A Level Set Model for Image Classification

We present a supervised classification model based on a variational approach. This model is devoted to find an optimal partition composed of homogeneous classes with regular interfaces. The originality of the proposed approach concerns the definition of a partition by the use of level sets. Each set of regions and boundaries associated to a class is defined by a unique level set function. We use as many level sets as different classes and all these level sets are moving together thanks to forces which interact in order to get an optimal partition. We show how these forces can be defined through the minimization of a unique fonctional. The coupled Partial Differential Equations (PDE) related to the minimization of the functional are considered through a dynamical scheme. Given an initial interface set (zero level set), the different terms of the PDE's are governing the motion of interfaces such that, at convergence, we get an optimal partition as defined above. Each interface is guided by internal forces (regularity of the interface), and external ones (data term, no vacuum, no regions overlapping). Several experiments were conducted on both synthetic and real images.