The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
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15 results for “LDDMM”
Cardiac motion modeling using LDDMM and shape splines.
problem Difficulties in probing cardiac function due to shape and deformation interactions.
method LDDMM framework, parallel transport, normalization, shape splines.
result Significant differences in model parameters between pathologies, revealing insights into disease dynamics.
The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant…
LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamicsstat.ML
Generative model learns shape drift for quantifying domain uncertainty in hemodynamics.
problem Quantifying domain uncertainty in medical image segmentation for biomarker estimation.
method Conditional stochastic interpolant framework based on LDDMM registration.
result Generative model can create random perturbations of shapes for biomarker estimation.
These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.
New method uses image registration to recover complex signals from amplitude data.
problem Recovering complex-valued signals from amplitude measurements.
method Indirect registration using LDDMM formalism with exterior calculus.
result Algorithm performs well under various conditions including noise and topology.
Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphismscs.CV
We present a method for metric optimization in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, by treating the induced Riemannian metric on the space of diffeomorphisms as a kernel in a machine learning context. For simplicity, we choose the kernel Fischer Linear Discriminant Analysis (KLDA) as th…
New method for partial matching of shapes with Varifolds.
problem Matching structures with topological or shape differences.
method Varifold shape representation and LDDMM framework.
result Effective partial matching despite topological differences.
Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, appl…
The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.
problem Modeling smooth, invertible transformations between shapes using Lie groups and diffeomorphisms.
method Develops a registration model that decouples the actions of Lie groups and diffeomorphisms, using semidirect products and right-invariant sub-Riemannian structures.
result Joint optimization over both deformation groups improves registration accuracy and disentangles contributions.
In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…
Study characterizes bladder motion using dynamic MRI and statistical analysis.
problem Limited volume coverage in dynamic MRI sequences hinders 3D shape reconstruction.
method 3D dense velocity measurements, LDDMM framework, statistical characterization, mean curvature changes, surface deformation analysis.
result Stable shape descriptor for characterizing bladder surface dynamics.
Prediction of the progression of subcortical brain structures in Alzheimer's disease from baselinecs.CV
We propose a method to predict the subject-specific longitudinal progression of brain structures extracted from baseline MRI, and evaluate its performance on Alzheimer's disease data. The disease progression is modeled as a trajectory on a group of diffeomorphisms in the context of large deformation diffeomorphic metri…
Extended orbit model theory for shape analysis using graded group action framework.
problem Limitations of standard orbit model theory in shape analysis.
method Developed graded group action (GGA) framework with regularity conditions.
result Uniqueness result for momentum map trajectory in multi-scale shape spaces.
In this paper, we address the problem of orientation that naturally arises when representing shapes like curves or surfaces as currents. In the field of computational anatomy, the framework of currents has indeed proved very efficient to model a wide variety of shapes. However, in such approaches, orientation of shapes…