Methods are introduced for analysing the shape and orientation of planar fibres from greyscale images of fibrous systems. The sequence of image processing techniques needed for segmentation of fibres is described. The identified fibres were interpreted as deformed line segments for which two shape and two orientation parameters are estimated by the maximum likelihood method. The methods introduced are shown to perform quite well for simulated systems of deformed line segments with known properties. They were applied to TEM images of carbon nanotubes embedded in polycarbonate.