A method and apparatus for machine learning based detection of vessel orientation tensors of a target vessel from a medical image is disclosed. For each of a plurality of voxels in a medical image, such as a computed tomography angiography (CTA), features are extracted from sampling patches oriented to each of a plurality of discrete orientations in the medical image. A classification score is calculated for each of the plurality of discrete orientations at each voxel based on the features extracted from the sampling patches oriented to each of the plurality of discrete orientations using a trained vessel orientation tensor classifier. A vessel orientation tensor at each voxel is calculated based on the classification scores of the plurality of discrete orientations at that voxel.