Computed tomography is a non-destructive testing technique based on X-ray absorption that permits the 3D-visualisation of materials at micron-range resolutions. In this article, computed tomography is used to investigate fibre orientation and fibre position in various fibre-reinforced materials such as ceramic matrix composites, glass fibre-reinforced plastics or reinforced concrete. The goal of this article is to determine the quantitative orientation of fibres in fibre-reinforced materials. For this purpose, a mathematical technique based on the structure tensor is used to determine the local orientation of fibres. The structure tensor is easy to implement and results in a fast algorithm relying solely on local properties of the given reconstruction. In addition, the local X-ray transform is used to denoise fibres and to segment them from the matrix.