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This paper proposes a texture characterization method that extracts data from images using the Hilbert curve. Three information theory quantifiers are then computed: permutation entropy, permutation complexity, and Fisher information measure. The proposal exhibits some important properties: (i) it allows discrimination between figures according to varying degrees of correlations (as measured by the Hurst exponent), (ii) it is invariant to rotation and symmetry transformations, (iii) it is invariant to image scaling, (iv) it can be used for both black and white and color images. 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