This paper describes a method for the enhancement of curvilinear structures such as vessels and bronchi in three-dimensional (3-D) medical images. A 3-D line enhancement filter is developed with the aim of discriminating line structures from other structures and recovering line structures of various widths. The 3-D line filter is based on a combination of the eigenvalues of the 3-D Hessian matrix. Multi-scale integration is formulated by taking the maximum among single-scale filter responses, and its characteristics are examined to derive criteria for the selection of parameters in the formulation. The resultant multi-scale line-filtered images provide significantly improved segmentation and visualization of curvilinear structures. The usefulness of the method is demonstrated by the segmentation and visualization of brain vessels from magnetic resonance imaging (MRI) and magnetic resonance angiography (MRA), bronchi from a chest CT, and liver vessels (portal veins) from an abdominal CT.