<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling"^^ . "In this thesis, we focus on the image labeling problem which is the task of performing unique\r\npixel-wise label decisions to simplify the image while reducing its redundant information. We\r\nbuild upon a recently introduced geometric approach for data labeling by assignment flows\r\n[\r\nAPSS17\r\n] that comprises a smooth dynamical system for data processing on weighted graphs.\r\nHereby we pursue two lines of research that give new application and theoretically-oriented\r\ninsights on the underlying segmentation task.\r\nWe demonstrate using the example of Optical Coherence Tomography (OCT), which is the\r\nmostly used non-invasive acquisition method of large volumetric scans of human retinal tis-\r\nsues, how incorporation of constraints on the geometry of statistical manifold results in a novel\r\npurely data driven\r\ngeometric\r\napproach for order-constrained segmentation of volumetric data\r\nin any metric space. In particular, making diagnostic analysis for human eye diseases requires\r\ndecisive information in form of exact measurement of retinal layer thicknesses that has be done\r\nfor each patient separately resulting in an demanding and time consuming task. To ease the\r\nclinical diagnosis we will introduce a fully automated segmentation algorithm that comes up\r\nwith a high segmentation accuracy and a high level of built-in-parallelism. As opposed to many\r\nestablished retinal layer segmentation methods, we use only local information as input without\r\nincorporation of additional global shape priors. Instead, we achieve physiological order of reti-\r\nnal cell layers and membranes including a new formulation of ordered pair of distributions in an\r\nsmoothed energy term. This systematically avoids bias pertaining to global shape and is hence\r\nsuited for the detection of anatomical changes of retinal tissue structure. To access the perfor-\r\nmance of our approach we compare two different choices of features on a data set of manually\r\nannotated\r\n3\r\nD OCT volumes of healthy human retina and evaluate our method against state of\r\nthe art in automatic retinal layer segmentation as well as to manually annotated ground truth\r\ndata using different metrics.\r\nWe generalize the recent work [\r\nSS21\r\n] on a variational perspective on assignment flows and\r\nintroduce a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs.\r\nThe G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was\r\nintroduced in\r\nJ. Math. Imaging & Vision\r\n58(2), 2017. Due to this parameterization, solving the\r\nG-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with re-\r\nspect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions\r\n(DC) decomposition of this potential and show that the basic geometric Euler scheme for inte-\r\ngrating the assignment flow is equivalent to solving the G-PDE by an established DC program-\r\nming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit\r\nhigher-order information of the vector field that drives the assignment flow, in order to devise a\r\nnovel accelerated DC programming scheme. A detailed convergence analysis of both numerical\r\nschemes is provided and illustrated by numerical experiments."^^ . "2023" . . . . . . . "Dmitrij"^^ . "Sitenko"^^ . "Dmitrij Sitenko"^^ . . . . . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling (PDF)"^^ . . . "Thesis.pdf"^^ . . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #33387 \n\nNonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling\n\n" . "text/html" . . . "500 Naturwissenschaften und Mathematik"@de . "500 Natural sciences and mathematics"@en . . . "510 Mathematik"@de . "510 Mathematics"@en . .