  Shortest paths play an important role in mathematical modeling and image
processing. Usually, shortest path problems are formulated on planar graphs
that consist of vertices and weighted arcs. In this context, one is interested
in finding a path of minimum weight from a start vertex to an end vertex. The
concept of minimum-weight surfaces extends shortest paths to 3d. The
minimum-weight surface problem is formulated on a cellular complex with
weighted facets. A cycle on the arcs of the complex serves as input and one is
interested in finding a surface of minimum weight bounded by that cycle. In
practice, minimum-weight surfaces can be used to segment 3d images. Vice versa,
it is possible to use them as a modeling tool for geometric structures such as
cracks. In this work, we present an approach for using minimum-weight surfaces
in bounded Voronoi diagrams to generate synthetic 3d images of cracks.
