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

Jesus Angulo

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 Lp 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.

Keywords
Riemannian averaging; Riemannian center-of-mass; structure tensor; tensor image denoising; tensor image enhancement; tensor-valued images

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DOI: 10.5566/ias.v33.p95-105

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)