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This paper addresses the analysis of textured images using the symmetric positive semi-definite matrix. In particular, a field of symmetric positive semi-definite matrices is used to estimate the structural information represented by the local orientation and the degree of anisotropy in structured and sinusoid-like textured images. In order to ensure faithful local structure estimation, an adaptive algorithm for the regularization of the extent of gradient fields smoothing is proposed. Results obtained on different texture samples show the strength of the proposed method in accurately representing the local variation of orientations in the underlying textured images, which paves the way towards an accurate analysis of the texture structures.