The geometry of the generalized gamma manifold and an application to medical imaging

Sana Rebbah (1, 2) , Florence Nicol (1) , Stéphane Puechmorel (1)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 ToNIC - Toulouse NeuroImaging Center

The Fisher information metric provides parameterized probability densities with a Riemannian manifold structure, yielding the so-called information geometry. The information geometry of the gamma manifold associated to the family of gamma distributions has been well studied. However, only a few results are known for the generalized gamma family, that adds an extra shape parameter. The present article gives some new results about the generalized gamma 5manifold. This paper also introduces an application in medical imaging that is the classification of Alzheimer's disease population. In the medical field, over the past two decades, a growing number of quantitative image analysis techniques have been developed, including histogram analysis, which is widely used to quantify the diffuse pathological changes of some neurological diseases. This method presents several drawbacks. Indeed, all the information included in the histogram is not used and the histogram is an overly simplistic estimate of a probability distribution. Thus, in this study we present how using information geometry and the generalized gamma manifold improved the performance of the classification of Alzheimer's disease population.

Domaines: Statistiques [math.ST]; Applications [stat.AP]; Géométrie différentielle [math.DG]; Imagerie

Sana Rebbah, Florence Nicol, Stéphane Puechmorel. The geometry of the generalized gamma manifold and an application to medical imaging. Mathematics , 2019, 7 (8), pp.art. no. 674. ⟨10.3390/math7080674⟩. ⟨hal-02159244⟩