The Fshape Framework for the Variability Analysis of Functional Shapes

Charlier, Benjamin; Charon, Nicolas; Trouvé, Alain

doi:10.1007/s10208-015-9288-2

Cited by 42 publications

(99 citation statements)

References 30 publications

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“…Of note, this work focuses on practical applications of the proposed multidirectional varifold representation for cortical surface registration. Although a theoretical proof of convergence as the one developed for functional varifolds in (Charlier and Trouvé, 2014, 2015) would be of interest to demonstrate, this sidesteps the main focus of our study.…”

Section: Proposed Strategies For Improving Varifold-based Corticalmentioning

confidence: 84%

Multidirectional and Topography-based Dynamic-scale Varifold Representations with Application to Matching Developing Cortical Surfaces

Rekik

Lin

et al. 2016

NeuroImage

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The human cerebral cortex is marked by great complexity as well as substantial dynamic changes during early postnatal development. To obtain a fairly comprehensive picture of its age-induced and/or disorder-related cortical changes, one needs to match cortical surfaces to one another, while maximizing their anatomical alignment. Methods that geodesically shoot surfaces into one another as currents (a distribution of oriented normals) and varifolds (a distribution of non-oriented normals) provide an elegant Riemannian framework for generic surface matching and reliable statistical analysis. However, both conventional current and varifold matching methods have two key limitations. First, they only use the normals of the surface to measure its geometry and guide the warping process, which overlooks the importance of the orientations of the inherently convoluted cortical sulcal and gyral folds. Second, the ‘conversion’ of a surface into a current or a varifold operates at a fixed scale under which geometric surface details will be neglected, which ignores the dynamic scales of cortical foldings. To overcome these limitations and improve varifold-based cortical surface registration, we propose two different strategies. The first strategy decomposes each cortical surface into its normal and tangent varifold representations, by integrating principal curvature direction field into the varifold matching framework, thus providing rich information of the orientation of cortical folding and better characterization of the complex cortical geometry. The second strategy explores the informative cortical geometric features to perform a dynamic-scale measurement of the cortical surface that depends on the local surface topography (e.g., principal curvature), thereby we introduce the concept of a topography-based dynamic-scale varifold. We tested the proposed varifold variants for registering 12 pairs of dynamically developing cortical surfaces from 0 to 6 months of age. Both variants improved the matching accuracy in terms of closeness to the target surface and the goodness of alignment with regional anatomical boundaries, when compared with three state-of-the-art methods: (1) diffeomorphic spectral matching, (2) conventional current-based surface matching, and (3) conventional varifold-based surface matching.

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Section: Proposed Strategies For Improving Varifold-based Corticalmentioning

confidence: 84%

Multidirectional and Topography-based Dynamic-scale Varifold Representations with Application to Matching Developing Cortical Surfaces

Rekik

Lin

et al. 2016

NeuroImage

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“…For instance, the development and aging of cortical thickness was shown to correspond to genetic organization patterns in (Fjell et al, 2015). Hence, learning to accurately predict longitudinal changes in brain multishapes would be of great clinical interest and will exhibit a nascent ability to learn more challenging shape evolution models, such as functional shapes (Charlier et al, 2014). Last, in our prediction framework, we assumed that the evolution of multishape at a vertex (or in an ROI) is independent of that at a remote vertex (or in other ROIs).…”

Section: Discussionmentioning

confidence: 99%

Joint prediction of longitudinal development of cortical surfaces and white matter fibers from neonatal MRI

Rekik

Yap

et al. 2017

NeuroImage

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The human brain can be modeled as multiple interrelated shapes (or a multishape), each for characterizing one aspect of the brain, such as the cortex and white matter pathways. Predicting the developing multishape is a very challenging task due to the contrasting nature of the developmental trajectories of the constituent shapes: smooth for the cortical surface and non-smooth for white matter tracts due to changes such as bifurcation. We recently addressed this problem and proposed an approach for predicting the multishape developmental spatiotemporal trajectories of infant brains based only on neonatal MRI data using a set of geometric, dynamic, and fiber-to-surface connectivity features. In this paper, we propose two key innovations to further improve the prediction of multishape evolution. First, for a more accurate cortical surface prediction, instead of simply relying on one neonatal atlas to guide the prediction of the multishape, we propose to use multiple neonatal atlases to build a spatially heterogeneous atlas using the multidirectional varifold representation. This individualizes the atlas by locally maximizing its similarity to the testing baseline cortical shape for each cortical region, thereby better representing the baseline testing cortical surface, which founds the multishape prediction process. Second, for temporally consistent fiber prediction, we propose to reliably estimate spatiotemporal connectivity features using low-rank tensor completion, thereby capturing the variability and richness of the temporal development of fibers. Experimental results confirm that the proposed variants significantly improve the prediction performance of our original multishape prediction framework for both cortical surfaces and fiber tracts shape at 3, 6, and 9 months of age. Our pioneering model will pave the way for learning how to predict the evolution of anatomical shapes with abnormal changes. Ultimately, devising accurate shape evolution prediction models that can help quantify and predict the severity of a brain disorder as it progresses will be of great aid in individualized treatment planning.

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“…Second, the initial and target surface may have different discretizations and even different topologies. Third, texture information can be incorporated into the varifold matching term similarly to the fshape framework [8,6]. .…”

Section: 4mentioning

confidence: 99%

Inexact Elastic Shape Matching in the Square Root Normal Field Framework

Bauer

Charon²,

Harms

2019

Lecture Notes in Computer Science

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This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel framework, which has several potential advantages over previous works. First, our variational formulation allows us to minimize over reparametrizations without discretizing the reparametrization group. Second, the objective function and gradient are easy to implement and efficient to evaluate numerically. Third, the initial and target surface may have different samplings and even different topologies. Fourth, texture can be incorporated as additional information in the matching term similarly to the fshape framework. We demonstrate the usefulness of this approach with several numerical examples of curves and surfaces.2010 Mathematics Subject Classification. 68U05, 49Q10, 58D10.

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The Fshape Framework for the Variability Analysis of Functional Shapes

Cited by 42 publications

References 30 publications

Multidirectional and Topography-based Dynamic-scale Varifold Representations with Application to Matching Developing Cortical Surfaces

Multidirectional and Topography-based Dynamic-scale Varifold Representations with Application to Matching Developing Cortical Surfaces

Joint prediction of longitudinal development of cortical surfaces and white matter fibers from neonatal MRI

Inexact Elastic Shape Matching in the Square Root Normal Field Framework

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