Multiple Shape Registration using Constrained Optimal Control

Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) only allow for the study of a single shape. In this paper, we introduce and discuss both a theoretical and practical setting for the simultaneous study of multiple shapes that are either stitched to one another or slide along a submanifold. The method is described within the optimal control formalism, and optimality conditions are given, together with the equations that are needed to implement augmented Lagrangian methods. Experimental results are provided for stitched and sliding surfaces

Predicting infant cortical surface development using a 4D varifold-based learning framework and local topography-based shape morphing

Longitudinal neuroimaging analysis methods have remarkably advanced our understanding of early postnatal brain development. However, learning predictive models to trace forth the evolution trajectories of both normal and abnormal cortical shapes remains broadly absent. To fill this critical gap, we pioneered the first prediction model for longitudinal developing cortical surfaces in infants using a spatiotemporal current-based learning framework solely from the baseline cortical surface. In this paper, we detail this prediction model and even further improve its performance by introducing two key variants. First, we use the varifold metric to overcome the limitations of the current metric for surface registration that was used in our preliminary study. We also extend the conventional varifold-based surface registration model for pairwise registration to a spatiotemporal surface regression model. Second, we propose a morphing process of the baseline surface using its topographic attributes such as normal direction and principal curvature sign. Specifically, our method learns from longitudinal data both the geometric (vertices positions) and dynamic (temporal evolution trajectories) features of the infant cortical surface, comprising a training stage and a prediction stage. In the training stage, we use the proposed varifold-based shape regression model to estimate geodesic cortical shape evolution trajectories for each training subject. We then build an empirical mean spatiotemporal surface atlas. In the prediction stage, given an infant, we select the best learnt features from training subjects to simultaneously predict the cortical surface shapes at all later timepoints, based on similarity metrics between this baseline surface and the learnt baseline population average surface atlas. We used a leave-one-out cross validation method to predict the inner cortical surface shape at 3, 6, 9 and 12 months of age from the baseline cortical surface shape at birth. Our method attained a higher prediction accuracy and better captured the spatiotemporal dynamic change of the highly folded cortical surface than the previous proposed prediction method

Structural Surface Mapping for Shape Analysis

Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing. This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications

Surface-Based Analysis on Shape and Fractional Anisotropy of White Matter Tracts in Alzheimer's Disease

10.1371/journal.pone.0009811PLoS ONE53

Regionally Specific White Matter Disruptions of Fornix and Cingulum in Schizophrenia

Limbic circuitry disruptions have been implicated in the psychopathology and cognitive deficits of schizophrenia, which may involve white matter disruptions of the major tracts of the limbic system, including the fornix and the cingulum. Our study aimed to investigate regionally specific abnormalities of the fornix and cingulum in schizophrenia using diffusion tensor imaging (DTI). We determined the fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD) profiles along the fornix and cingulum tracts using a fibertracking technique and a brain mapping algorithm, the large deformation diffeomorphic metric mapping (LDDMM), in the DTI scans of 33 patients with schizophrenia and 31 age-, gender-, and handedness-matched healthy controls. We found that patients with schizophrenia showed reduction in FA and increase in RD in bilateral fornix, and increase in RD in left anterior cingulum when compared to healthy controls. In addition, tract-based analysis revealed specific loci of these white matter differences in schizophrenia, that is, FA reductions and AD and RD increases occur in the region of the left fornix further from the hippocampus, FA reductions and RD increases occur in the rostral portion of the left anterior cingulum, and RD and AD increases occur in the anterior segment of the left middle cingulum. In patients with schizophrenia, decreased FA in the specific loci of the left fornix and increased AD in the right cingulum adjoining the hippocampus correlated with greater severity of psychotic symptoms. These findings support precise disruptions of limbic-cortical integrity in schizophrenia and disruption of these structural networks may contribute towards the neural basis underlying the syndrome of schizophrenia and clinical symptomatology

Learning task-optimal image registration with applications in localizing structure and function in the cerebral cortex

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 127-141).In medical image analysis, registration is necessary to establish spatial correspondences across two or more images. Registration is rarely the end-goal, but instead, the results of image registration are used in other tasks, such as voxel-based morphometry, functional group analysis, image segmentation and tracking. In this thesis, we argue that the quality of image registration should be evaluated in the context of the application. Consequently, we develop a framework for learning registration cost functions optimized for specific tasks. We demonstrate that by taking into account the application, we not only achieve better registration, but also potentially resolve certain ambiguities and ill-posed nature of image registration. We first develop a generative model for joint registration and segmentation of images. By jointly modeling registration and the application of image segmentation, we demonstrate improvements in parcellation of the cerebral cortex into different structural units. In this thesis, we work with spherical representations of the human cerebral cortex. Consequently, we develop a fast algorithm for registering spherical images. Application to the cortex shows that our algorithm achieves state-of-the-art accuracy, while being an order of magnitude faster than competing diffeomorphic, landmark-free algorithms. Finally, we consider the problem of automatically determining the "free" parameters of registration cost functions.(cont.) Registration is usually formulated as an optimization problem with multiple tunable parameters that are manually set. By introducing a second layer of optimization over and above the usual registration, this thesis provides the first effective approach to optimizing thousands of registration parameters to improve alignment of a new image as measured by an application-specific performance measure. Much previous work has been devoted to developing generic registration algorithms, which are then specialized to particular imaging modalities (e.g., MR), particular imaging targets (e.g., cardiac) and particular post- registration analyses (e.g., segmentation). Our framework provides a principled method for adapting generic algorithms to specific applications. For example, we estimate the optimal weights or cortical folding template of the generic weighted Sum of Squared Differences dissimilarity measure for localizing underlying cytoarchitecture and functional regions of the cerebral cortex. The generality of the framework suggests potential applications to other problems in science and engineering formulated as optimization problems.by B.T. Thomas Yeo.Ph.D

Proceedings of the Fourth International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Biological Shape Variability Modeling (MFCA 2013), Nagoya, Japan

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the first edition of this workshop in 2006, second edition in New-York in 2008, the third edition in Toronto in 2011, the forth edition was held in Nagoya Japan on September 22 2013

Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)