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Fisher Information Geometry for Shape Analysis
* 1 , 2
1  Department of Management and Business Administration, University ”G. d’Annunzio” of Chieti-Pescara, Pescara, Italy
2  Department of Philosophical, Pedagogical and Quantitative Economic Sciences, University G. D’Annunzio, Chieti–Pescara, Italy


The aim of this study is to model shapes from complex systems using Information Geometry tools. It is well-known that the Fisher information endows the statistical manifold, defined by a family of probability distributions, with a Riemannian metric, called the Fisher-Rao metric. With respect to this, geodesic paths are determined, minimizing information in Fisher sense. Under the hypothesis that it is possible to extract from the shape a finite number of representing points, called landmarks, we propose to model each of them with a probability distribution, as for example a multivariate Gaussian distribution. Then using the geodesic distance, induced by the Fisher-Rao metric, we can define a shape metric which enables us to quantify differences between shapes. The discriminative power of the proposed shape metric is tested performing a cluster analysis on the shapes of three different groups of specimens corresponding to three species of flatfish. Results show a better ability in recovering the true cluster structure with respect to other existing shape distances.

Keywords: Landmarks; Shape Analysis; Fisher-Rao metric; Information Geometry; Geodesics