The matching problem between functional shapes via a BV-penalty term: a Γ\Gamma-convergence result

In this paper we study a variant of the matching model between functional shapes introduced in \cite{ABN}. Such a model allows to compare surfaces equipped with a signal and the matching energy is defined by the $L^2$-norm of the signal on the surface and a varifold-type attachment term. In this work we study the problem with fixed geometry which means that we optimize the initial signal (supported on the initial surface) with respect to a target signal supported on a different surface. In particular, we consider a $BV$ or $H^1$-penalty for the signal instead of its $L^2$-norm. Several numerical examples are shown in order to prove that the $BV$-penalty improves the quality of the matching. Moreover, we prove a $\Gamma$-convergence result for the discrete matching energy towards the continuous-one

Corticosterone and foraging behaviour in a pelagic seabird

Because endocrine mechanisms are thought to mediate behavioral responses to changes in the environment, examining these mechanisms is essential for understanding how long-lived seabirds adjust their foraging decisions to contrasting environmental conditions in order to maximize their fitness. In this context, the hormone corticosterone (CORT) deserves specific attention because of its major connections with locomotor activities. We examined for the first time the relationships between individual CORT levels and measurements of foraging success and behavior using satellite tracking and blood sampling from wandering albatrosses (Diomedea exulans) before (pretrip CORT levels) and after (posttrip CORT levels) foraging trips during the incubation period. Plasma CORT levels decreased after a foraging trip, and the level of posttrip CORT was negatively correlated with individual foraging success, calculated as total mass gain over a foraging trip. Pretrip CORT levels were not linked to time spent at sea but were positively correlated with daily distance traveled and maximum range at sea. In this study, we were able to highlight the sensitivity of CORT levels to variation in energy intake, and we showed for the first time that individual CORT levels can be explained by variation in foraging success. Relationships between pretrip CORT levels and daily distance traveled and maximum range were independent of pretrip body mass, suggesting that slight elevations in pretrip CORT levels might facilitate locomotor activity. However, because both foraging behavior and pretrip CORT levels could be affected by individual quality, future experimental studies including manipulation of CORT levels are needed to test whether CORT can mediate foraging decisions according to foraging conditions

Averaged Template Matching Equations

By exploiting an analogy with averaging procedures in fluid dynamics, we present a set of averaged template matching equations. These equations are analogs of the exact template matching equations that retain all the geometric properties associated with the diffeomorphismgrou p, and which are expected to average out small scale features and so should, as in hydrodynamics, be more computationally efficient for resolving the larger scale features. Froma geometric point of view, the new equations may be viewed as coming from a change in norm that is used to measure the distance between images. The results in this paper represent first steps in a longer termpro gram: what is here is only for binary images and an algorithm for numerical computation is not yet operational. Some suggestions for further steps to develop the results given in this paper are suggested

Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping

The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Polyrigid and Polyaffine Transformations: A New Class of Diffeomorphisms for Locally Rigid or Affine Registration

MICCAI 2003 Best Student Award in Image Processing and Visualization.International audienceOBJECTIVE: The goal of this work is to improve the usability of a non-rigid registration software for medical images. METHOD: We have built a registration grid service in order to use the interactivity of a visualization workstation and the computing power of a cluster. On the user side, the system is composed of a graphical interface that interacts in a complex and fluid manner with the registration software running on a remote cluster. CONCLUSION: Although the transmission of images back and forth between the computer running the user interface and the cluster running the registration service adds to the total registration time, it provides a user-friendly way of using the registration software without heavy infrastructure investments in hospitals. The system exhibits good performances even if the user is connected to the grid service through a low throughput network such as a wireless network interface or ADSL