Jean-Claude Nunes

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.

Multivariate empirical mode decomposition and application to multichannel filtering

Empirical Mode Decomposition (EMD) is an emerging topic in signal processing research, applied in various practical fields due in particular to its data-driven filter bank properties. In this paper, a novel EMD approach called X-EMD (eXtended-EMD) is proposed, which allows for a straightforward decomposition of mono- and multivariate signals without any change in the core of the algorithm. Qualitative results illustrate the good behavior of the proposed algorithm whatever the signal dimension is. Moreover, a comparative study of X-EMD with classical mono- and multivariate methods is presented and shows its competitiveness. Besides, we show that X-EMD extends the filter bank properties enjoyed by monovariate EMD to the case of multivariate EMD. Finally, a practical application on multichannel sleep recording is presented.

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.

Turning Tangent Empirical Mode Decomposition: A Framework for Mono- and Multivariate Signals

A novel empirical mode decomposition (EMD) algorithm, called 2T-EMD, for both mono- and multivariate signals is proposed in this correspondence. It differs from the other approaches by its computational lightness and its algorithmic simplicity. The method is essentially based on a redefinition of the signal mean envelope, computed thanks to new characteristic points, which offers the possibility to decompose multivariate signals without any projection. The scope of application of the novel algorithm is specified, and a comparison of the 2T-EMD technique with classical methods is performed on various simulated mono- and multivariate signals. The monovariate behaviour of the proposed method on noisy signals is then validated by decomposing a fractional Gaussian noise and an application to real life EEG data is finally presented.

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.

L0 constrained sparse reconstruction for multi-slice helical CT reconstruction

In this paper, we present a Bayesian maximum a posteriori method for multi-slice helical CT reconstruction based on an L0-norm prior. It makes use of a very low number of projections. A set of surrogate potential functions is used to successively approximate the L0-norm function while generating the prior and to accelerate the convergence speed. Simulation results show that the proposed method provides high quality reconstructions with highly sparse sampled noise-free projections. In the presence of noise, the reconstruction quality is still significantly better than the reconstructions obtained with L1-norm or L2-norm priors.

Empirical mode decomposition synthesis of fractional processes in 1D- and 2D-space

We report here on image texture analysis and on numerical simulation of fractional Brownian textures based on the newly emerged Empirical Mode Decomposition (EMD). EMD introduced by N.E. Huang et al. is a promising tool to non-stationary signal representation as a sum of zero-mean AM-FM components called Intrinsic Mode Functions (IMF). Recent works published by P. Flandrin et al. relate that, in the case of fractional Gaussian noise (fGn), EMD acts essentially as a dyadic filter bank that can be compared to wavelet decompositions. Moreover, in the context of fGn identification, P. Flandrin et al. show that variance progression across IMFs is related to Hurst exponent H through a scaling law. Starting with these recent results, we propose a new algorithm to generate fGn, and fractional Brownian motion (fBm) of Hurst exponent H from IMFs obtained from EMD of a White noise, i.e. ordinary Gaussian noise (fGn with H=1/2).

Robust rigid registration of retinal angiograms through optimization

Retinal fundus photographs are employed as standard diagnostic tools in ophthalmology. Serial photographs of the flow of fluorescein and indocyanine green (ICG) dye are used to determine the areas of the retinal lesions. For objective measurements of features, the registration of the images is a necessity. In this paper, we employ optimization techniques for registration with the help of 2-parameter translational motion model of retinal angiograms, based on non-linear pre-processing (Wiener filtering and morphological gradient) and computation of the similarity criteria for the alignment of the two gradient images for any given rigid transformation. The optimization methods are effectively employed to minimize the similarity criterion. The presence of noise, the variations in the background and the temporal variation of the fluorescence level pose serious problems in obtaining a robust registration of the retinal images. Moreover, local search strategies are not robust in the case of ICG angiograms, even if one uses a multiresolution approach. The present work makes a systematic comparison of different optimization techniques, namely the minimization method derived from the optical flow formulation, the Nelder-Mead local search and the HCIAC ant colony metaheuristic, each optimizing a similarity criterion for the gradient images. The impact of the resolution and median filtering of gradient image is studied and the robustness of the approaches is tested through experimental studies, performed on macular fluorescein and ICG angiographies. Our proposed optimization techniques have shown interesting results especially for high resolution difficult registration problems. Moreover, this approach seems promising for affine (6-parameter motion model) or elastical registrations.