The 3d Marching Lines Algorithm and Its Application to Crest Lines Extraction

This paper presents a powerful and general purpose tool designed to extract characteristic lines from 3D images . The algorithm, called Marching Lines, is inspired from the Marching Cubes algorithm, which is used to extract iso-value surfaces from 3D images. The Marching Lines algorithm extracts with sub-pixel accuracy the 3D lines corresponding to the intersection of two iso-surfaces from two di erent 3D Images. We show how to implement this algorithm to ensure that the reconstructed 3D lines have good topological properties, mainly that they are continuous and closed. We also present a new method to compute the di erential characteristics of iso-surfaces, and show an application to the extraction of crest lines in 3D Images. We explain that a crest line can be locally de ned as the intersection of two surfaces, one corresponding to an iso-value in the image, and the other one to a crest surface which we de ne in this paper, and whose implicit equation can be directly computed from the voxel values of the 3D image. Finally, experimental results for 3D images of the skull are presented, where crest lines are extracted, and used to compute automatically the geometric transform between two 3D scanner images of the same subject, taken in two di erent positions.