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

Construction of Bayesian Deformable Models via Stochastic Approximation Algorithm: A Convergence Study

The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is especially true in shape modelling in the computer vision community or in probabilistic atlas building for Computational Anatomy (CA). A first coherent statistical framework modelling the geometrical variability as hidden variables has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the problem in a Bayesian context they proved the consistency of the MAP estimator and provided a simple iterative deterministic algorithm with an EM flavour leading to some reasonable approximations of the MAP estimator under low noise conditions. In this paper we present a stochastic algorithm for approximating the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence to a critical point of the observed likelihood with an illustration on images of handwritten digits

Shape deformation analysis from the optimal control viewpoint

A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we provide a new general approach to shape deformation analysis, within the framework of optimal control theory, in which a deformation is represented as the flow of diffeomorphisms generated by time-dependent vector fields. Using reproducing kernel Hilbert spaces of vector fields, the general shape deformation analysis problem is specified as an infinite-dimensional optimal control problem with state and control constraints. In this problem, the states are diffeomorphisms and the controls are vector fields, both of them being subject to some constraints. The functional to be minimized is the sum of a first term defined as geometric norm of the control (kinetic energy of the deformation) and of a data attachment term providing a geometric distance to the target shape. This point of view has several advantages. First, it allows one to model general constrained shape analysis problems, which opens new issues in this field. Second, using an extension of the Pontryagin maximum principle, one can characterize the optimal solutions of the shape deformation problem in a very general way as the solutions of constrained geodesic equations. Finally, recasting general algorithms of optimal control into shape analysis yields new efficient numerical methods in shape deformation analysis. Overall, the optimal control point of view unifies and generalizes different theoretical and numerical approaches to shape deformation problems, and also allows us to design new approaches. The optimal control problems that result from this construction are infinite dimensional and involve some constraints, and thus are nonstandard. In this article we also provide a rigorous and complete analysis of the infinite-dimensional shape space problem with constraints and of its finite-dimensional approximations

Multiple Shape Registration using Constrained Optimal Control

Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) only allow for the study of a single shape. In this paper, we introduce and discuss both a theoretical and practical setting for the simultaneous study of multiple shapes that are either stitched to one another or slide along a submanifold. The method is described within the optimal control formalism, and optimality conditions are given, together with the equations that are needed to implement augmented Lagrangian methods. Experimental results are provided for stitched and sliding surfaces

Degrés de connaissance littéraire

Plaisir de lire et plaisir de connaître s’enrichissent mutuellement dans l’expérience littéraire. Si l’expérience littéraire, comme toute expérience esthétique, est d’abord associative, linéaire, horizontale, et paraît distincte de la connaissance par concepts, de type vertical (Schaeffer), elle peut aussi ouvrir la voie à une connaissance de troisième degré, connaissance de l’autre comme sujet ou comme relation subjective au monde. Tel est notamment le cas lorsque l’expérience littéraire prend la forme de la lecture littéraire et de son corollaire, le texte de lecture. Ce degré de la connaissance prend appui sur la faculté de juger réfléchissante telle qu’elle semble analysée dans la troisième Critique de Kant : contrairement à la vulgate kantienne qui en souligne la dimension anti-conceptuelle, la faculté de juger réfléchissante est ici envisagée comme fonction régulatrice susceptible de dépasser l’antinomie de l’objectif et du subjectif.In literary experience the pleasure of reading and the pleasure of knowing are mutually enriching. Even if literary experience, like all aesthetic experience, is first of all associative, linear and horizontal, and appears to be distinct from knowledge by concepts, of the vertical type (Schaeffer), it may also open up the way to knowledge of the third degree, that is knowledge of the other as subject or as subjective relation to the world. Such is the case in particular when literary experience takes the shape of literary reading and of its corollary, the reader’s own reformulation of the text. This degree of knowledge leans on the reflective faculty of judgment as it seems to be analyzed in Kant’s third “Critique”: contrary to the Kantian vulgate which underlines its anti-conceptual dimension, the reflective faculty of judgment is viewed here as a governing function likely to go beyond the antinomy of the objective and the subjective

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