Supervised and Transductive Multi-Class Segmentation Using p-Laplacians and RKHS methods

• This 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, (vector-valued) 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. This direction is motivated by image colorization, where a given dab of color is extended to a nearby region of similar features or to another image. The connection between colorization and multi-class segmentation is explored in this paper with an application to medical image segmentation. We further consider an improvement using a combined method. Each model is carefully considered with numerical experiments for validation, followed by medical image segmentation at the end.

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Author: Sung Ha Kang, Behrang Shafei, Gabriele Steidl urn:nbn:de:hbz:386-kluedo-31695 Preprint English 2012/06/08 2012 Technische Universität Kaiserslautern 2012/06/08 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 518 Numerische Analysis Standard gemäß KLUEDO-Leitlinien vom 15.02.2012

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