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.

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

A novel approach for bidimensional empirical mode decomposition (BEMD) is proposed in this paper. BEMD decomposes an image into multiple hierarchical components known as bidimensional intrinsic mode functions (BIMFs). In each iteration of the process, two-dimensional (2D) interpolation is applied to a set of local maxima (minima) points to form the upper (lower) envelope. But, 2D scattered data interpolation methods cause huge computation time and other artifacts in the decomposition. This paper suggests a simple, but effective, method of envelope estimation that replaces the surface interpolation. In this method, order statistics filters are used to get the upper and lower envelopes, where filter size is derived from the data. Based on the properties of the proposed approach, it is considered as fast and adaptive BEMD (FABEMD). Simulation results demonstrate that FABEMD is not only faster and adaptive, but also outperforms the original BEMD in terms of the quality of the BIMFs.

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Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation

Bidimensional empirical mode decomposition (BEMD) techniques are associated with high computation time and other artifacts because of the application of two dimensional (2D) scattered data interpolation methods. In this paper, order statistics filters are employed to get the upper and lower envelopes in the BEMD process, instead of the surface interpolation. Based on the achieved characteristics of the proposed approach, it is considered as fast and adaptive BEMD (FABEMD). Simulation results demonstrate that besides reducing the computation time, FABEMD outperforms the original BEMD in terms of the quality in some cases.

A novel approach of fast and adaptive bidimensional empirical mode decomposition

A novel boundary processing technique is proposed for bidimensional empirical mode decomposition (BEMD). BEMD is a new form of multiscale decomposition and has superior quality in extracting intrinsic components of textures. Although the boundary effect of BEMD is one of its main questions, there have been no concrete discussions or effective methods for it. A modified algorithm of nonparametric sampling for texture synthesis is used to extend images before applying BEMD. Experiments indicate that the technique proposed in This work can form better decomposition compared with past algorithms not only for textures but also for natural images.

Boundary Processing of bidimensional EMD using texture synthesis

Image empirical mode decomposition (IEMD) is an empirical mode decomposition concept used in Hilbert–Huang transform (HHT) expanded into two dimensions for the use on images. IEMD provides a tool for image processing by its special ability to locally separate superposed spatial frequencies. The tendency is that the intrinsic mode functions (IMFs) other than the first are low-frequency images. In this study we give an overview of the state-of-the-art methods to decompose an image into a number of IMFs and a residue image with a minimum number of extrema points, together with the use of the method. Ideas and open problems are presented.

Image empirical mode decomposition: a new tool for image processing

In this paper the technique of directional empirical mode decomposition (DEMD) and its application to texture segmentation are presented. Empirical mode decomposition (EMD) decomposes signals by sifting and then analyzes the instantaneous frequency of the obtained components called intrinsic mode functions (IMF). As a new form of extending 1D EMD to the 2D case, DEMD considers the directional frequency and envelope at each point. One type of 2D Hilbert transform is introduced to compute the analytical functions for the frequency and envelope. The technique of selecting directions for DEMD based on texture's Wold theory is also presented. Experimental results indicate the effectiveness of the method for texture segmentation.

Texture segmentation using directional empirical mode decomposition

This work presents a method for texture classification through directional empirical mode decomposition (DEMD). Although there have been many filtering based techniques proposed for texture retrieval, problems of non-adaptivity and redundancy are still hard to solve simultaneously. As a technique being introduced into signal processing, empirical mode decomposition (EMD) is an adaptive and approximately orthogonal filtering process. To apply EMD to texture classification, we propose a new method of extending 1-D EMD to 2-D case called DEMD. The approach adaptively decomposes images into local narrow band ingredients-intrinsic mode functions (IMFs) and extracts their features including frequency and envelopes. To improve its classification ability the fractal dimensions of the IMFs are also considered. Decomposition of several directions is computed for rotation invariance. Experiments for textures in Brodatz set and USC database indicate the effectiveness of our technique.

Texture classification through directional empirical mode decomposition

In this paper a new algorithm for image magnification is presented. Because linear magnification/interpolation techniques diminish the contrast and produce sawtooth effects, in recent years, many nonlinear interpolation methods, especially nonlinear diffusion based approaches, have been proposed to solve these problems. Two recently proposed techniques for interpolation by diffusion, forward and backward diffusion (FAB) and level-set reconstruction (LSR), cannot enhance the contrast and smooth edges simultaneously. In this article, a novel Partial Differential Equations (PDE) based approach is presented. The contributions of the paper include: firstly, a unified form of diffusion joining FAB and LSR is constructed to have all of their virtues; secondly, to eliminate artifacts of the joint diffusion, soft constraint takes the place of hard constraint presented by LSR; thirdly, the determination of joint coefficients, criterion for stopping time and color image processing are also discussed. The results demonstrate that the method is visually and quantitatively better than Bicubic, FAB and LSR.

Image magnification method using joint diffusion

Recently, there has been a growing interest in investigating signal-adaptive multirate filter banks. In this paper, we propose a direct method of constructing signal-adaptive orthogonal wavelet filter banks with better energy compaction performance than that of Daubechies wavelet filters of same length. The speed of this method is fast, so it can be constructed in real time.

A novel method for designing adaptive compaction orthogonal wavelet filter banks

Breast cancer is the most common cancer for women worldwide. 3D Ultrasound Computed Tomography (3D USCT) is a novel imaging method for early breast cancer diagnosis, which allows reconstruction of quantitative tissue parameters like speed of sound and attenuation. For reconstruction we use the paraxial approximation of the Helmholtz equation as forward model. We have realized the forward solution, backprojection and reconstruction for a ring transducer arrangement. The reconstruction software was evaluated with data simulated with k-Wave, resulting in the mean error for the speed of sound map of 12.6 m/s for a pixel size of 0.3 mm. Spatial resolution was estimated with a resolution phantom containing circular inclusions with realistic speed of sound values for breast tissues, allowing maximum resolution of 2 mm. In this paper we show that our method has accurate forward solution, we present the new backprojection technique and initial results of reconstructing simulated data.

Hongjian Wang

Papers

Texture segmentation using directional empirical mode decomposition

Texture classification through directional empirical mode decomposition

Image magnification method using joint diffusion

A novel method for designing adaptive compaction orthogonal wavelet filter banks

Wave-based ultrasound transmission tomography using the paraxial approximation in 2D