Presents a novel, parameter-free technique for the segmentation and local description of line structures on multiple scales, both in 2D and in 3D. The algorithm is based on a nonlinear combination of linear filters and searches for elongated, symmetric line structures, while suppressing the response to edges. The filtering process creates one sharp maximum across the line-feature profile and across the scale-space. The multi-scale response reflects local contrast and is independent of the local width. The filter is steerable in both the orientation and scale domains, leading to an efficient, parameter-free implementation. A local description is obtained that describes the contrast, the position of the center-line, the width, the polarity, and the orientation of the line. Examples of images from different application domains demonstrate the generic nature of the line segmentation scheme. The 3D filtering is applied to magnetic resonance volume data in order to segment cerebral blood vessels.>