Detecting tubular structures such as airways or vessels in medical images is important for diagnosis and surgical planning. Many state-of-the-art approaches address this problem by starting from the root and progressing towards thinnest tubular structures usually guided by image filtering techniques. These approaches need to be tailored for each application and can fail in noisy or low-contrast regions. In this work, we address these challenges by a two-layer model which consists of a low-level likelihood measure and a high-level measure verifying tubular branches. The algorithm starts by computing a robust measure of tubular presence using a discriminative classifier at multiple image scales. The measure is then used in an efficient multi-scale shortest path algorithm to generate candidate centerline branches and corresponding radii measurements. Finally, the branches are verified by a learning-based indicator function that discards false candidate branches. The experiments on detecting airways in rotational X-ray volumes show that the technique is robust to noise and correctly finds airways even in the presence of imaging artifacts.