Nonlocal image filters suppress noise and other distortions by searching for similar patches at different locations
within the image, thus exploiting the self-similarity present in natural images. This similarity is typically assessed
by a windowed distance of the patches pixels. Inspired by the human visual system, we introduce a patch foveation
operator and measure patch similarity through a foveated distance, where each patch is blurred with spatially
variant point-spread functions having standard deviation increasing with the spatial distance from the patch
center. In this way, we install a different form of self-similarity in images: the foveated self-similarity.
We consider the Nonlocal Means algorithm (NL-means) for the removal of additive white Gaussian noise as
a simple prototype of nonlocal image filtering and derive an explicit construction of its corresponding foveation
operator, thus yielding the Foveated NL-means algorithm.
Our analysis and experimental study show that, to the purpose of image denoising, the foveated self-similarity
can be a far more effective regularity assumption than the conventional windowed self-similarity. In the comparison
with NL-means, the proposed foveated algorithm achieves a substantial improvement in denoising quality,
according to both objective criteria and visual appearance, particularly due to better contrast and sharpness.
Moreover, foveation is introduced at a negligible cost in terms of computational complexity.
We propose a powerful video denoising algorithm that exploits temporal and spatial redundancy characterizing
natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative filtering,
where a higher-dimensional transform-domain representation is leveraged to enforce sparsity and thus regularize
the data. The proposed algorithm exploits the mutual similarity between 3-D spatiotemporal volumes constructed
by tracking blocks along trajectories defined by the motion vectors. Mutually similar volumes are grouped
together by stacking them along an additional fourth dimension, thus producing a 4-D structure, termed group,
where different types of data correlation exist along the different dimensions: local correlation along the two
dimensions of the blocks, temporal correlation along the motion trajectories, and nonlocal spatial correlation
(i.e. self-similarity) along the fourth dimension. Collaborative filtering is realized by transforming each group
through a decorrelating 4-D separable transform and then by shrinkage and inverse transformation. In this way,
collaborative filtering provides estimates for each volume stacked in the group, which are then returned and
adaptively aggregated to their original position in the video. Experimental results demonstrate the effectiveness
of the proposed procedure which outperforms the state of the art.
The deblurring of images corrupted by radial blur is studied. This type of blur appears in images acquired during an
camera translation having a substantial component orthogonal to the image plane. The point spread functions (PSF PSF)
describing this blur are spatially varying. However, this blurring process does not mix together pixels lying on differen different
radial lines, i.e. lines stemming from a unique point in the image, the so called "blur center". Thus, in suitable pola polar
coordinates, the blurring process is essentially a 1-D linear operator, described by the multiplication with the blurrin blurring
We consider images corrupted simultaneously by radial blur and noise. The proposed deblurring algorithm is base
on two separate forms of regularization of the blur inverse. First, in the polar domain, we invert the blurring matri matrix
using the Tikhonov regularization. We then derive a particular modeling of the noise spectrum after both the regularize regularized
inversion and the forward and backward coordinate transformations. Thanks to this model, we successfully use a denoisin denoising
algorithm in the Cartesian domain. We use a non-linear spatially adaptive filter, the Pointwise Shape-Adaptive DCT, i in
order to exploit the image structures and attenuate noise and artifacts.
Experimental results demonstrate that the proposed algorithm can effectively restore radial blurred images corrupted by additive white Gaussian noise.
Conference Committee Involvement (2)
Image Processing: Algorithms and Systems XIII
10 February 2015 | San Francisco, California, United States
Image Processing: Algorithms and Systems XII
3 February 2014 | San Francisco, California, United States