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Fibre orientation is an important structural property of fibre-based materials. For example, in paper the orientation of the fibres influences the dimensional strength of the sheet and the tendency of the sheet to curl and twist at moisture changes. Here, we present a three-dimensional image analysis method for estimating the fibre orientation and the orientation anisotropy. The proposed method can be applied directly to greyscale volume images and is based on local orientation estimates using quadrature filters and structure tensors. From the tensor field the fibre orientation can be estimated together with a corresponding certainty measurement. Good results are obtained for both synthetic fibre data sets and fibre based materials imaged using X-ray microtomography.