On the Length and Area Regularization for Multiphase Level Set Segmentation
In this paper we introduce novel regularization techniques for level set segmentation that target specifically the problem of multiphase segmentation. When the multiphase model is used to obtain a partitioning of the image in more than two regions, a new set of issues arise with respect to the single phase case in terms of regularization strategies. For example, if smoothing or shrinking each contour individually could be a good model in the single phase case, this is not necessarily true in the multiphase scenario. In this paper, we address these issues designing enhanced length and area regularization terms, whose minimization yields evolution equations in which each level set function involved in the multiphase segmentation can "sense" the presence of the other level set functions and evolve accordingly. In other words, the coupling of the level set function, which before was limited to the data term (i.e. the proper segmentation driving force), is extended in a mathematically principled way to the regularization terms as well. The resulting regularization technique is more suitable to eliminate spurious regions and other kind of artifacts. An extensive experimental evaluation supports the model we introduce in this paper, showing improved segmentation performance with respect to traditional regularization techniques.
area regularization image segmentation multiphase flows level set methods length regularization