852 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
A Review of Bandlet Methods for Geometrical Image Representation
International audienceThis article reviews bandlet approaches to geometric image repre- sentations. Orthogonal bandlets using an adaptive segmentation and a local geometric flow well suited to capture the anisotropic regularity of edge struc- tures. They are constructed with a “bandletization” which is a local orthogonal transformation applied to wavelet coeffi cients. The approximation in these bandlet bases exhibits an asymptotically optimal decay for images that are regular outside a set of regular edges. These bandlets can be used to perform image compression and noise removal. More flexible orthogonal bandlets with less vanishing moments are constructed with orthogonal grouplets that group wavelet coeffi cients alon a multiscale association field. Applying a translation invariant grouplet transform over a translation invariant wavelet frame leads to state of the art results for image denoising and super-resolution
Subset Warping: Rubber Sheeting with Cuts
Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself
Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements
This paper addresses the problem of distributed coding of images whose
correlation is driven by the motion of objects or positioning of the vision
sensors. It concentrates on the problem where images are encoded with
compressed linear measurements. We propose a geometry-based correlation model
in order to describe the common information in pairs of images. We assume that
the constitutive components of natural images can be captured by visual
features that undergo local transformations (e.g., translation) in different
images. We first identify prominent visual features by computing a sparse
approximation of a reference image with a dictionary of geometric basis
functions. We then pose a regularized optimization problem to estimate the
corresponding features in correlated images given by quantized linear
measurements. The estimated features have to comply with the compressed
information and to represent consistent transformation between images. The
correlation model is given by the relative geometric transformations between
corresponding features. We then propose an efficient joint decoding algorithm
that estimates the compressed images such that they stay consistent with both
the quantized measurements and the correlation model. Experimental results show
that the proposed algorithm effectively estimates the correlation between
images in multi-view datasets. In addition, the proposed algorithm provides
effective decoding performance that compares advantageously to independent
coding solutions as well as state-of-the-art distributed coding schemes based
on disparity learning
On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
We explore some general consequences of a consistent formulation of
relativistic quantum field theory (QFT) on the Groenewold-Moyal-Weyl
noncommutative versions of Minkowski space with covariance under the twisted
Poincare' group of Chaichian et al. [12], Wess [44], Koch et al. [31], Oeckl
[34]. We argue that a proper enforcement of the latter requires braided
commutation relations between any pair of coordinates
generating two different copies of the space, or equivalently a -tensor
product (in the parlance of Aschieri et al. [3]) between any
two functions depending on . Then all differences behave like
their undeformed counterparts. Imposing (minimally adapted) Wightman axioms one
finds that the -point functions fulfill the same general properties as on
commutative space. Actually, upon computation one finds (at least for scalar
fields) that the -point functions remain unchanged as functions of the
coordinates' differences both if fields are free and if they interact (we treat
interactions via time-ordered perturbation theory). The main, surprising
outcome seems a QFT physically equivalent to the undeformed counterpart (to
confirm it or not one should however first clarify the relation between
-point functions and observables, in particular S-matrix elements).
These results are mainly based on a joint work [24] with J. WessComment: Latex file, 21 page
Frequency-warped autoregressive modeling and filtering
This thesis consists of an introduction and nine articles. The articles are related to the application of frequency-warping techniques to audio signal processing, and in particular, predictive coding of wideband audio signals. The introduction reviews the literature and summarizes the results of the articles.
Frequency-warping, or simply warping techniques are based on a modification of a conventional signal processing system so that the inherent frequency representation in the system is changed. It is demonstrated that this may be done for basically all traditional signal processing algorithms. In audio applications it is beneficial to modify the system so that the new frequency representation is close to that of human hearing. One of the articles is a tutorial paper on the use of warping techniques in audio applications.
Majority of the articles studies warped linear prediction, WLP, and its use in wideband audio coding. It is proposed that warped linear prediction would be particularly attractive method for low-delay wideband audio coding. Warping techniques are also applied to various modifications of classical linear predictive coding techniques. This was made possible partly by the introduction of a class of new implementation techniques for recursive filters in one of the articles. The proposed implementation algorithm for recursive filters having delay-free loops is a generic technique. This inspired to write an article which introduces a generalized warped linear predictive coding scheme. One example of the generalized approach is a linear predictive algorithm using almost logarithmic frequency representation.reviewe
Warped Wavelet and Vertical Thresholding
Let be an i.i.d. sample from the random
design regression model with .
In dealing with such a model, adaptation is naturally to be intended in terms
of norm where denotes the (known) marginal
distribution of the design variable . Recently much work has been devoted to
the construction of estimators that adapts in this setting (see, for example,
[5,24,25,32]), but only a few of them come along with a easy--to--implement
computational scheme. Here we propose a family of estimators based on the
warped wavelet basis recently introduced by Picard and Kerkyacharian [36] and a
tree-like thresholding rule that takes into account the hierarchical
(across-scale) structure of the wavelet coefficients. We show that, if the
regression function belongs to a certain class of approximation spaces defined
in terms of , then our procedure is adaptive and converge to the
true regression function with an optimal rate. The results are stated in terms
of excess probabilities as in [19].Comment: Submitted to the Electronic Journal of Statistics
(http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Biologically inspired feature extraction for rotation and scale tolerant pattern analysis
Biologically motivated information processing has been an important area of scientific research for decades. The central topic addressed in this dissertation is utilization of lateral inhibition and more generally, linear networks with recurrent connectivity along with complex-log conformal mapping in machine based implementations of information encoding, feature extraction and pattern recognition. The reasoning behind and method for spatially uniform implementation of inhibitory/excitatory network model in the framework of non-uniform log-polar transform is presented. For the space invariant connectivity model characterized by Topelitz-Block-Toeplitz matrix, the overall network response is obtained without matrix inverse operations providing the connection matrix generating function is bound by unity. It was shown that for the network with the inter-neuron connection function expandable in a Fourier series in polar angle, the overall network response is steerable. The decorrelating/whitening characteristics of networks with lateral inhibition are used in order to develop space invariant pre-whitening kernels specialized for specific category of input signals. These filters have extremely small memory footprint and are successfully utilized in order to improve performance of adaptive neural whitening algorithms. Finally, the method for feature extraction based on localized Independent Component Analysis (ICA) transform in log-polar domain and aided by previously developed pre-whitening filters is implemented. Since output codes produced by ICA are very sparse, a small number of non-zero coefficients was sufficient to encode input data and obtain reliable pattern recognition performance
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