1,423 research outputs found
The multi-fractal structure of contrast changes in natural images: from sharp edges to textures
We present a formalism that leads very naturally to a hierarchical
description of the different contrast structures in images, providing precise
definitions of sharp edges and other texture components. Within this formalism,
we achieve a decomposition of pixels of the image in sets, the fractal
components of the image, such that each set only contains points characterized
by a fixed stregth of the singularity of the contrast gradient in its
neighborhood. A crucial role in this description of images is played by the
behavior of contrast differences under changes in scale. Contrary to naive
scaling ideas where the image is thought to have uniform transformation
properties \cite{Fie87}, each of these fractal components has its own
transformation law and scaling exponents. A conjecture on their biological
relevance is also given.Comment: 41 pages, 8 figures, LaTe
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
Detection and estimation of image blur
The airborne imagery consisting of infrared (IR) and multispectral (MSI) images collected in 2009 under airborne mine and minefield detection program by Night Vision and Electronic Sensors Directorate (NVESD) was found to be severely blurred due to relative motion between the camera and the object and some of them with defocus blurs due to various reasons. Automated detection of blur due to motion and defocus blurs and the estimation of blur like point spread function for severely degraded images is an important task for processing and detection in such airborne imagery. Although several full reference and reduced reference methods are available in the literature, using no reference methods are desirable because there was no information of the degradation function and the original image data. In this thesis, three no reference algorithms viz. Haar wavelet (HAAR), modified Haar using singular value decomposition (SVD), and intentional blurring pixel difference (IBD) for blur detection are compared and their performance is qualified based on missed detections and false alarms. Three human subjects were chosen to perform subjective testing on randomly selected data sets and the truth for each frame was obtained from majority voting. The modified Haar algorithm (SVD) resulted in the least number of missed detections and least number of false alarms. This thesis also evaluates several methods for estimating the point spread function (PSF) of these degraded images. The Auto-correlation function (ACF), Hough transform (Hough) and steer Gaussian filter (SGF) based methods were tested on several synthetically motion blurred images and further validated on naturally blurred images. Statistics of pixel error estimate using these methods were computed based on 8640 artificially blurred image frames --Abstract, page iii
Direct Imaging of Graphene Edges: Atomic Structure and Electronic Scattering
We report an atomically-resolved scanning tunneling microscopy (STM)
investigation of the edges of graphene grains synthesized on Cu foils by
chemical vapor deposition (CVD). Most of the edges are macroscopically parallel
to the zigzag directions of graphene lattice. These edges have microscopic
roughness that is found to also follow zigzag directions at atomic scale,
displaying many ~120 degree turns. A prominent standing wave pattern with
periodicity ~3a/4 (a being the graphene lattice constant) is observed near a
rare-occurring armchair-oriented edge. Observed features of this wave pattern
are consistent with the electronic intervalley backscattering predicted to
occur at armchair edges but not at zigzag edges
Detecting Activations over Graphs using Spanning Tree Wavelet Bases
We consider the detection of activations over graphs under Gaussian noise,
where signals are piece-wise constant over the graph. Despite the wide
applicability of such a detection algorithm, there has been little success in
the development of computationally feasible methods with proveable theoretical
guarantees for general graph topologies. We cast this as a hypothesis testing
problem, and first provide a universal necessary condition for asymptotic
distinguishability of the null and alternative hypotheses. We then introduce
the spanning tree wavelet basis over graphs, a localized basis that reflects
the topology of the graph, and prove that for any spanning tree, this approach
can distinguish null from alternative in a low signal-to-noise regime. Lastly,
we improve on this result and show that using the uniform spanning tree in the
basis construction yields a randomized test with stronger theoretical
guarantees that in many cases matches our necessary conditions. Specifically,
we obtain near-optimal performance in edge transitive graphs, -nearest
neighbor graphs, and -graphs
Multiscale analysis of waves reflected by complex interfaces: Basic principles and experiments
International audience[1] This paper considers the reflection of waves by multiscale interfaces in the framework of the wavelet transform. First, we show how the wavelet transform is efficient to detect and characterize abrupt changes present in a signal. Locally homogeneous abrupt changes have conspicuous cone-like signatures in the wavelet transform from which their regularity may be obtained. Multiscale clusters of nearby singularities produce a hierarchical arrangement of conical patterns where the multiscale structure of the cluster may be identified. Second, the wavelet response is introduced as a natural extension of the wavelet transform when the signal to be analyzed (i.e., the velocity structure of the medium) can only be remotely probed by propagating wavelets into the medium instead of being directly convolved as in the wavelet transform. The reflected waves produced by the incident wavelets onto the reflectors present in the medium constitute the wavelet response. We show that both transforms are equivalent when multiple scattering is neglected and that cone-like features and ridge functions can be recognized in the wavelet response as well. Experimental applications of the acoustical wavelet response show how useful information can be obtained about remote multiscale reflectors. A first experiment implements the synthetic cases discussed before and concerns the characterization of planar reflectors with finite thicknesses. Another experiment concerns the multiscale characterization of a complex interface constituted by the surface of a layer of monodisperse glass beads immersed in water. Citation: Le Gonidec, Y., D. Gibert, and J.-N. Proust , Multiscale analysis of waves reflected by complex interfaces: Basic principles and experiments
Study of Lipschitz regularity - Feature extraction on regular and irregular grids
In this paper we study the pointwise Lipschitz regularity, covering several aspects: theoretical and practical, methods for its estimation on regular and irregular grids. The relevance of this value of regularity lies in its invariance properties to several transformations, and its fast computation thanks to wavelets. We study the influence of scale on wavelets transforms and show invariance properties this value of regularity. We also put forward an original technique for its estimation on regular grids. We also address the issue of irregular grids, based on the behavior of smoothing kernels with respect to scale. The obtained results emphasize the usefulness of such features for the applications, and motivate further work on this topic.
Keywords: Lipschitz regularity, wavelets, smoothing kernels, robust feature extraction, regular and irregular gridsJRC.G.2-Global security and crisis managemen
"Rewiring" Filterbanks for Local Fourier Analysis: Theory and Practice
This article describes a series of new results outlining equivalences between
certain "rewirings" of filterbank system block diagrams, and the corresponding
actions of convolution, modulation, and downsampling operators. This gives rise
to a general framework of reverse-order and convolution subband structures in
filterbank transforms, which we show to be well suited to the analysis of
filterbank coefficients arising from subsampled or multiplexed signals. These
results thus provide a means to understand time-localized aliasing and
modulation properties of such signals and their subband
representations--notions that are notably absent from the global viewpoint
afforded by Fourier analysis. The utility of filterbank rewirings is
demonstrated by the closed-form analysis of signals subject to degradations
such as missing data, spatially or temporally multiplexed data acquisition, or
signal-dependent noise, such as are often encountered in practical signal
processing applications
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