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Fri, 08 Jun 2012 23:03:52 +0200
Fri, 08 Jun 2012 23:03:52 +0200

Supervised and Transductive MultiClass Segmentation Using pLaplacians and RKHS methods
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/3169
This paper considers supervised multiclass 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 pLaplacians, (vectorvalued) Reproducing Kernel Hilbert
Spaces (RKHSs) and combinations of both. In all approaches we construct segment membership
vectors. In the pLaplacian 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 2Laplacian model gives a good general segmentation, the case of the 1Laplacian 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 multiclass 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.
Sung Ha Kang; Behrang Shafei; Gabriele Steidl
preprint
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/3169
Fri, 08 Jun 2012 23:03:52 +0200

Homogeneous Penalizers and Constraints in Convex Image Restoration
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/2866
Recently convex optimization models were successfully applied for solving various problems in image analysis and restoration. In this paper, we are interested in relations between convex constrained optimization problems of the form \(min\{\Phi(x)\) subject to \(\Psi(x)\le\tau\}\) and their nonconstrained, penalized counterparts \(min\{\Phi(x)+\lambda\Psi(x)\}\). We start with general considerations of the topic and provide a novel proof which ensures that a solution of the constrained problem with given \(\tau\) is also a solution of the onconstrained problem for a certain \(\lambda\). Then we deal with the special setting that \(\Psi\) is a seminorm and \(\Phi=\phi(Hx)\), where \(H\) is a linear, not necessarily invertible operator and \(\phi\) is essentially smooth and strictly convex. In this case we can prove via the dual problems that there exists a bijective function which maps \(\tau\) from a certain interval to \(\lambda\) such that the solutions of the constrained problem coincide with those of the nonconstrained problem if and only if \(\tau\) and \(\lambda\) are in the graph of this function. We illustrate the relation between \(\tau\) and \(\lambda\) by various problems arising in image processing. In particular, we demonstrate the performance of the constrained model in restoration tasks of images corrupted by Poisson noise and in inpainting models with constrained nuclear norm. Such models can be useful if we have a priori knowledge on the image rather than on the noise level.
RenĂ© Ciak; Behrang Shafei; Gabriele Steidl
preprint
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/2866
Thu, 02 Feb 2012 05:02:50 +0000