The segmentation of 3D brain vessels is an important issue for physicians in order to operate an aneurysm. We introduce new vessel models for selecting a subset of interesting points near the vessel center. We also present a new approach to segment and reconstruct 3D brain vessels. The response at one scale is obtained by integrating along a circle the first derivative of the intensity in the radial direction. We also use a vessel model to choose a good parameter for a gamma-normalizatio- n of the response obtained at each scale. Once the parameter gamma is fixed, we find the relation between a vessel radius and the scale at which it is detected. From the multiscale response, we create a smoothed skeleton of the vessels and we reconstruct the vessels from their centerlines and their radii. The method has been tested on a large variety of 3D images of cerebral vessels, with excellent results. Vessels of various size and contrast are detected with remarkable robustness, even when they are close or tangent to another vessel, and most junctions are preserved. Results are obtained in a few minutes on a Dec-Alpha workstation, for a 128^3 image. This work was done in collaboration with General Electric Medical Systems Europe (GEMSE).