A fast algorithm for bidimensional EMD Damerval, C.; Meignen, S.; Perrier, V.
IEEE signal processing letters,
2005-Oct., 2005-10-00, 20051001, Volume:
12, Issue:
10
Journal Article
Peer reviewed
In this letter, we describe a new method for bidimensional empirical mode decomposition (EMD). This decomposition is based on Delaunay triangulation and on piecewise cubic polynomial interpolation. ...Particular attention is devoted to boundary conditions that are crucial for the feasibility of the bidimensional EMD. The study of the behavior of the decomposition on a different kind of image shows its efficiency in terms of computational cost, and the decomposition of Gaussian white noises leads to bidimensional selective filter banks.
The empirical mode decomposition (EMD) is an algorithmic construction that aims at decomposing a signal into several modes called intrinsic mode functions. In this letter, we present a new approach ...for the EMD based on the direct construction of the mean envelope of the signal. The definition of the mean envelope is achieved through the resolution of a quadratic programming problem with equality and inequality constraints. Some numerical experiments conclude this letter, and comparisons are carried out with the classical EMD.
The modeling of sample distributions with generalized Gaussian density (GGD) has received a lot of interest. Most papers justify the existence of GGD parameters through the asymptotic behavior of ...some mathematical expressions (i.e., the sample is supposed to be large). In this paper, we show that the computation of GGD parameters on small samples is not the same as on larger ones. In a maximum likelihood framework, we exhibit a necessary and sufficient condition for the existence of the parameters. We derive an algorithm to compute them and then compare it to some existing methods on random images of different sizes.
In this correspondence, we propose a new approach to scale-space filtering using a box spline representation of multidimensional signals. The use of box splines is motivated by their ability to ...handle complex geometries better than tensor-product B-splines. The box spline we use is defined by a set of vectors invariant under the multiplication by a sampling matrix. We show that such a box spline satisfies a dilation equation which is the basis for the scale-space filtering we propose. Several numerical applications in 2D conclude the correspondence.
The aim of this paper is to highlight the relevance in computer vision of the pointwise Lipschitz regularity
α
∈ℝ. The regularity
α
gives a measure of the local regularity of the intensity function ...associated to an image. Known wavelet methods provide an efficient computation of
α
at contour points of the image. From a theoretical point of view, we study the effect of geometric deformations and other specific transformations applied to the image, showing invariance properties. From a practical point of view, we assess the robustness of the regularity
α
when the image undergoes various transformations. The results we obtain show the Lipschitz regularity
α
is a suitable feature for applications in computer vision.
In this paper, we address the problem of the retrieval of the components from a multicomponent signal using ideas from the synchrosqueezing framework. The emphasis is on the wavelet choice and we ...propose a novel algorithm based first on the detection of components followed by their reconstruction. Simulations illustrate how the proposed procedure compares with the empirical mode decomposition and other related methods in terms of mode-mixing. We conclude the paper by studying the sensitivity of the proposed technique to sampling and an application to signal denoising.
Blob Detection With Wavelet Maxima Lines Damerval, C.; Meignen, S.
IEEE signal processing letters,
2007-Jan., 2007-1-00, 20070101, 2007-01, Volume:
14, Issue:
1
Journal Article
Peer reviewed
In this letter, we propose a novel approach to blob detection based on wavelet transform modulus maxima. We use maxima lines in scale-space to build a new blob detector. The algorithm we propose ...enables automatic blob detection and blob size determination. The robustness to noise of the blob detector we propose is also shown
We first recall the relation between discrete B-splines and the control points of B-splines. We then use some convergence properties of the control points of B-splines to derive a new algorithm that ...approximates the wavelet decomposition at rational scales and rational location. We conclude the paper by some numerical experiments illustrating the behavior of our algorithm and by a discussion on an efficient implementation of the proposed method.
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