Orientation Based Second-Order Statistics for Texture Description

This paper focuses on directional textures and proposes a new statistical approach for the second order description of an orientation vector field. We tackle two of the main high level properties that drive the perceptual grouping of texture: directionality and periodicity. Our method is based on the measure of similarity between two orientation vectors separated by a given displacement. We propose two implementations of the similarity measure. The first one is a 2-D Orientation Similarity Map which can be described in terms of blobs and lines that reflect texture periodicity and symmetry. The second implementation consists in a Curvilinear Orientation Similarity Function which provides a measure of the average resemblance between orientation vectors along a parametrized curve and brings out periodicity. We also provide experiments on both synthetic and natural images which show the relevance of our approach for the high level description of textures.