A discrete graph Laplacian for signal processing

Gomo, Panganai (2011). A discrete graph Laplacian for signal processing. University of Birmingham. M.Phil.

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In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature.

We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions.

With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance.

Type of Work: Thesis (Masters by Research > M.Phil.)
Award Type: Masters by Research > M.Phil.
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Electronic, Electrical and Computer Engineering
Funders: None/not applicable
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
URI: http://etheses.bham.ac.uk/id/eprint/3232


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