STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS

Abstract

Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n), representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n) matrices. This contribution deals with structure tensor image filtering based on L^p geometric averaging. In particular, L¹ center-of-mass (Riemannian median or Fermat-Weber point) and L^∞ center-of-mass (Riemannian circumcenter) can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L¹ and L^∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i) structure tensor image denoising; (ii) anomaly detection in structure tensor images.