87 research outputs found
Large Deformation Diffeomorphic Metric Mapping And Fast-Multipole Boundary Element Method Provide New Insights For Binaural Acoustics
This paper describes how Large Deformation Diffeomorphic Metric Mapping
(LDDMM) can be coupled with a Fast Multipole (FM) Boundary Element Method (BEM)
to investigate the relationship between morphological changes in the head,
torso, and outer ears and their acoustic filtering (described by Head Related
Transfer Functions, HRTFs). The LDDMM technique provides the ability to study
and implement morphological changes in ear, head and torso shapes. The FM-BEM
technique provides numerical simulations of the acoustic properties of an
individual's head, torso, and outer ears. This paper describes the first
application of LDDMM to the study of the relationship between a listener's
morphology and a listener's HRTFs. To demonstrate some of the new capabilities
provided by the coupling of these powerful tools, we examine the classical
question of what it means to ``listen through another individual's outer
ears.'' This work utilizes the data provided by the Sydney York Morphological
and Acoustic Recordings of Ears (SYMARE) database.Comment: Submitted as a conference paper to IEEE ICASSP 201
Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets
International audienceA common approach for analysis of anatomical variability relies on the stimation of a template representative of the population. The Large Deformation Diffeomorphic Metric Mapping is an attractive framework for that purpose. However, template estimation using LDDMM is computationally expensive, which is a limitation for the study of large datasets. This paper presents an iterative method which quickly provides a centroid of the population in the shape space. This centroid can be used as a rough template estimate or as initialization of a template estimation method. The approach is evaluated on datasets of real and synthetic hippocampi segmented from brain MRI. The results show that the centroid is correctly centered within the population and is stable for different orderings of subjects. When used as an initialization, the approach allows to substantially reduce the computation time of template estimation
Craniofacial reconstruction as a prediction problem using a Latent Root Regression model
International audienceIn this paper, we present a computer-assisted method for facial reconstruction. This method provides an estimation of the facial shape associated with unidentified skeletal remains. Current computer-assisted methods using a statistical framework rely on a common set of extracted points located on the bone and soft-tissue surfaces. Most of the facial reconstruction methods then consist of predicting the position of the soft-tissue surface points, when the positions of the bone surface points are known. We propose to use Latent Root Regression for prediction. The results obtained are then compared to those given by Principal Components Analysis linear models. In conjunction, we have evaluated the influence of the number of skull landmarks used. Anatomical skull landmarks are completed iteratively by points located upon geodesics which link these anatomical landmarks, thus enabling us to artificially increase the number of skull points. Facial points are obtained using a mesh-matching algorithm between a common reference mesh and individual soft-tissue surface meshes. The proposed method is validated in term of accuracy, based on a leave-one-out cross-validation test applied to a homogeneous database. Accuracy measures are obtained by computing the distance between the original face surface and its reconstruction. Finally, these results are discussed referring to current computer-assisted reconstruction facial techniques
Fast Template-based Shape Analysis using Diffeomorphic Iterative Centroid
International audienceA common approach for the analysis of anatomical variability relies on the estimation of a representative template of the population, followed by the study of this population based on the parameters of the deformations going from the template to the population. The Large Deformation Diffeomorphic Metric Mapping framework is widely used for shape analysis of anatomical structures, but computing a template with such framework is computationally expensive. In this paper we propose a fast approach for template-based analysis of anatomical variability. The template is estimated using a recently proposed iterative approach which quickly provides a centroid of the population. Statistical analysis is then performed using Kernel-PCA on the initial momenta that define the deformations between the centroid and each subject of the population. This approach is applied to the analysis of hippocampal shape on 80 patients with Alzheimer's Disease and 138 controls from the ADNI database
Modelling morphological variability of the hippocampus using manifold learning and large deformations
International audienceThe hippocampus is a structure of the temporal lobe of the brain which plays an important role in memory processes and in many neuropsychiatric disorders, including Alzheimer's disease, epilepsy and schizophrenia. Here, we present a method to infer the anatomical variability of the hippocampus, based on the LDDMM (Large Deformation Diffeomorphic Metric Mapping) framework and a manifold learning approach to capture the geometry of the population in the space of shapes
Constructing reparametrization invariant metrics on spaces of plane curves
Metrics on shape space are used to describe deformations that take one shape
to another, and to determine a distance between them. We study a family of
metrics on the space of curves, that includes several recently proposed
metrics, for which the metrics are characterised by mappings into vector spaces
where geodesics can be easily computed. This family consists of Sobolev-type
Riemannian metrics of order one on the space of
parametrized plane curves and the quotient space of unparametrized curves. For the space of open
parametrized curves we find an explicit formula for the geodesic distance and
show that the sectional curvatures vanish on the space of parametrized and are
non-negative on the space of unparametrized open curves. For the metric, which
is induced by the "R-transform", we provide a numerical algorithm that computes
geodesics between unparameterised, closed curves, making use of a constrained
formulation that is implemented numerically using the RATTLE algorithm. We
illustrate the algorithm with some numerical tests that demonstrate it's
efficiency and robustness.Comment: 27 pages, 4 figures. Extended versio
Soliton Dynamics in Computational Anatomy
Computational anatomy (CA) has introduced the idea of anatomical structures
being transformed by geodesic deformations on groups of diffeomorphisms. Among
these geometric structures, landmarks and image outlines in CA are shown to be
singular solutions of a partial differential equation that is called the
geodesic EPDiff equation. A recently discovered momentum map for singular
solutions of EPDiff yields their canonical Hamiltonian formulation, which in
turn provides a complete parameterization of the landmarks by their canonical
positions and momenta. The momentum map provides an isomorphism between
landmarks (and outlines) for images and singular soliton solutions of the
EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as
well as new data representation.Comment: published in NeuroImag
Joint T1 and Brain Fiber Log-Demons Registration Using Currents to Model Geometry
International audienceWe present an extension of the diffeomorphic Geometric Demons algorithm which combines the iconic registration with geometric constraints. Our algorithm works in the log-domain space, so that one can efficiently compute the deformation field of the geometry. We represent the shape of objects of interest in the space of currents which is sensitive to both location and geometric structure of objects. Currents provides a distance between geometric structures that can be defined without specifying explicit point-to-point correspondences. We demonstrate this framework by registering simultaneously T1 images and 65 fiber bundles consistently extracted in 12 subjects and compare it against non-linear T1, tensor, and multi-modal T1+ Fractional Anisotropy (FA) registration algorithms. Results show the superiority of the Log-domain Geometric Demons over their purely iconic counterparts
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