You need to segment the DICOM image before you can extract centerline. Vessel segmentation of very well contrasted large vessels can be trivial, so that you can use any of the automatic segmentation methods (thresholding, region growing, fast marching, etc.). However, for most images you need to use a a combination of a few semi-automatic segmentation tools, such as those implemented in 3D Slicer’s Segment Editor (this page is a good starting point).
Once you have the segmentation, you can export it to a polygonal mesh (.vtp file) and automatically extract centerline.
Here is a short video of a typical vessel segmentation and centerline extraction workflow: