Computing Histogram of Tensor Images using Orthogonal Series Density Estimation and Riemannian Metrics

Emmanuel Chevallier (1) , Augustin Chevallier (2) , Jesus Angulo (1)

1 CMM - Centre de Morphologie Mathématique
2 ENS Cachan - École normale supérieure - Cachan

This paper deals with the computation of the histogram of tensor images, that is, images where at each pixel is given a n by n positive definite symmetric matrix, SPD(n). An approach based on orthogonal series density estimation is introduced, which is particularly useful for the case of measures based on Riemannian metrics. By considering SPD(n) as the space of the covariance matrices of multivariate gaussian distributions, we obtain the corresponding density estimation for the measure of both the Fisher metric and the Wasserstein metric. Experimental results on the application of such histogram estimation to DTI image segmentation, texture segmentation and texture recognition are included.

Mots clés: Histogram; Density estimation; Symmetric positive definite matrices; Riemannian volume form; DTI

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Emmanuel Chevallier, Augustin Chevallier, Jesus Angulo. Computing Histogram of Tensor Images using Orthogonal Series Density Estimation and Riemannian Metrics. 2013. ⟨hal-00941147v1⟩