Tracking Meteorological Structures through Curves Matching Using Geodesic Paths Isaac COHEN Isabelle HERLIN INRIA – Projet AIR B.P. 78153 Le Chesnay CEDEX, France Isaac.Cohen@inria.fr Isabelle.Herlin@inria.fr Abstract This paper is concerned with the problem of tracking clouds structures like vortices in meteorological images. For this purpose we characterize the deformation between two successive occurrences, by matching their two boundary curves. Our approach is based on the computation of the set of paths connecting the two curves to be matched. It min- imizes a cost function which measures the local similarity of the two curves. These matching paths are obtained as geodesic curves on this cost surface. Moreover our method allows to consider complex curves of arbitrary topologysince these curves are represented through an implicit function rather than through a parameterization. Experimental results are given to illustrate the properties of the method in process- ing synthetic and then meteorologic remotely-sensed data. Keywords: Curves matching, Image sequence analysis, Geodesic distance computation, Eulerian formulation. 1 Introduction Images sequences obtained from environmental satellites platforms present a new challenge for geosciences and com- puter vision. The wide range of remote sensors allow to char- acterize natural phenomena and infer some physical mea- surements used in atmospheric models. For example, me- teorologist use clouds in meteosat images as landmarks for estimating their motion and characterize some subtropical phenomena. Several approaches can be used to track these phenomena: optical flow methods [4] or a method based on pointwise tracking of moving structures like vortices and fronts [1]. In this paper, we develop a new method for pointwise tracking of structures by matching their contours. Hence, the deformation between two temporal occurrences will be obtained through a set of trajectories provided by the matching process. Our method is based on the computation of a set of paths connecting the two curves to be matched. Each path minimize a cost function which measures the lo- cal similarity between the starting and ending points of the path. In the following we explain how our method differs from classical ones and define its properties. Several authors proposed methods based on invariant geo- metrical properties in order to measure the similarity between the curves. Often these models rely on curvature informa- tion [3, 12] and are applied in case of rigid motion or when the small deformation hypothesis is valid. When this last assumption is no more satisfied, curvature measure is not reliable. Some other approaches are based on a parameterization of the deformation in order to derive a similaritymeasure: Berroir et al [1] proposed a method based on the geometry of the surface generated by the two curves to be matched. This method performs well as long as the sur- face remains smooth and differentiable. Unfortunately this approach cannot handle changes in topology nor large defor- mations since it uses a uniform parameterization. In this paper we present a new method, which computes the set of paths joining the curves to be matched, within the applicative framework of atmospheric structure match- ing. This applicative framework will mainly be used to jus- tify our different hypothesis and to present experimental re- sults at the end of the paper. Our approach defines a set of paths starting from the first curve (the source ) and ending at the second curve (the des- tination ). These paths are computed by minimizing a cost function which measures the local similarity of the curves and , and they are defined as geodesics of this cost function surface. In order to satisfy the requirements of our application, we consider the following approach: The cost function is defined through a graph surface and measures, as we previously explained, the similarity be- tween the source and destination areas. As this function will be defined over the whole 2D plane, computation may be achieved independently of the topology of the curves. This surface is the graph surface on which the connecting paths are computed. We choose to define the source and destination curves through two level set functions. This allows to con- sider a large family of curves with complex and variable topology. Moreover the source and destination area will not be constrained to have the same topology nor to be geometrically similar. Finally, matching the two curves is done through the computation of paths of minimal cost connecting the two curves. Hence the matching is not restricted to a dis- placement field as it is the case in most curves matching 1