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19
A New Geometric Metric in the Space of Curves, and Applications to Tracking Deforming Objects by Prediction and Filtering
, 2010
"... We define a novel metric on the space of closed planar curves. According to this metric centroid translations, scale changes and deformations are orthogonal, and the metric is also invariant with respect to reparameterizations of the curve. The Riemannian structure that is induced on the space of cu ..."
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We define a novel metric on the space of closed planar curves. According to this metric centroid translations, scale changes and deformations are orthogonal, and the metric is also invariant with respect to reparameterizations of the curve. The Riemannian structure that is induced on the space of curves is a smooth Riemannian manifold, which is isometric to a classical wellknown manifold. As a consequence, geodesics and gradients of energies defined on the space can be computed using fast closedform formulas, and this has obvious benefits in numerical applications. The obtained Riemannian manifold of curves is apt to address complex problems in computer vision; one such example is the tracking of highly deforming objects. Previous works have assumed that the object deformation is smooth, which is realistic for the tracking problem, but most have restricted the deformation to belong to a finitedimensional group – such as affine motions – or to finitelyparameterized models. This is too restrictive for highly deforming objects such as the contour of a beating heart. We adopt the smoothness assumption implicit in previous work, but we lift the restriction to finitedimensional motions/deformations. We define a dynamical model in this Riemannian manifold of curves, and use it to perform filtering and prediction to infer and extrapolate not just the pose (a finitely parameterized quantity) of an object, but its deformation (an infinitedimensional quantity) as well. We illustrate these ideas using a simple firstorder dynamical model, and show that it can be effective even on data sets where existing methods fail. 1
Pressure image assimilation for atmospheric motion estimation
, 2008
"... Geophysical motion characterization and image sequence analysis are crucial issues for numerous scientific domains involved in the study of climate change, weather ..."
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Cited by 11 (4 self)
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Geophysical motion characterization and image sequence analysis are crucial issues for numerous scientific domains involved in the study of climate change, weather
An Optimal Control Approach for Deformable Registration
"... This paper addresses largedisplacementdiffeomorphic mapping registration from an optimal control perspective. This viewpoint leads to two complementary formulations. One approach requires the explicit computation of coordinate maps, whereas the other is formulated strictly in the image domain (thu ..."
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This paper addresses largedisplacementdiffeomorphic mapping registration from an optimal control perspective. This viewpoint leads to two complementary formulations. One approach requires the explicit computation of coordinate maps, whereas the other is formulated strictly in the image domain (thus making it also applicable to manifolds which require multiple coordinate charts). We discuss their intrinsic relation as well as the advantages and disadvantages of the two approaches. Further, we propose a novel formulation for unbiased image registration, which naturally extends to the case of timeseries of images. We discuss numerical implementation details and carefully evaluate the properties of the alternative algorithms. 1.
Stochastic level set dynamics to track closed curves through image data
 in "Journal of Mathematical Imaging and Vision", August 2013 [DOI : 10.1007/S1085101304641], http:// hal.inria.fr/hal00854420 20 Activity Report INRIA 2013
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2012: Stochastic uncertainty models for the luminance consistency assumption
 IEEE Trans. Image Processing
"... In this paper, a stochastic formulation of the brightness consistency used in many computer vision problems involving dynamic scenes (motion estimation or point tracking for instance) is proposed. Usually, this model which assumes that the luminance of a point is constant along its trajectory is exp ..."
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In this paper, a stochastic formulation of the brightness consistency used in many computer vision problems involving dynamic scenes (motion estimation or point tracking for instance) is proposed. Usually, this model which assumes that the luminance of a point is constant along its trajectory is expressed in a differential form through the total derivative of the luminance function. This differential equation links linearly the point velocity to the spatial and temporal gradients of the luminance function. However when dealing with images, the available informations only hold at discrete time and on a discrete grid. In this paper we formalize the image luminance as a continuous function transported by a flow known only up to some uncertainties related to such a discretization process. Relying on stochastic calculus, we define a formulation of the luminance function preservation in which these uncertainties are taken into account. From such a framework, it can be shown that the usual deterministic optical flow constraint equation corresponds to our stochastic evolution under some strong constraints. These constraints can be relaxed by imposing a weaker temporal assumption on the luminance function and also in introducing anisotropic intensitybased uncertainties. We in addition show that these uncertainties can be computed at each point of the image grid from the image data and provide hence meaningful information on the reliability of the motion estimates. To demonstrate the benefit of such a stochastic formulation of the brightness consistency assumption, we have considered a local least squares motion estimator relying on this new constraint. This new motion estimator improves significantly the quality of the results. I.
Continuous Tracking of Structures from an Image Sequence
, 2013
"... The paper describes an innovative approach to estimate velocity on an image sequence and simultaneously segment and track a given structure. It relies on the underlying dynamics ’ equations of the studied physical system. A data assimilation method is applied to solve evolution equations of image br ..."
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The paper describes an innovative approach to estimate velocity on an image sequence and simultaneously segment and track a given structure. It relies on the underlying dynamics ’ equations of the studied physical system. A data assimilation method is applied to solve evolution equations of image brightness, those of motion’s dynamics, and those of distance map modelling the tracked structures. Results are first quantified on synthetic data with comparison to groundtruth. Then, the method is applied on meteorological satellite acquisitions of a tropical cloud, in order to track this structure on the sequence. The outputs of the approach are the continuous estimation of both motion and structure’s boundary. The main advantage is that the method only relies on image data and on a rough segmentation of the structure at initial date. 1
Data Assimilation for Convective Cells Tracking on Meteorological Image Sequences
, 2011
"... This paper focuses on the tracking and analysis of convective clouds systems from Meteosat Second Generation images. The highly deformable nature of convective clouds, the complexity of the physic processes involved, but also the partially hidden measurements available from image data make difficult ..."
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This paper focuses on the tracking and analysis of convective clouds systems from Meteosat Second Generation images. The highly deformable nature of convective clouds, the complexity of the physic processes involved, but also the partially hidden measurements available from image data make difficult a direct use of conventional image analysis techniques for tasks of detection, tracking and characterization. In this paper, we face these issues using variational data assimilation tools. Such techniques enable to perform the estimation of an unknown state function according to a given dynamical model and to noisy and incomplete measurements. The system state we are setting in this study for the clouds representation is composed of two nested curves corresponding to the exterior frontiers of the clouds and to the interior coldest parts (core) of the convective clouds. Since no reliable simple dynamical model exists for such phenomena at the image grid scale, the dynamics on which we are relying has been directly defined from image based motion measurements and takes into account an uncertainty modeling of the curves dynamics along time. In addition to this assimilation technique, we show in appendix how each cell of the recovered clouds system can be labeled and associated to characteristic parameters (birth or death time, mean temperature, velocity, growth, etc.) of great interest for meteorologists.
velocity fields tracking
, 2008
"... A stochastic filtering technique for fluid flows ..."
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THEME Observation and Modeling for Environmental
"... IN PARTNERSHIP WITH: Institut national de recherche en sciences et technologies pour l’environnement et l’agriculture ..."
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IN PARTNERSHIP WITH: Institut national de recherche en sciences et technologies pour l’environnement et l’agriculture
Author manuscript, published in "Ninth Asian Conference on Computer Vision (ACCV 2009), Xi'an: China (2009)" Crowd Flow Characterization with Optimal Control Theory
, 2010
"... Abstract. Analyzing the crowd dynamics from video sequences is an open challenge in computer vision. Under a high crowd density assumption, we characterize the dynamics of the crowd flow by two related information: velocity and a disturbance potential which accounts for several elements likely to di ..."
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Abstract. Analyzing the crowd dynamics from video sequences is an open challenge in computer vision. Under a high crowd density assumption, we characterize the dynamics of the crowd flow by two related information: velocity and a disturbance potential which accounts for several elements likely to disturb the flow (the density of pedestrians, their interactions with the flow and the environment). The aim of this paper to simultaneously estimate from a sequence of crowded images those two quantities. While the velocity of the flow can be observed directly from the images with traditional techniques, this disturbance potential is far more trickier to estimate. We propose here to couple, through optimal control theory, a dynamical crowd evolution model with observations from the image sequence in order to estimate at the same time those two quantities from a video sequence. For this purpose, we derive a new and original continuum formulation of the crowd dynamics which appears to be well adapted to dense crowd video sequences. We demonstrate the efficiency of our approach on both synthetic and real crowd videos. 1