Segmentation of Stochastic Images using Stochastic Partial Differential Equations

  • The task of segmentation, the separation of an image into foreground and background, is typically performed on noisy images, and it is a great challenge to get satisfactory results. The noise in the images depends on the acquisition modality, the acquisition parameters, and extrinsic parameters. The acquisition step is a physical measurement and has to be equipped with information about the measurement error. This quantification of the measurement error is typically omitted in image processing. Neglecting the error leads to a loss of information about the influence of the input error to the result of the image processing steps. A possibility to model the image noise is to perceive a pixel inside the image as a random variable. These images are called stochastic images. Applying segmentation methods based on partial differential equations (PDEs) on stochastic images leads to stochastic PDEs (SPDEs). In this thesis, the focus is on intrusive methods for the discretization of SPDEs, because classical sampling strategies are time-consuming. The approximation of random variables uses the Wiener-Askey polynomial chaos and the discretization of the SPDEs uses the generalized spectral decomposition and finite difference schemes for random variables. This thesis investigates random walker segmentation, Ambrosio-Tortorelli segmentation and level set based segmentation methods for stochastic extensions. Furthermore, a sensitivity analysis of the classical segmentation approaches uses the stochastic framework by making segmentation parameters random variables. The result of the presented work is a framework carrying the probability distribution of the stochastic gray values, i.e. the random variables, through all steps of the segmentation pipeline. This yields segmentation results containing, for each pixel, a probability of belonging to the object. Furthermore, this stochastic segmentation identifies regions where the image noise has an important impact on the segmentation result.

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Meta data
Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Jacobs Univ.
Author:Torben Pätz
Referee:Tobias Preusser, Marcel Oliver, Joachim Weickert
Advisor:Tobias Preusser
Persistent Identifier (URN):urn:nbn:de:101:1-2013052812538
Document Type:PhD Thesis
Language:English
Date of Successful Oral Defense:2012/01/13
Date of First Publication:2012/02/09
PhD Degree:Mathematics
School:SES School of Engineering and Science
Library of Congress Classification:Q Science / QA Mathematics (incl. computer science) / QA273-280 Probabilities. Mathematical statistics

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