Kang, S.H.S.H.KangShafei, B.B.ShafeiSteidl, G.G.Steidl2022-03-042022-03-042014https://publica.fraunhofer.de/handle/publica/23726410.1016/j.jvcir.2014.03.010This paper considers supervised multi-class image segmentation: from a labeled set of pixels in one image, we learn the segmentation and apply it to the rest of the image or to other similar images. We study approaches with p-Laplacians, Reproducing Kernel Hilbert Spaces (RKHSs) and combinations of both. In all approaches we construct segment membership vectors. In the p-Laplacian model the segment membership vectors have to fulfill a certain probability simplex constraint. Interestingly, we could prove that this is not really a constraint in the case p=2 but is automatically fulfilled. While the 2-Laplacian model gives a good general segmentation, the case of the 1-Laplacian tends to neglect smaller segments. The RKHS approach has the benefit of fast computation. We further consider an improvement by combining p-Laplacian and RKHS methods. Finally, we present challenging applications to medical image segmentation.en006journal article