816 research outputs found
Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications
We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation
A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data
In this paper we consider denoising and inpainting problems for higher
dimensional combined cyclic and linear space valued data. These kind of data
appear when dealing with nonlinear color spaces such as HSV, and they can be
obtained by changing the space domain of, e.g., an optical flow field to polar
coordinates. For such nonlinear data spaces, we develop algorithms for the
solution of the corresponding second order total variation (TV) type problems
for denoising, inpainting as well as the combination of both. We provide a
convergence analysis and we apply the algorithms to concrete problems.Comment: revised submitted versio
Edge Guided Reconstruction for Compressive Imaging
We propose EdgeCS—an edge guided compressive sensing reconstruction approach—to recover images
of higher quality from fewer measurements than the current methods. Edges are important
image features that are used in various ways in image recovery, analysis, and understanding. In
compressive sensing, the sparsity of image edges has been successfully utilized to recover images.
However, edge detectors have not been used on compressive sensing measurements to improve the
edge recovery and subsequently the image recovery. This motivates us to propose EdgeCS, which
alternatively performs edge detection and image reconstruction in a mutually beneficial way. The
edge detector of EdgeCS is designed to faithfully return partial edges from intermediate image reconstructions
even though these reconstructions may still have noise and artifacts. For complex-valued
images, it incorporates joint sparsity between the real and imaginary components. EdgeCS has
been implemented with both isotropic and anisotropic discretizations of total variation and tested
on incomplete k-space (spectral Fourier) samples. It applies to other types of measurements as well.
Experimental results on large-scale real/complex-valued phantom and magnetic resonance (MR)
images show that EdgeCS is fast and returns high-quality images. For example, it exactly recovers
the 256×256 Shepp–Logan phantom from merely 7 radial lines (3.03% k-space), which is impossible
for most existing algorithms. It is able to accurately reconstruct a 512 Ă— 512 MR image with 0.05
white noise from 20.87% radial samples. On complex-valued MR images, it obtains recoveries with
faithful phases, which are important in many medical applications. Each of these tests took around
30 seconds on a standard PC. Finally, the algorithm is GPU friendly
Generalized Max Pooling
State-of-the-art patch-based image representations involve a pooling
operation that aggregates statistics computed from local descriptors. Standard
pooling operations include sum- and max-pooling. Sum-pooling lacks
discriminability because the resulting representation is strongly influenced by
frequent yet often uninformative descriptors, but only weakly influenced by
rare yet potentially highly-informative ones. Max-pooling equalizes the
influence of frequent and rare descriptors but is only applicable to
representations that rely on count statistics, such as the bag-of-visual-words
(BOV) and its soft- and sparse-coding extensions. We propose a novel pooling
mechanism that achieves the same effect as max-pooling but is applicable beyond
the BOV and especially to the state-of-the-art Fisher Vector -- hence the name
Generalized Max Pooling (GMP). It involves equalizing the similarity between
each patch and the pooled representation, which is shown to be equivalent to
re-weighting the per-patch statistics. We show on five public image
classification benchmarks that the proposed GMP can lead to significant
performance gains with respect to heuristic alternatives.Comment: (to appear) CVPR 2014 - IEEE Conference on Computer Vision & Pattern
Recognition (2014
PVR: Patch-to-Volume Reconstruction for Large Area Motion Correction of Fetal MRI
In this paper we present a novel method for the correction of motion
artifacts that are present in fetal Magnetic Resonance Imaging (MRI) scans of
the whole uterus. Contrary to current slice-to-volume registration (SVR)
methods, requiring an inflexible anatomical enclosure of a single investigated
organ, the proposed patch-to-volume reconstruction (PVR) approach is able to
reconstruct a large field of view of non-rigidly deforming structures. It
relaxes rigid motion assumptions by introducing a specific amount of redundant
information that is exploited with parallelized patch-wise optimization,
super-resolution, and automatic outlier rejection. We further describe and
provide an efficient parallel implementation of PVR allowing its execution
within reasonable time on commercially available graphics processing units
(GPU), enabling its use in the clinical practice. We evaluate PVR's
computational overhead compared to standard methods and observe improved
reconstruction accuracy in presence of affine motion artifacts of approximately
30% compared to conventional SVR in synthetic experiments. Furthermore, we have
evaluated our method qualitatively and quantitatively on real fetal MRI data
subject to maternal breathing and sudden fetal movements. We evaluate
peak-signal-to-noise ratio (PSNR), structural similarity index (SSIM), and
cross correlation (CC) with respect to the originally acquired data and provide
a method for visual inspection of reconstruction uncertainty. With these
experiments we demonstrate successful application of PVR motion compensation to
the whole uterus, the human fetus, and the human placenta.Comment: 10 pages, 13 figures, submitted to IEEE Transactions on Medical
Imaging. v2: wadded funders acknowledgements to preprin
Bayesian inference and uncertainty quantification for medical image reconstruction with Poisson data
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