This paper proposes a method to extract the airway tree from CT images by continually extending the tree with locally optimal paths. This is in contrast to commonly used region growing based approaches that only search the space of the immediate neighbors. The result is a much more robust method for tree extraction that can overcome local occlusions. The cost function for obtaining the optimal paths takes into account of an airway probability map as well as measures of airway shape and orientation derived from multi-scale Hessian eigen analysis on the airway probability. Significant improvements were achieved compared to a region growing based method, with up to 36% longer trees at a slight increase of false positive rate.