### Collaborations

- 2006-2009 Jean-Marie Favreau
- 2007-2010. CNR Imati, Genova (Silvia Biasotti)

### Method

Subdividing a surface into tubular regions is an abstraction of many segmentation problems, stemming from various applications from medical imaging to computer graphics. A tubular region, we will call a (topological) cylinder, can be defined as a surface homeomorphic to a cylinder, i.e. of genus zero with two boundaries. Tiling a surface with cylinders is a topological question, since the minimal number of cylindrical patches that will segment the surface is defined by its topology. Itâ€™s also a geometrical issue, since the connections between cylinders have to be driven by the shape of the surface. Moreover, some specific extrusions can be described by their own cylinder. We describe a formalism for segmenting a surface into cylinders using n-loops (an original generalization of the loops) as a cutting tool, to monitor the shape and length of the junctions. Using this formalism, the combinatorial configurations of the junctions between cylinders are precisely described, and the structure of the tilings can be exploited in the applicative fields.