Éric Deléchelle

Image analysis by bidimensional empirical mode decomposition

Recent developments in analysis methods on the non-linear and non-stationary data have received large attention by the image analysts. In 1998, Huang introduced the empirical mode decomposition (EMD) in signal processing. The EMD approach, fully unsupervised, proved reliable monodimensional (seismic and biomedical) signals. The main contribution of our approach is to apply the EMD to texture extraction and image filtering, which are widely recognized as a difficult and challenging computer vision problem. We developed an algorithm based on bidimensional empirical mode decomposition (BEMD) to extract features at multiple scales or spatial frequencies. These features, called intrinsic mode functions, are extracted by a sifting process. The bidimensional sifting process is realized using morphological operators to detect regional maxima and thanks to radial basis function for surface interpolation. The performance of the texture extraction algorithms, using BEMD method, is demonstrated in the experiment with both synthetic and natural images.

Texture analysis based on local analysis of the Bidimensional Empirical Mode Decomposition

Abstract.The main contribution of our approach is to apply the Hilbert-Huang Transform (which consists of two parts: (a) Empirical Mode Decomposition (EMD), and (b) the Hilbert spectral analysis) to texture analysis. The EMD is locally adaptive and suitable for analysis of non-linear or non-stationary processes. This one-dimensional decomposition technique extracts a finite number of oscillatory components or “well-behaved” AM-FM functions, called Intrinsic Mode Function (IMF), directly from the data. Firstly, we extend the EMD to 2D-data (i.e. images), the so called bidimensional EMD (BEMD), the process being called 2D-sifting process. The 2D-sifting process is performed in two steps: extrema detection by neighboring window or morphological operators and surface interpolation by radial basis functions or multigrid B-splines. Secondly, we analyse each 2D-IMF obtained by BEMD by studying local properties (amplitude, phase, isotropy and orientation) extracted from the monogenic signal of each one of them. The monogenic signal is a 2D-generalization of the analytic signal, where the Riesz Transform replaces the Hilbert Transform. The performance of this texture analysis method, using the BEMD and Riesz Transform, is demonstrated with both synthetic and natural images.

Empirical mode decomposition: an analytical approach for sifting process

The present letter proposes an alternate procedure that can be effectively employed to replace the essentially algorithmic sifting process in Huangs empirical mode decomposition (EMD) method. Recent works have demonstrated that EMD acts essentially as a dyadic filter bank that can be compared to wavelet decompositions. However, the origin of EMD is algorithmic in nature and, hence, lacks a solid theoretical framework. The present letter proposes to resolve the major problem in the EMD method-the mean envelope detection of a signal-by a parabolic partial differential equation (PDE)-based approach. The proposed approach is validated by employing several numerical studies where the PDE-based sifting process is applied to some synthetic composite signals.

Bidimensional empirical mode decomposition modified for texture analysis

This study introduces a new approach based on Bidimensional Empirical Mode Decomposition (BEMD) to extract texture features at multiple scales or spatial frequencies. Moreover, it can resolve the intrawave frequency modulation provided the frequency modulation. This decomposition, obtained by the bidimensional sifting process, plays an important role in the characterization of regions in textured images. The sifting process is realized using morphological operators to analyze the spatial frequencies and thanks to radial basis functions (RBF) for surface interpolation. We modified the original sifting algorithm to permit a pseudo bandpass decomposition of images by inserting scale criterion. Its effectiveness is demonstrated on synthetic and natural textures. In particular, we show that many different elements in textures can be extracted through the bidimensional empirical mode decomposition, which is fully unsupervised.

Texture analysis based on the bidimensional empirical mode decomposition with gray-level co-occurrence models

We present a texture analysis algorithm based on gray-level cooccurrence (GLC) model and bidimensional empirical mode decomposition (BEMD) of a texture field. The EMD, which has been recently introduced in signal processing by Huang in 1998, is adaptive for nonlinear and nonstationary data analysis. The main contribution of our approach is to apply the empirical mode decomposition to texture extraction and image denoising. This decomposition, obtained by the bidimensional sifting process, plays an important role in the characterization of regions in textured images. The sifting process is realized using morphological operators to detect regional extrema and thanks to radial basis functions (RBF) for interpolation. We modified the original sifting process to permit a texture decomposition of images by inserting criteria proposed by second-order statistics from GLCs.

A Spectral Approach for Sifting Process in Empirical Mode Decomposition

In this paper, we propose an alternative to the algorithmic definition of the sifting process used in the original Huangs empirical mode decomposition (EMD) method. Although it has been proven to be particularly effective in many applications, EMD method has several drawbacks. The major problem with EMD is the lack of theoretical Framework which leads to difficulties for the characterization and evaluation this approach. On top of the mathematical model, there are other concerns with mode mixing and transient phenomena, such as intermittency or pure tones separation. This paper follows a previous published nonlinear diffusion-based filtering to solve the mean-envelope estimation in sifting process. The major improvements made in this present work are a non-iterative resolution scheme for the previously proposed partial differential equation (PDE), a new definition of the stopping function used in the PDE framework, and finally an automatic regularization process based on inverse problem theory to deal with mode mixing or transient detection problem. Obtained results confirm good properties of the new version of the PDE-based sifting process and its usefulness for decomposition of various kinds of data. The efficiency of the method is illustrated on some examples using informative and pathological signals for which standard EMD algorithm fails.

A multiscale elastic registration scheme for retinal angiograms

The present paper describes a new and efficient method for registration of retinal angiogram. The presence of noise, the variations in the background, and the temporal variation of fluorescence level poses serious problems in obtaining a robust registration of the retinal image. Here, a multiscale registration scheme is proposed which comprises of three steps. The first step of this work proposes an edge preserving smoothing of the vascular tree. This morphological filtering approach is based on opening and closing with a linear rotating structuring element. For complete preservation of the linear shape of the vascular structures, a morphological reconstruction by dilation of the opened image and a reconstruction by erosion of the closed image are applied. It is proposed to compute the registration transform between two successive original frames, from their morphological gradient. Then, the second step consists in computing the morphological gradient of the two filtered images and radiometrically correcting these gradient images. To take into account the intensity variations, our model incorporates two constant multiplicative and additive factors (based on contrast and brightness) estimated employing a simple analysis of the local histograms (based on a sliding window). In the third step, the proposed method computes the registering transform through a coarse-to-fine (or multiscale) hierarchical approach. After computing the dominant registering transform (which implies the translation) between two successive frames, an elastic transform (also called local affine transform) is carried out to achieve a residual correction. The proposed method is tested by experimental studies, performed on macular fluorescein and Indo cyanine green angiographies. It has been sufficiently demonstrated that our proposed registering method is robust, accurate and fully automated, and it is not based on the extraction of the features or landmarks.

Partial Differential Equation-Based Approach for Empirical Mode Decomposition: Application on Image Analysis

The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called “sifting process” used in the original Huangs EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.

Spectral Intrinsic Decomposition Method for Adaptive Signal Representation

In this paper we propose a new method called Spectral Intrinsic Decomposition (SID) for the representation of non-linear signals. This approach is based on the spectral decomposition of Partial Differential Equations (PDE)- based operators which interpolate the characteristic points of a signal. The SIDs components which are the eigenvectors of these PDE interpolation operators underlie the new signal decomposition-reconstruction method. The usefulness and the efficiency of this method is illustrated, in signal reconstruction or denoising aim, on some examples using artifical and pathological signals.

Railway Infrastructure System Diagnosis Using Empirical Mode Decomposition and Hilbert Transform

This paper introduces a diagnosis scheme of a railway infrastructure component based on a combined use of empirical mode decomposition (EMD) and Hilbert transform. This component is dedicated to track/vehicle transmission referred as track circuit. The aim is to detect its working state from one measurement signal which can be viewed as a superposition of several oscillations and periodic patterns called intrinsic mode functions (IMFs). For this application, it will be shown that physical meaning can be assigned to each mode that EMD tries to extract. Furthermore, when the Hubert transform of the IMFs is performed, we show that the changing of instantaneous frequency can be linked to the existence of defect. The performances are illustrated on both simulated and experimental signals