<p>DEMs (digital elevation models) are very important in many fields, such as in Geomatics and in water conservation of mountainous areas. Geomorphic feature lines are necessary data for the topography interpolation and computation from DEMs. Instead of the parameter space, we propose a novel automatic extraction of Geomorphic feature lines in the feature space from discrete airborne LiDAR (Light detection and ranging) data by TVM (tensor voting method) developed originally for image data in this article. A tensor field for discrete airborne LiDAR points is first established and then utilizing the TVM, a new geometric feature metric of data, the line feature strength, was captured. A practical line growing method based on the local maximum line feature strength is proposed in the article. Compared with the conventional line growing that is based on a certain threshold, our line growing method is quite effective, for the extraction of primary and minor ridge and valley lines in mountainous areas, particularly. The method presented in this paper is fast and automated and can furnish operators with a wealth of detailed information about minor line features. This will enable the extraction of ridge and valley lines tailored to specific requirements. There is no doubt that the method developed here can be generalized to a large amount of LiDAR data.</p>