This research report is a compilation of two articles describing new results concerning the 3D Marching Lines algorithm. The Marching Lines extracts, with sub-voxel accuracy characteristic 3D lines out of 3D images, such as the crest lines. Those feature lines can then be used to perform higher level image processing tasks, such as 3D image registration, or automatic labeling of anatomical structures, when medical images are processed. The first paper concentrates on the computation of the differential characteristics of iso-intensity surfaces and shows how to characterize crest lines points directly from the differentials of the 3D image. The second paper brings the proof of the good topological properties of the reconstructed surfaces and 3D curves obtained with the Marching Lines algorithm. New experiments on real and synthetic data are also presented, showing the high precision and stability of the extracted features lines.