The variational particle-mesh method for matching curves

Diffeomorphic matching (only one of several names for this technique) is a technique for non-rigid registration of curves and surfaces in which the curve or surface is embedded in the flow of a time-series of vector fields. One seeks the flow between two topologically-equivalent curves or surfaces which minimises some metric defined on the vector fields, \emph{i.e.} the flow closest to the identity in some sense. In this paper, we describe a new particle-mesh discretisation for the evolution of the geodesic flow and the embedded shape. Particle-mesh algorithms are very natural for this problem because Lagrangian particles (particles moving with the flow) can represent the movement of the shape whereas the vector field is Eulerian and hence best represented on a static mesh. We explain the derivation of the method, and prove conservation properties: the discrete method has a set of conserved momenta corresponding to the particle-relabelling symmetry which converge to conserved quantities in the continuous problem. We also introduce a new discretisation for the geometric current matching condition of (Vaillant and Glaunes, 2005). We illustrate the method and the derived properties with numerical examples.Comment: I uploaded the wrong paper before! Here is the correct on

A Second Order Variational Approach For Diffeomorphic Matching Of 3D Surfaces

In medical 3D-imaging, one of the main goals of image registration is to accurately compare two observed 3D-shapes. In this dissertation, we consider optimal matching of surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. We first formulate, in an abstract setting, the optimal matching as an optimal control problem, where a vector field flow is sought to minimize a cost functional that consists of the kinetic energy and the matching quality. To make the problem computationally accessible, we then incorporate reproducing kernel Hilbert spaces with the Gaussian kernels and weighted sums of Dirac measures. We propose a second order method based the Bellman's optimality principle and develop a dynamic programming algorithm. We apply successfully the second order method to diffeomorphic matching of anterior leaflet and posterior leaflet snapshots. We obtain a quadratic convergence for data sets consisting of hundreds of points. To further enhance the computational efficiency for large data sets, we introduce new representations of shapes and develop a multi-scale method. Finally, we incorporate a stretching fraction in the cost function to explore the elastic model and provide a computationally feasible algorithm including the elasticity energy. The performance of the algorithm is illustrated by numerical results for examples from medical 3D-imaging of the mitral valve to reduce excessive contraction and stretching.Mathematics, Department o

Measuring Geodesic Distances on the Space of Bounded Diffeomorphisms

This paper considers the problem of measuring the differences between deformations. It is intende

Recalage non rigide et segmentation automatique d'images de perfusion du foie

Contexte médicale -- Revue de littérature -- Recalage avec contrainte d'incompressibilité -- Segmentation basée sur le recalage de grandes déformations -- Cadre de travail unifié et efficace -- Discussion générale

Measuring geodesic distances on the space of bounded diffeomorphisms

Manuscrito. -- 1 h.; papel; folio. -- Fondo Universidad de Salamanca; sección Claustros; serie Borradores de claustros. -- Buena conservación. -- Fechas: 09/09/1826

Groupwise non-rigid registration for automatic construction of appearance models of the human craniofacial complex for analysis, synthesis and simulation

Finally, a novel application of 3D appearance modelling is proposed: a faster than real-time algorithm for statistically constrained quasi-mechanical simulation. Experiments demonstrate superior realism, achieved in the proposed method by employing statistical appearance models to drive the simulation, in comparison with the comparable state-of-the-art quasi-mechanical approaches.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Groupwise non-rigid registration for automatic construction of appearance models of the human craniofacial complex for analysis, synthesis and simulation

Finally, a novel application of 3D appearance modelling is proposed: a faster than real-time algorithm for statistically constrained quasi-mechanical simulation. Experiments demonstrate superior realism, achieved in the proposed method by employing statistical appearance models to drive the simulation, in comparison with the comparable state-of-the-art quasi-mechanical approaches