10,100 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
A superior edge preserving filter with a systematic analysis
A new, adaptive, edge preserving filter for use in image processing is presented. It had superior performance when compared to other filters. Termed the contiguous K-average, it aggregates pixels by examining all pixels contiguous to an existing cluster and adding the pixel closest to the mean of the existing cluster. The process is iterated until K pixels were accumulated. Rather than simply compare the visual results of processing with this operator to other filters, some approaches were developed which allow quantitative evaluation of how well and filter performs. Particular attention is given to the standard deviation of noise within a feature and the stability of imagery under iterative processing. Demonstrations illustrate the performance of several filters to discriminate against noise and retain edges, the effect of filtering as a preprocessing step, and the utility of the contiguous K-average filter when used with remote sensing data
Edge-enhancing Filters with Negative Weights
In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by
projecting the noisy image to a lower dimensional Krylov subspace of the graph
Laplacian, constructed using nonnegative weights determined by distances
between image data corresponding to image pixels. We~extend the construction of
the graph Laplacian to the case, where some graph weights can be negative.
Removing the positivity constraint provides a more accurate inference of a
graph model behind the data, and thus can improve quality of filters for
graph-based signal processing, e.g., denoising, compared to the standard
construction, without affecting the costs.Comment: 5 pages; 6 figures. Accepted to IEEE GlobalSIP 2015 conferenc
Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space
This paper focuses on devising graph signal processing tools for the
treatment of data defined on the edges of a graph. We first show that
conventional tools from graph signal processing may not be suitable for the
analysis of such signals. More specifically, we discuss how the underlying
notion of a `smooth signal' inherited from (the typically considered variants
of) the graph Laplacian are not suitable when dealing with edge signals that
encode a notion of flow. To overcome this limitation we introduce a class of
filters based on the Edge-Laplacian, a special case of the Hodge-Laplacian for
simplicial complexes of order one. We demonstrate how this Edge-Laplacian leads
to low-pass filters that enforce (approximate) flow-conservation in the
processed signals. Moreover, we show how these new filters can be combined with
more classical Laplacian-based processing methods on the line-graph. Finally,
we illustrate the developed tools by denoising synthetic traffic flows on the
London street network.Comment: 5 pages, 2 figur
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