is closed if the curve is contained within the 3D grid. In its more general application, the input is two 3D functions, f This paper presents a general purpose tool designed to extract characteristic curves from 3D images. Our algorithm, called and g, which give two real values for each point (x, y, z) of the Marching Lines, is inspired by isointensity techniques, such a 3D grid, but it can be also two 3D digital images.
as the Marching Cubes. Marching Lines extracts, with subpixel
The first section briefly presents the extraction of isoconaccuracy, the 3D lines corresponding to the intersection of tours in 2D and of isosurfaces in 3D, care being taken to two isosurfaces in a 3D grid. The algorithm ensures that each ensure that the reconstructed surface is without holes. reconstructed curve is formed of a connected set of segments, Then we describe the Marching Lines algorithm, which is is closed if the curve is entirely contained in the grid, does not purely local, but also ensures that the reconstructed disintersect itself, and is oriented. The main idea is to define crete curve elements are connected. Last, we present exisosurfaces as interfaces ( f ี 0, f ฯฝ 0) instead of implicit perimental results of the automatic extraction of curves equation solutions ( f โซุโฌ 0). The singularities are solved with for both synthetic and real 3D images, such as the parabolic an offset technique. Results are presented for synthetic data curves (Gaussian curvature equal to zero), the isoand for 3D medical image applications.