We consider Large Deformation Diffeomorphic Metric Mapping of general m-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of thi...

We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinitedimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X/F is infinite-dimensional, then X and X \ F are real-analytic diffeom...

In this paper, we present a free-form deformation (FFD) approach to manipulate point-sampled surface. Our approach provides users the powerful free-form deformation directly on point-sampled surface. In the preprocessing, we use a robust extension of hierarchical clustering scheme to partition a point-sampled model into clusters, fit a moving least square (MLS) surface to each of them, and defi...

Abstract. To achieve sparse parametrizations that allows intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the LDDMM registration framework. While the zeroth ...

First Fit Decreasing is a classical bin packing algorithm: the items are ordered into their nonincreasing order, and then in this order the next item is always packed into the first bin where it fits. For an instance I let FFD(I) and OPT (I) denote the number of the used bins by algorithm FFD, and an optimal algorithm, respectively. We show in this paper that FFD(I) ≤ 11/9OPT (I) + 6/9, (1) and...

Computing a template in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework is a key step for the study of large databases of anatomical surfaces, but can lead to very computationally expensive algorithms in the case of large databases. Here we present an iterative method to compute a better initialization for the template estimation method proposed in [1]. The method provides ...

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. Cardiac magnetic resonance imaging (MRI) provides detailed quantitative data about cardiac function and geometry. Cardiac MRI ...

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 di↵eomorphisms in the context of large deformation di↵eomorphic metric mapping (LDDMM). We first exhibit the limited predictive abilities of geodesi...

A previous paper described an algorithm for accurate B-spline free-form deformation of polygonal objects to produce triangular Bézier patches. However that algorithm computed the control points of resulting patches using a generalized de Casteljau algorithm, which is expensive to compute. In this short note, we describe an algorithm that instead uses polynomial interpolation; both theoretical a...

In this paper, we propose an image registration algorithm named statistically-based FFD registration (SFFD). This registration method is a modification of a well-known free-form deformations (FFD) approach. Our framework dramatically reduces the number of parameters to optimise and only needs to perform a single-resolution optimisation to account for coarse and fine local displacements, in cont...