functions (PDF). Here, both curve and surface meshes are modelled as Gaussian random varifolds, using a finite-dimensional approximation space on which PDFs can be defined. Using this framework, we can automatically estimate the parameters balancing data-terms and deformation regularity, which previously required user tuning. Moreover, it is also possible to estimate a well-conditioned covariance matrix of the deformation parameters. We also extend the proposed framework to data-sets with multiple group labels. Groups share the same template and their deformation parameters are modelled with different distributions. We can statistically compare the groups'distributions since they are defined on the same space. We test our algorithm on 20 Gilles de la Tourette patients and 20 control subjects, using three sub-cortical regions and their incident white matter fiber bundles. We compare their morphological characteristics and variations using a single diffeomorphism in the ambient space. The proposed method will be integrated with the Deformetrica software package, publicly available at www.deformetrica.org.

Covariant Image Representation with Applications to Classification Problems in Medical Imaging

Images are often considered as functions defined on the image domains, and as functions, their (intensity) values are usually considered to be invariant under the image domain transforms. This functional viewpoint is both influential and prevalent, and it provides the justification for comparing images using functional Lp -norms. However, with the advent of more advanced sensing technologies and data processing methods, the definition and the variety of images has been broadened considerably, and the long-cherished functional paradigm for images is becoming inadequate and insufficient. In this paper, we introduce the formal notion of covariant images and study two types of covariant images that are important in medical image analysis, symmetric positive-definite tensor fields and Gaussian mixture fields, images whose sample values covary i.e., jointly vary with image domain transforms rather than being invariant to them. We propose a novel similarity measure between a pair of covariant images considered as embedded shapes (manifolds) in the ambient space, a Cartesian product of the image and its sample-value domains. The similarity measure is based on matching the two embedded low-dimensional shapes, and both the extrinsic geometry of the ambient space and the intrinsic geometry of the shapes are incorporated in computing the similarity measure. Using this similarity as an affinity measure in a supervised learning framework, we demonstrate its effectiveness on two challenging classification problems: classification of brain MR images based on patients' age and (Alzheimer's) disease status and seizure detection from high angular resolution diffusion magnetic resonance scans of rat brains.

Medial Demons Registration Localizes The Degree of Genetic Influence Over Subcortical Shape Variability: An N= 1480 Meta-Analysis

We present a multi-cohort shape heritability study, extending the fast spherical demons registration to subcortical shapes via medial modeling. A multi-channel demons registration based on vector spherical harmonics is applied to medial and curvature features, while controlling for metric distortion. We registered and compared seven subcortical structures of 1480 twins and siblings from the Queensland Twin Imaging Study and Human Connectome Project: Thalamus, Caudate, Putamen, Pallidum, Hippocampus, Amygdala, and Nucleus Accumbens. Radial distance and tensor-based morphometry (TBM) features were found to be highly heritable throughout the entire basal ganglia and limbic system. Surface maps reveal subtle variation in heritability across functionally distinct parts of each structure. Medial Demons reveals more significantly heritable regions than two previously described surface registration methods. This approach may help to prioritize features and measures for genome-wide association studies.

A Riemannian Framework for Intrinsic Comparison of Closed Genus-Zero Shapes

We present a framework for intrinsic comparison of surface metric structures and curvatures. This work parallels the work of Kurtek et al. on parameterization-invariant comparison of genus zero shapes. Here, instead of comparing the embedding of spherically parameterized surfaces in space, we focus on the first fundamental form. To ensure that the distance on spherical metric tensor fields is invariant to parameterization, we apply the conjugation-invariant metric arising from the L2 norm on symmetric positive definite matrices. As a reparameterization changes the metric tensor by a congruent Jacobian transform, this metric perfectly suits our purpose. The result is an intrinsic comparison of shape metric structure that does not depend on the specifics of a spherical mapping. Further, when restricted to tensors of fixed volume form, the manifold of metric tensor fields and its quotient of the group of unitary diffeomorphisms becomes a proper metric manifold that is geodesically complete. Exploiting this fact, and augmenting the metric with analogous metrics on curvatures, we derive a complete Riemannian framework for shape comparison and reconstruction. A by-product of our framework is a near-isometric and curvature-preserving mapping between surfaces. The correspondence is optimized using the fast spherical fluid algorithm. We validate our framework using several subcortical boundary surface models from the ADNI dataset.

Bayesian Multiscale Modeling of Closed Curves in Point Clouds

Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model's latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a 'central curve' that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem.

Elastic shape analysis of cylindrical surfaces for 3D/2D registration in endometrial tissue characterization

We study the problem of joint registration and deformation analysis of endometrial tissue using 3D magnetic resonance imaging (MRI) and 2D trans-vaginal ultrasound (TVUS) measurements. In addition to the different imaging techniques involved in the two modalities, this problem is complicated due to: 1) different patient pose during MRI and TVUS observations, 2) the 3D nature of MRI and 2D nature of TVUS measurements, 3) the unknown intersecting plane for TVUS in MRI volume, and 4) the potential deformation of endometrial tissue during TVUS measurement process. Focusing on the shape of the tissue, we use expert manual segmentation of its boundaries in the two modalities and apply, with modification, recent developments in shape analysis of parametric surfaces to this problem. First, we extend the 2D TVUS curves to generalized cylindrical surfaces through replication, and then we compare them with MRI surfaces using elastic shape analysis. This shape analysis provides a simultaneous registration (optimal reparameterization) and deformation (geodesic) between any two parametrized surfaces. Specifically, it provides optimal curves on MRI surfaces that match with the original TVUS curves. This framework results in an accurate quantification and localization of the deformable endometrial cells for radiologists, and growth characterization for gynecologists and obstetricians. We present experimental results using semi-synthetic data and real data from patients to illustrate these ideas.

Multiple Atlas construction from a heterogeneous brain MR image collection

In this paper, we propose a novel framework for computing single or multiple atlases (templates) from a large population of images. Unlike many existing methods, our proposed approach is distinguished by its emphasis on the sharpness of the computed atlases and the requirement of rotational invariance. In particular, we argue that sharp atlas images that retain crucial and important anatomical features with high fidelity are more useful for many medical imaging applications when compared with the blurry and fuzzy atlas images computed by most existing methods. The geometric notion that underlies our approach is the idea of manifold learning in a quotient space, the quotient space of the image space by the rotations. We present an extension of the existing manifold learning approach to quotient spaces by using invariant metrics, and utilizing the manifold structure for partitioning the images into more homogeneous sub-collections, each of which can be represented by a single atlas image. Specifically, we propose a three-step algorithm. First, we partition the input images into subgroups using unsupervised or semi-supervised learning methods on manifolds. Then we formulate a convex optimization problem in each subgroup to locate the atlases and determine the crucial neighbors that are used in the realization step to form the template images. We have evaluated our algorithm using whole brain MR volumes from OASIS database. Experimental results demonstrate that the atlases computed using the proposed algorithm not only discover the brain structural changes in different age groups but also preserve important structural details and generally enjoy better image quality.

Elastic geodesic paths in shape space of parameterized surfaces

This paper presents a novel Riemannian framework for shape analysis of parameterized surfaces. In particular, it provides efficient algorithms for computing geodesic paths which, in turn, are important for comparing, matching, and deforming surfaces. The novelty of this framework is that geodesics are invariant to the parameterizations of surfaces and other shape-preserving transformations of surfaces. The basic idea is to formulate a space of embedded surfaces (surfaces seen as embeddings of a unit sphere in IR3) and impose a Riemannian metric on it in such a way that the reparameterization group acts on this space by isometries. Under this framework, we solve two optimization problems. One, given any two surfaces at arbitrary rotations and parameterizations, we use a path-straightening approach to find a geodesic path between them under the chosen metric. Second, by modifying a technique presented in [25], we solve for the optimal rotation and parameterization (registration) between surfaces. Their combined solution provides an efficient mechanism for computing geodesic paths in shape spaces of parameterized surfaces. We illustrate these ideas using examples from shape analysis of anatomical structures and other general surfaces.

Nonlinear analysis of actigraphic signals for the assessment of the attention-deficit/hyperactivity disorder (ADHD)

Attention-deficit/hyperactivity disorder (ADHD) is the most common neurobehavioral disorder in children and adolescents; however, its etiology is still unknown, which hinders the existence of reliable, fast and inexpensive standard diagnostic methods. In this paper, we propose a novel methodology for automatic diagnosis of the combined type of ADHD based on nonlinear signal processing of 24h-long actigraphic registries. Since it relies on actigraphy measurements, it constitutes an inexpensive and non-invasive objective diagnostic method. Our results on real data reach 96.77% sensitivity and 84.38% specificity by means of multidimensional classifiers driven by combined features from different time intervals. Our analysis also reveals that, if features from a single time interval are used, the whole 24-h interval is the only one that yields classification figures with practical diagnostic capabilities. Overall, our figures overcome those obtained by actigraphy-based methods reported and are comparable with others based on more expensive (and not so convenient) adquisition methods.

Topology preserving atlas construction from shape data without correspondence using sparse parameters

Statistical analysis of shapes, performed by constructing an atlas composed of an average model of shapes within a population and associated deformation maps, is a fundamental aspect of medical imaging studies. Usual methods for constructing a shape atlas require point correspondences across subjects, which are difficult in practice. By contrast, methods based on currents do not require correspondence. However, existing atlas construction methods using currents suffer from two limitations. First, the template current is not in the form of a topologically correct mesh, which makes direct analysis on shapes difficult. Second, the deformations are parametrized by vectors at the same location as the normals of the template current which often provides a parametrization that is more dense than required. In this paper, we propose a novel method for constructing shape atlases using currents where topology of the template is preserved and deformation parameters are optimized independently of the shape parameters. We use an L1-type prior that enables us to adaptively compute sparse and low dimensional parameterization of deformations. We show an application of our method for comparing anatomical shapes of patients with Down's syndrome and healthy controls, where the sparse parametrization of diffeomorphisms decreases the parameter dimension by one order of magnitude.