623 research outputs found
Fast High-Dimensional Kernel Filtering
The bilateral and nonlocal means filters are instances of kernel-based
filters that are popularly used in image processing. It was recently shown that
fast and accurate bilateral filtering of grayscale images can be performed
using a low-rank approximation of the kernel matrix. More specifically, based
on the eigendecomposition of the kernel matrix, the overall filtering was
approximated using spatial convolutions, for which efficient algorithms are
available. Unfortunately, this technique cannot be scaled to high-dimensional
data such as color and hyperspectral images. This is simply because one needs
to compute/store a large matrix and perform its eigendecomposition in this
case. We show how this problem can be solved using the Nystr\"om method, which
is generally used for approximating the eigendecomposition of large matrices.
The resulting algorithm can also be used for nonlocal means filtering. We
demonstrate the effectiveness of our proposal for bilateral and nonlocal means
filtering of color and hyperspectral images. In particular, our method is shown
to be competitive with state-of-the-art fast algorithms, and moreover it comes
with a theoretical guarantee on the approximation error
Fast Separable Non-Local Means
We propose a simple and fast algorithm called PatchLift for computing
distances between patches (contiguous block of samples) extracted from a given
one-dimensional signal. PatchLift is based on the observation that the patch
distances can be efficiently computed from a matrix that is derived from the
one-dimensional signal using lifting; importantly, the number of operations
required to compute the patch distances using this approach does not scale with
the patch length. We next demonstrate how PatchLift can be used for patch-based
denoising of images corrupted with Gaussian noise. In particular, we propose a
separable formulation of the classical Non-Local Means (NLM) algorithm that can
be implemented using PatchLift. We demonstrate that the PatchLift-based
implementation of separable NLM is few orders faster than standard NLM, and is
competitive with existing fast implementations of NLM. Moreover, its denoising
performance is shown to be consistently superior to that of NLM and some of its
variants, both in terms of PSNR/SSIM and visual quality
On a fast bilateral filtering formulation using functional rearrangements
We introduce an exact reformulation of a broad class of neighborhood filters,
among which the bilateral filters, in terms of two functional rearrangements:
the decreasing and the relative rearrangements.
Independently of the image spatial dimension (one-dimensional signal, image,
volume of images, etc.), we reformulate these filters as integral operators
defined in a one-dimensional space corresponding to the level sets measures.
We prove the equivalence between the usual pixel-based version and the
rearranged version of the filter. When restricted to the discrete setting, our
reformulation of bilateral filters extends previous results for the so-called
fast bilateral filtering. We, in addition, prove that the solution of the
discrete setting, understood as constant-wise interpolators, converges to the
solution of the continuous setting.
Finally, we numerically illustrate computational aspects concerning quality
approximation and execution time provided by the rearranged formulation.Comment: 29 pages, Journal of Mathematical Imaging and Vision, 2015. arXiv
admin note: substantial text overlap with arXiv:1406.712
Color-compressive bilateral filter and nonlocal means for high-dimensional images
We propose accelerated implementations of bilateral filter (BF) and nonlocal means (NLM) called color-compressive bilateral filter (CCBF) and color-compressive nonlocal means (CCNLM). CCBF and CCNLM are random filters, whose Monte-Carlo averaged output images are identical to the output images of conventional BF and NLM, respectively. However, CCBF and CCNLM are considerably faster because the spatial processing of multiple color channels are combined into a single random filtering process. This implies that the complexity of CCBF and CCNLM is less sensitive to color dimension (e.g., hyperspectral images) relatively to other BF and NLM methods. We experimentally verified that the execution time of CCBF and CCNLM are faster than the existing fast implementations of BF and NLM, respectively
BLADE: Filter Learning for General Purpose Computational Photography
The Rapid and Accurate Image Super Resolution (RAISR) method of Romano,
Isidoro, and Milanfar is a computationally efficient image upscaling method
using a trained set of filters. We describe a generalization of RAISR, which we
name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable
edge-adaptive filtering framework that is general, simple, computationally
efficient, and useful for a wide range of problems in computational
photography. We show applications to operations which may appear in a camera
pipeline including denoising, demosaicing, and stylization
Accelerated graph-based nonlinear denoising filters
Denoising filters, such as bilateral, guided, and total variation filters,
applied to images on general graphs may require repeated application if noise
is not small enough. We formulate two acceleration techniques of the resulted
iterations: conjugate gradient method and Nesterov's acceleration. We
numerically show efficiency of the accelerated nonlinear filters for image
denoising and demonstrate 2-12 times speed-up, i.e., the acceleration
techniques reduce the number of iterations required to reach a given peak
signal-to-noise ratio (PSNR) by the above indicated factor of 2-12.Comment: 10 pages, 6 figures, to appear in Procedia Computer Science, vol.80,
2016, International Conference on Computational Science, San Diego, CA, USA,
June 6-8, 201
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
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