Optimal Transport for Diffeomorphic Registration

Feydy, Jean; Charlier, Benjamin; Vialard, François-Xavier; Peyré, Gabriel

doi:10.1007/978-3-319-66182-7_34

Cited by 77 publications

(81 citation statements)

References 11 publications

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“…The theory of OT seeks the most feasible way to redistribute mass from one given distribution to another while minimizing the associated cost of transportation ( [9], [12]). OT has been used for registration and connectivity analysis of brain white matter [7], image morphing [4], and has recently been extended to the case of measures of different total mass [2].…”

Section: Introductionmentioning

confidence: 99%

GlymphVIS: Visualizing Glymphatic Transport Pathways Using Regularized Optimal Transport

Elkin

Nadeem

Haber

et al. 2018

Medical Image Computing and Computer Assisted Intervention – MICCAI 2018

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The glymphatic system (GS) is a transit passage that facil-itates brain metabolic waste removal and its dysfunction has been asso-ciated with neurodegenerative diseases such as Alzheimer’s disease. The GS has been studied by acquiring temporal contrast enhanced magnetic resonance imaging (MRI) sequences of a rodent brain, and tracking the cerebrospinal fluid injected contrast agent as it flows through the GS. We present here a novel visualization framework, GlymphVIS, which uses regularized optimal transport (OT) to study the flow behavior between time points at which the images are taken. Using this regularized OT app-roach, we can incorporate diffusion, handle noise, and accurately capture and visualize the time varying dynamics in GS transport. Moreover, we are able to reduce the registration mean-squared and infinity-norm error across time points by up to a factor of 5 as compared to the current state-of-the-art method. Our visualization pipeline yields flow patterns that align well with experts’ current findings of the glymphatic system.

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Section: Introductionmentioning

confidence: 99%

GlymphVIS: Visualizing Glymphatic Transport Pathways Using Regularized Optimal Transport

Elkin

Nadeem

Haber

et al. 2018

Medical Image Computing and Computer Assisted Intervention – MICCAI 2018

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“…Since δq and p are absolutely continuous, t → (p t | δq t ) is also absolutely continuous. We deduce from the expressions ofq t ,ṗ t , and δq t given by equations (20), (21), and (18) that…”

Section: Expression Of the Gradientmentioning

confidence: 99%

“…However, this reserve of mass can only be used at the ends of a geodesic path. In a recent work, Feydy et al [20] use unbalanced regularized optimal transport methods as a fidelity term for diffeomorphic registration purpose.…”

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confidence: 99%

Estimation of a growth development with partial diffeomorphic mappings

Kaltenmark

Trouvé

2018

Quart. Appl. Math.

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In the field of computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has proved to be highly efficient for addressing the problem of modeling and analyzing of the variability of populations of shapes, allowing for the direct comparison and quantization of diffeomorphic morphometric changes. However, with the progress achieved in medical imaging analysis, the interest for longitudinal data set has substantially increased in the last years and requires the processing of more complex changes, which especially appear during growth or aging phenomena. The observed organisms are subject to transformations over time that are no longer diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material. The evolution of the shape can then be described by the joint action of a deformation process and a creation process.In this paper, we extend the LDDMM framework to address the problem of non diffeomorphic structural variations in longitudinal data. We keep the geometric central concept of a group of deformations acting on embedded shapes. The need for partial mappings leads to a timevarying dynamic that modifies the action of the group of deformations. We develop a theoretical framework and two algorithms to estimate realistic individual growth scenarios from a set of observations sparsely distributed in time. We present few numerical experiments on animal horns where the shapes are modeled by oriented varifolds. Each computed scenario is parametrized by low-dimensional variables providing the support for statistical analysis.

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“…Contribution. At MICCAI 2017, we introduced the theory of Optimal Transport to the medical imaging community [5]. Leveraging the ideas and algorithms presented in [11], we showed that using globally optimal spring systems to drive a registration routine is tractable, and improves the robustness of pipelines to large deformations.…”

Section: Introductionmentioning

confidence: 99%

Global Divergences Between Measures: From Hausdorff Distance to Optimal Transport

Feydy¹,

Trouvé²

2018

Shape in Medical Imaging

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The data fidelity term is a key component of shape registration pipelines: computed at every step, its gradient is the vector field that drives a deformed model towards its target. Unfortunately, most classical formulas are at most semi-local: their gradients saturate and stop being informative above some given distance, with appalling consequences on the robustness of shape analysis pipelines. In this paper, we build on recent theoretical advances on Sinkhorn entropies and divergences [6] to present a unified view of three fidelities between measures that alleviate this problem: the Energy Distance from statistics; the (weighted) Hausdorff distance from computer graphics; the Wasserstein distance from Optimal Transport theory. The ε-Hausdorff and ε-Sinkhorn divergences are positive fidelities that interpolate between these three quantities, and we implement them through efficient, freely available GPU routines. They should allow the shape analyst to handle large deformations without hassle.

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Optimal Transport for Diffeomorphic Registration

Cited by 77 publications

References 11 publications

GlymphVIS: Visualizing Glymphatic Transport Pathways Using Regularized Optimal Transport

GlymphVIS: Visualizing Glymphatic Transport Pathways Using Regularized Optimal Transport

Estimation of a growth development with partial diffeomorphic mappings

Global Divergences Between Measures: From Hausdorff Distance to Optimal Transport

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