3,130 research outputs found
Accelerated graph-based spectral polynomial filters
Graph-based spectral denoising is a low-pass filtering using the
eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial
filtering avoids costly computation of the eigendecomposition by projections
onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the
bilateral and guided filters. We propose constructing accelerated polynomial
filters by running flexible Krylov subspace based linear and eigenvalue solvers
such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG)
method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop
on Machine Learning for Signal Processin
Learning Sparse High Dimensional Filters: Image Filtering, Dense CRFs and Bilateral Neural Networks
Bilateral filters have wide spread use due to their edge-preserving
properties. The common use case is to manually choose a parametric filter type,
usually a Gaussian filter. In this paper, we will generalize the
parametrization and in particular derive a gradient descent algorithm so the
filter parameters can be learned from data. This derivation allows to learn
high dimensional linear filters that operate in sparsely populated feature
spaces. We build on the permutohedral lattice construction for efficient
filtering. The ability to learn more general forms of high-dimensional filters
can be used in several diverse applications. First, we demonstrate the use in
applications where single filter applications are desired for runtime reasons.
Further, we show how this algorithm can be used to learn the pairwise
potentials in densely connected conditional random fields and apply these to
different image segmentation tasks. Finally, we introduce layers of bilateral
filters in CNNs and propose bilateral neural networks for the use of
high-dimensional sparse data. This view provides new ways to encode model
structure into network architectures. A diverse set of experiments empirically
validates the usage of general forms of filters
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 Convex Model for Edge-Histogram Specification with Applications to Edge-preserving Smoothing
The goal of edge-histogram specification is to find an image whose edge image
has a histogram that matches a given edge-histogram as much as possible.
Mignotte has proposed a non-convex model for the problem [M. Mignotte. An
energy-based model for the image edge-histogram specification problem. IEEE
Transactions on Image Processing, 21(1):379--386, 2012]. In his work, edge
magnitudes of an input image are first modified by histogram specification to
match the given edge-histogram. Then, a non-convex model is minimized to find
an output image whose edge-histogram matches the modified edge-histogram. The
non-convexity of the model hinders the computations and the inclusion of useful
constraints such as the dynamic range constraint. In this paper, instead of
considering edge magnitudes, we directly consider the image gradients and
propose a convex model based on them. Furthermore, we include additional
constraints in our model based on different applications. The convexity of our
model allows us to compute the output image efficiently using either
Alternating Direction Method of Multipliers or Fast Iterative
Shrinkage-Thresholding Algorithm. We consider several applications in
edge-preserving smoothing including image abstraction, edge extraction, details
exaggeration, and documents scan-through removal. Numerical results are given
to illustrate that our method successfully produces decent results efficiently
Segmentation-Aware Convolutional Networks Using Local Attention Masks
We introduce an approach to integrate segmentation information within a
convolutional neural network (CNN). This counter-acts the tendency of CNNs to
smooth information across regions and increases their spatial precision. To
obtain segmentation information, we set up a CNN to provide an embedding space
where region co-membership can be estimated based on Euclidean distance. We use
these embeddings to compute a local attention mask relative to every neuron
position. We incorporate such masks in CNNs and replace the convolution
operation with a "segmentation-aware" variant that allows a neuron to
selectively attend to inputs coming from its own region. We call the resulting
network a segmentation-aware CNN because it adapts its filters at each image
point according to local segmentation cues. We demonstrate the merit of our
method on two widely different dense prediction tasks, that involve
classification (semantic segmentation) and regression (optical flow). Our
results show that in semantic segmentation we can match the performance of
DenseCRFs while being faster and simpler, and in optical flow we obtain clearly
sharper responses than networks that do not use local attention masks. In both
cases, segmentation-aware convolution yields systematic improvements over
strong baselines. Source code for this work is available online at
http://cs.cmu.edu/~aharley/segaware
A discrete graph Laplacian for signal processing
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
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