The 3 D Marching Lines

This paper presents a powerful and general purpose tool designed to extract characteristic lines from 3D images 1. 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 diierent 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 diierential 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 deened 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 deene 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 diierent positions. 1 This process is part of a patent taken out by the INRIA 1 L'algorithme du \Marching Lines" et son application a l'extraction des lignes de cr^ ete. Cet article pr esente un outil nouveau et puissant, conn cu pour extraire des lignes caract eristiques a partir d'images tri-dimmensionnelles 2. Cet algorithme, appel e Marching Lines, est inspir e de l'algorithme du Marching Cubes qui sert pour sa part a extraire des surfaces d'iso-valeurs d'images 3D. Le Marching Lines permet d'extraire, avec une pr ecision sup erieure au pixel, les lignes 3D correspondant a l'intersection de deux iso-surfaces, obtenues a partir de deux images 3D dii erentes. Nous montrons comment impl ementer l'algorithme de mani ere a garantir que les lignes 3D reconstruites ont de bonnes propri et es topologiques; principalement que ces derni eres sont continues et ferm ees. Nous pr esentons egalement dans le m^ eme article une faa con nouvelle de calculer les caract eristiques dii erentielles des iso-surfaces, directe-ment a partir de l'image 3D, et nous en montrons l'application a l'extraction des lignes de cr^ ete. Nous expliquons qu'une ligne de cr^ ete peut ^ etre d eenie lo-calement …