4,124 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
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
Bilateral Filter: Graph Spectral Interpretation and Extensions
In this paper we study the bilateral filter proposed by Tomasi and Manduchi,
as a spectral domain transform defined on a weighted graph. The nodes of this
graph represent the pixels in the image and a graph signal defined on the nodes
represents the intensity values. Edge weights in the graph correspond to the
bilateral filter coefficients and hence are data adaptive. Spectrum of a graph
is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian
matrix. We use this spectral interpretation to generalize the bilateral filter
and propose more flexible and application specific spectral designs of
bilateral-like filters. We show that these spectral filters can be implemented
with k-iterative bilateral filtering operations and do not require expensive
diagonalization of the Laplacian matrix
Chebyshev and Conjugate Gradient Filters for Graph Image Denoising
In 3D image/video acquisition, different views are often captured with
varying noise levels across the views. In this paper, we propose a graph-based
image enhancement technique that uses a higher quality view to enhance a
degraded view. A depth map is utilized as auxiliary information to match the
perspectives of the two views. Our method performs graph-based filtering of the
noisy image by directly computing a projection of the image to be filtered onto
a lower dimensional Krylov subspace of the graph Laplacian. We discuss two
graph spectral denoising methods: first using Chebyshev polynomials, and second
using iterations of the conjugate gradient algorithm. Our framework generalizes
previously known polynomial graph filters, and we demonstrate through numerical
simulations that our proposed technique produces subjectively cleaner images
with about 1-3 dB improvement in PSNR over existing polynomial graph filters.Comment: 6 pages, 6 figures, accepted to 2014 IEEE International Conference on
Multimedia and Expo Workshops (ICMEW
Filtering Random Graph Processes Over Random Time-Varying Graphs
Graph filters play a key role in processing the graph spectra of signals
supported on the vertices of a graph. However, despite their widespread use,
graph filters have been analyzed only in the deterministic setting, ignoring
the impact of stochastic- ity in both the graph topology as well as the signal
itself. To bridge this gap, we examine the statistical behavior of the two key
filter types, finite impulse response (FIR) and autoregressive moving average
(ARMA) graph filters, when operating on random time- varying graph signals (or
random graph processes) over random time-varying graphs. Our analysis shows
that (i) in expectation, the filters behave as the same deterministic filters
operating on a deterministic graph, being the expected graph, having as input
signal a deterministic signal, being the expected signal, and (ii) there are
meaningful upper bounds for the variance of the filter output. We conclude the
paper by proposing two novel ways of exploiting randomness to improve (joint
graph-time) noise cancellation, as well as to reduce the computational
complexity of graph filtering. As demonstrated by numerical results, these
methods outperform the disjoint average and denoise algorithm, and yield a (up
to) four times complexity redution, with very little difference from the
optimal solution
Deep Graph Laplacian Regularization for Robust Denoising of Real Images
Recent developments in deep learning have revolutionized the paradigm of
image restoration. However, its applications on real image denoising are still
limited, due to its sensitivity to training data and the complex nature of real
image noise. In this work, we combine the robustness merit of model-based
approaches and the learning power of data-driven approaches for real image
denoising. Specifically, by integrating graph Laplacian regularization as a
trainable module into a deep learning framework, we are less susceptible to
overfitting than pure CNN-based approaches, achieving higher robustness to
small datasets and cross-domain denoising. First, a sparse neighborhood graph
is built from the output of a convolutional neural network (CNN). Then the
image is restored by solving an unconstrained quadratic programming problem,
using a corresponding graph Laplacian regularizer as a prior term. The proposed
restoration pipeline is fully differentiable and hence can be end-to-end
trained. Experimental results demonstrate that our work is less prone to
overfitting given small training data. It is also endowed with strong
cross-domain generalization power, outperforming the state-of-the-art
approaches by a remarkable margin
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