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

Diffeomorphic matching of distributions: A new approach for unlabelled point-sets and sub-manifolds matching

In the paper, we study the problem of optimal matching of two generalized functions (distributions) via a diffeomorphic transformation of the ambient space. In the particular case of discrete distributions (weighted sums of Dirac measures), we provide a new algorithm to compare two arbitrary unlabelled sets of points, and show that it behaves properly in limit of continuous distributions on submanifolds. As a consequence, the algorithm may apply to various matching problems, such as curve or surface matching (via a sub-sampling), or mixings of landmark and curve data. As the solution forbids high energy solutions, it is also robust towards addition of noise and the technique can be used for nonlinear projection of datasets. We present 2D and 3D experiments. 1

Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l'anatomie numérique

[Résumé en français] ce travail concerne plusieurs extensions de la théorie des appariements difféomorphiques introduite par Dupuis, Grenander, Miller, Trouvé et Younés pour l'étude quantitative de la variabilité anatomique. Il s'ouvre sur l'extension de la théorie au cas de difféomorphismes définis sur l'espace euclidien entier, et l'étude des noyaux reproduisants des espaces de champs de déformations. Le troisième chapitre étudie l'appariement de points sur la sphère. On introduit ensuite les notions d'appariement de mesures et de courants, permettant de traiter le cas de groupes de points non labellisés et de sous-variétés. Pour ces deux méthodes, des expériences sur des segmentations de surfaces corticales sont représentées. Le traitement de données réelles est rendu posible par l'utilisation de techniques numériques rapides, décrites à part. La thèse se termine par le développement d'un point de vue contrôle optimal pour des problèmes généraux d'appariement de courbes.PARIS13-BU Sciences (930792102) / SudocSudocFranceF

Morphological weighting improves individualized prediction of HRTF directivity patterns

In this work, we explore the potential for morphological weighting of different regions of the pinna (outer ear) to improve the prediction of acoustic directivity patterns associated with head-related transfer functions. Using a large deformation diffeomorphic metric mapping framework, we apply kernel principal component analysis to model the pinna morphology. Different regions of the pinna can be weighted differently prior to the kernel principal component analysis. By varying the weights applied to the various regions of the pinna, we begin to learn the relative importance of the various regions to the acoustic directivity of the ear as a function of frequency. The pinna is divided into nine parts comprising the helix, scaphoid fossa, triangular fossa, concha rim, cymba concha, cavum concha, conchal ridge, ear lobe, and back of the ear. Results indicate that weighting the conchal region (concha rim, cavum and cymba concha) improves the predicted acoustic directivity for frequency bands centered around 3 kHz, 7 kHz, 10 kHz and 13 kHz. Similarly, weighting the triangular and scaphoid fossa improves the prediction of acoustic directivity in frequency bands centered around 7 kHz, 13 kHz and 15.5 kHz

A controllability approach to shape identification

The main goal of this work is to discuss a controllability approach to the image matching/shape identification problem, an important issue in many applications, medical ones in particular. The matching problem is formulated as an approximate controllability problem involving a cost functional whose gradient is computed using an adjoint equation based methodology. The time discrete version of the image matching problem is also discussed in this work

Vestibular asymmetry as the cause of idiopathic scoliosis: a possible answer from Xenopus.

International audienceHuman idiopathic scoliosis is characterized by severe deformations of the spine and skeleton. The occurrence of vestibular-related deficits in these patients is well established but it is unclear whether a vestibular pathology is the common cause for the scoliotic syndrome and the gaze/posture deficits or if the latter behavioral deficits are a consequence of the scoliotic deformations. A possible vestibular origin was tested in the frog Xenopus laevis by unilateral removal of the labyrinthine endorgans at larval stages. After metamorphosis into young adult frogs, X-ray images and three-dimensional reconstructed micro-computer tomographic scans of the skeleton showed deformations similar to those of scoliotic patients. The skeletal distortions consisted of a curvature of the spine in the frontal and sagittal plane, a transverse rotation along the body axis and substantial deformations of all vertebrae. In terrestrial vertebrates, the initial postural syndrome after unilateral labyrinthectomy recovers over time and requires body weight-supporting limb proprioceptive information. In an aquatic environment, however, this information is absent. Hence, the lesion-induced asymmetric activity in descending spinal pathways and the resulting asymmetric muscular tonus persists. As a consequence the mostly cartilaginous skeleton of the frog tadpoles progressively deforms. Lack of limb proprioceptive signals in an aquatic environment is thus the element, which links the Xenopus model with human scoliosis because a comparable situation occurs during gestation in utero. A permanently imbalanced activity in descending locomotor/posture control pathways might be the common origin for the observed structural and behavioral deficits in humans as in the different animal models of scoliosis

Matching Sparse Sets of Cardiac Image Cross-sections Using Large Deformation Diffeomorphic Metric Mapping Algorithm

Cardiac disease is often associated with remodeling. Ventricular shape and function is influenced by this remodeling. Assessing left ventricular shape and motion at the population level requires establishing anatomical correspondence using registration based techniques