We propose an algorithm to construct a set of interfaces that separate the connected components of a multi-valued volume dataset. While each single interface is a manifold triangle mesh, two or more interfaces may join consistently along their common boundaries, i.e. there are no T-junctions or gaps. In contrast to previous work, our algorithm classifies and removes the topological ambiguities from the volume before extracting the interfaces. This not only allows for a simple and stable extraction algorithm, but also makes it possible to include user constraints. 1 Motivation and previous work Let there be a three-dimensional voxel grid with one (tissue) label per voxel. Our goal is to extract the interfaces between all adjacent tissues as triangle meshes, i.e. the result is a set of triangle meshes each separating voxels of two different tissue types. These meshes can then be used in downstream applications, e.g. active contour models [1]. Of course, we want to guarantee certain quali...