Communications in Mathematical Sciences

Volume 12 (2014)

Number 7

Topology preserving active contours

Pages: 1329 – 1342

(Fast Communication)



Hayden Schaeffer (Department of Mathematics, University of California at Los Angeles)

Nóirín Duggan (Electrical and Electronic Engineering Building, National University of Ireland, Galway, Ireland)

Carole le Guyader (Laboratory of Mathematics, INSA de Rouen, Saint-Etienne-du-Rouvray, France)

Luminita Vese (Department of Mathematics, University of California at Los Angeles)


Active contours models are variational methods for segmenting complex scenes using edge or regional information. Many of these models employ the level set method to numerically minimize a given energy, which provides a simple representation for the resulting curve evolution problem. During the evolution, the curve can merge or break, thus these methods tend to have steady state solutions which are not homeomorphic to the initial condition. In many applications, the topology of the edge set is known, and thus can be enforced. In this work, we combine a topology preserving variational term with the region based active contour models in order to segment images with known structure. The advantage of this method over current topology preserving methods is its ability to locate boundaries of objects and not only edges. This is particularly useful for highly textured or noisy data.


active contour, topology preserving, region based models, non-local PDE

2010 Mathematics Subject Classification

65K10, 68U10

Full Text (PDF format)