Frédéric Barbaresco

Information Intrinsic Geometric Flows

Geometric Flow Theory is cross fertilized by diverse elements coming from Pure Mathematic and Mathematical Physic, but its foundation is mainly based on Riemannian Geometry, as explained by M. Berger in a recent panoramic view of this discipline, its extension to complex manifolds, the Erich Kahler’s Geometry, vaunted for its unabated vitality by J.P. Bourguignon, and Minimal Surface Theory. This paper would like to initiate seminal studies for applying intrinsic geometric flows in the framework of information geometry theory. More specifically, after having introduced Information metric deduced for Complex Auto‐Regressive (CAR) models from Fisher Matrix (Siegel Metric and Hyper‐Abelian Metric from Entropic Kahler Potential), we study asymptotic behavior of reflection coefficients of CAR models driven by intrinsic Information geometric Kahler‐Ricci and Calabi flows. These Information geometric flows can be used in different contexts to define distance between CAR models interpreted as geodesics of Entropy...

Rain clouds tracking with radar image processing based on morphological skeleton matching

The aim of this study is to perform a short term forecasting of dynamic radar clutter evolution (shape and position). This dynamic clutter, like thunderstorms, can be tracked by means of adapted algorithms based on the matching of the morphological skeleton polygonal approximation by relaxation labeling processes. The efficiency of our methods is demonstrated on meteorological radar images. The objective of this application is dedicated to civil traffic regulation according to severe atmospheric phenomenon, as described in Monnier & al. (1997). Through radar environment assessment, we observe radar clutter, like precipitation, submitted to very complex deformations that cannot be modelized easily. In Barbaresco (1999), we proposed a method based on morphological skeleton deformation to forecast the fluid topological evolution. This method allows management of very complex shapes evolution thanks to polygonal approximation of the skeletons and matching of their closed couple of elements by the relaxation algorithm. The skeleton simplifies shape analysis and deformation but also distinguishes clutter displacement and articulated deformation by skeleton matching from homothetic deformation (inflation and deflation) by medial axis (radius of maximal disks contained in the shape) tracking.

Motion-based segmentation and tracking of dynamic radar clutters

The aim of this study is to perform a classification and a short term spatial estimation of radar clutter. Motion-based segmentation allows one to part clutter into two sets: the static ones and the dynamic ones. A spatial segmentation can then be processed, using Doppler data, in order to obtain homogeneous clutter. The dynamic clutter can be tracked by means of adaptive algorithms based on new techniques such as active contours, front propagation combined with Kalman filtering and motion estimation. The efficiency of our methods is demonstrated on atmospheric clutter in meteorological radar images.

3D echographic data segmentation and carotid artery turbulences mapping by Doppler velocimetry by a common approach based on calculus of variations

The DOLPHINS project is supported in part by the 4/sup th/ European RTD Framework Program, and deals with echographic applications dedicated to arterial walls and plaque segmentation, plaque motion and degree of stenoses analysis. For this purpose, we have adapted geodesic active contours methods for arterial walls segmentation, to characterize stenose severity with regularized high resolution Doppler spectrum analysis by turbulences mapping from a Doppler spectral width measurement. The original contribution of our approach consists in using the same calculus of variations framework for image segmentation and Doppler velocimetry. We prove that we can, by analogy, find the equivalent mean curvature flow equation, used for geodesic active contours, for Doppler analysis by considering the complex autoregressive polynomial as a closed plane curve immersed in the oriented Euclidean plane.