Hierarchical fast bidimensional empirical mode decomposition and its hardware architecture

This paper presents a new method for BEMD. BEMD can decompose a source image into several two-dimensional intrinsic mode functions. During the image decomposition process, it is required to interpolate and draw the upper and lower envelopes. However, these interpolations and drawing the enveloping surface require a large amount of computing time and artificial screening. Thus, some scholars proposed the rapid realization of BEMD. Further, the window size being fixed during the decomposition process led to losses in the data-driven characteristics, adaptability and dimension consistency of the original BEMD. Therefore, this paper proposes a simple but effective means of keeping the original BEMD method features. The estimate reconstruction method is used to replace surface interpolation, and the variable neighborhood window method is adopted to replace the fixed neighborhood window method. In this article, an order filter is used to reconstruct the upper and lower envelopes, and then the filter size is obtained by using the fact that the image information itself is adaptively variable. Through an empirical analysis, this paper shows that this method can keep the original BEMD method’s rapid decomposition, data-driven characteristics, adaptivity and consistency of scale.

Gear and bearing are widely used in a variety of rotating machinery. They are considered as the most critical components of gearbox system. Vibration-based feature extraction is an effective approach to fault diagnosis of gear and bearing units. Fault diagnosis plays an important role in assuring equipment availability and reducing operational costs. This paper proposes a new fault diagnosis method that synthesizes time synchronous technique, fast empirical mode decomposition and correlated kurtosis. Our study shows that an improved fault feature extraction method can be obtained from sampled vibration signals. Energy of gear wheel rotational frequency and its harmonics are designated as the degradation indicators. The effectiveness of proposed method is verified and validated using the vibration data from gearbox test rigs and commercial wind turbines.

The data interpolation is an essential part of Bidimensional Empirical Mode Decomposition (BEMD) of an image. In the decomposition process, local maxima and minima of the image are extracted at each iteration and then interpolated to form the upper and lower envelopes, respectively. Because of the properties of radial basis function (RBF) interpolators, they are good candidates for use in BEMD. However, only one or two of the RBF interpolators have been utilized for BEMD so far. This paper employs many RBF interpolators for BEMD, compares their performances, and finds out the useful ones for BEMD especially in the image filtering application. We propose to apply the BEMD approach with the adequate interpolation function in the image denoising domain. After that, we combine the BEMD with the DWT to improve the BEMD denoising method. The analysis is done using real images. Simulations are made to focus mainly on the effect of interpolation methods by providing less or negligible control on the other parameters of the BEMD process. The study is believed to work as a guideline in the area of BEMD based real image in the filtering application.

Youzhi Zheng Tsinghua University, Department of Computer Science and Technology, Beijing, China 100084 Zheng Qin Tsinghua University, School of Software, Beijing, China 100084 We propose a novel multiscale decomposition (MSD) image fusion algorithm, which is region-based image fusion using bidimensional empirical mode decomposition (BEMD). BEMD is a 2-D data-driven decomposition derived from the empirical mode decomposition (EMD), which does not require predetermined filter or wavelet function. The input images are decomposed into a number of intrinsic mode functions (IMFs) as well as a residual image. The fusion is performed region by region based on the segmentations of the input images to produce composite BEMD representation, and then the inverse BEMD transform is applied to obtain the fused image. Experiments show that the proposed image fusion algorithm provides superior performance over traditional fusion schemes in terms of both objective metrics and visual quality.

In this paper, we introduce a robust image watermarking method based on bi-dimensional empirical mode decomposition (BEMD) against geometric distortion. Based on the characteristics of the image theory and human visual system, the proposed method makes use of orthogonal properties of empirical mode decomposition to achieve the BEMD transform on the image. The image is decomposed into a series of IMFs and residue which contain the different frequency parts of the image. So the watermark is adaptively weighed to the different positions of the middle frequency IMF region. The method makes use of the multi-scale analysis characteristics of image BEMD theory and the person's sense of vision and shows excellent advantage against shearing attack. The method could show the watermark clearly when half of the image has been cut. Experimental results show this method excellent robustness for image shearing. The watermark thus generated is invisible and performs well in StirMark test and is robust to geometrical attacks. Compared with other watermarking algorithms, this algorithm is more robust, especially against geometric distortion, while having excellent frequency properties.

To better analyze images with the Gaussian white noise, it is necessary to remove the noise before image processing. In this paper, we propose a self-adaptive image denoising method based on bidimensional empirical mode decomposition (BEMD). Firstly, normal probability plot confirms that 2D-IMF of Gaussian white noise images decomposed by BEMD follow the normal distribution. Secondly, energy estimation equation of the ith 2D-IMF (i=2,3,4,......) is proposed referencing that of ith IMF (i=2,3,4,......) obtained by empirical mode decomposition (EMD). Thirdly, the self-adaptive threshold of each 2D-IMF is calculated. Eventually, the algorithm of the self-adaptive image denoising method based on BEMD is described. From the practical perspective, this is applied for denoising of the magnetic resonance images (MRI) of the brain. And the results show it has a better denoising performance compared with other methods.

The interpolation causes the frequency aliasing in intrinsic mode functions (IMF) in bi-dimensional empirical mode decomposition (BEMD). The local orthogonality or the computational complexity of the improved BEMDs can not be met. In this paper, a novel BEMD - local estimation empirical mode decomposition (LEEMD) is proposed. Particularly, the local estimation instead of the interpolation without changing the framework of EMD is proposed to solve the problem. LEEMD will be applied in image fusion based on the proposed background/detail rule. In experiments, the objective and subjective experiments show that LEEMD and its application is effective.

The performance of interpolation algorithm used in bi-dimensional empirical mode decomposition directly affects its popularization and application. Therefore, the research on interpolation algorithm is more reasonable, accurate and fast. So far, in the interpolation algorithm adopted by the bi-dimensional empirical mode decomposition, an adaptive interpolation algorithm can be proposed according to the image characteristics. In view of this, this paper proposes an image interpolation algorithm based on the particle swarm and fractal. Its procedure includes: to analyze the given image by using the fractal brown function, to pick up the feature quantity from the image, and then to operate the adaptive image interpolation in terms of the obtained feature quantity. The parameters involved in the interpolation process are optimized by particle swarm optimization algorithm, and the optimal parameters are obtained, which can solve the problem of low efficiency and low precision of interpolation algorithm used in bi-dimensional empirical mode decomposition. It solves the problem that the image cannot be decomposed to obtain accurate and reliable bi-dimensional intrinsic modal function, and realize the fast decomposition of the image. It lays the foundation for the further popularization and application of the bi-dimensional empirical mode decomposition algorithm.

In this paper, we introduce a robust image watermarking method based on bi-dimensional empirical mode decomposition against geometric distortion. Based on the characteristics of the image theory and human visual system, the proposed method makes use of orthogonal properties of empirical mode decomposition to achieve the bi-dimensional empirical mode decomposition transform on the image. The image is decomposed into a series of IMFs and residue which contain the different frequency parts of the image. So the watermark is adaptively weighed to the different positions of the middle frequency IMF region. The method makes use of the multi-scale analysis characteristics of image bi-dimensional empirical mode decomposition theory and the person’s sense of vision and shows excellent advantage against shearing attack. The method could show the watermark clearly when half of the image has been cut. Experimental results show this method excellent robustness for image shearing. The watermark thus generated is invisible and performs well in StirMark test and is robust to geometrical attacks. Compared with other watermarking algorithms, this algorithm is more robust, especially against geometric distortion, while having excellent frequency properties.

This paper presents a new simple and robust texture analysis feature based on Bidimensional Empirical Mode Decomposition (BEMD) and Local Binary Pattern (LBP). BEMD is a locally adaptive decomposition method and suitable for the analysis of nonlinear or nonstationary signals. Texture images are decomposed to several Bidimensional Intrinsic Mode Functions (BIMFs) by BEMD, which present a new set multi-scale compo- nents of images. In our approach, firstly, saddle points are added as supporting points for interpolation to improve original BEMD, and then images are decomposed by the new BEMD to several components (BIMFs). After then, Local Binary Pattern (LBP) in different sizes is used to detect features from different BIMFs. At last, normalization and BIMFs selection method are adopted for features selection. The proposed feature presents invariant while preserving LBP's simplicity. Our method has also been evaluated in CuRet and KTH-TIPS2a texture image databases. It is experimentally demonstrated that the proposed feature achieves higher classification accuracy than other state-of-the- art texture representation methods, especially in small training samples condition.

With varying illumination conditions, facial features obtained from images are distorted nonlinearly by variant lighting intensity and direction, so face recognition becomes very difficult. According to the "common assumption", illumination varies slowly and the face intrinsic feature (including 3D surface and reflectance) varies rapidly in local area, we can then consider high frequency features that represent the face intrinsic structure. FABEMD8 (Fast and Adaptive Bidimensional Empirical Mode Decomposition) is a fast and adaptive method of BEMD22 (Bidimensional Empirical Mode Decomposition), and not using time-consuming plane interpolation computation, it can decompose the image into multilayer high frequency images representing detail features and low frequency images representing analogy features. But we cannot make a quantitative analysis of how many detail features can be used to eliminate illumination variation. So we propose two measures to quantify the detail features, and with these measure weights, we can activitate FABEMD based multilayer detail images matching for face recognition under varying illumination. With PCA, the experiments based on Yale face database B and MU PIE face database show that the method proposed in this paper can get remarkable performance.

Objective: The three steps of brain image processing – preprocessing, segmentation, and classification are becoming increasingly important in patient care. The aim of this article is to present a proposed method in the mentioned three-steps, with emphasis on the preprocessing step, which includes noise removal and contrast enhancement. Methods:The fast and adaptive bidimensional empirical mode decomposition and the anisotropic diffusion equation as well as the modified combination of top-hat and bottom-hat transforms are used for noise reduction and contrast enhancement. Fast C-means clustering with enhanced image is used to detect tumors and the tumor cluster corresponds to the maximum centroid. Finally, Ensemble learning is used for classification. Result:The Figshare brain tumor dataset contains magnetic resonance images used for data selection. The optimal parameters for both noise reduction and contrast enhancement are investigated using a tumor contaminated with Gaussian noise. The results are evaluated against state-of-the-art results and qualitative performance metrics to demonstrate the dominance of the proposed approach. The fast C-means algorithm is applied to detect tumors using twelve enhanced images. The detected tumors were compared to the ground truth and showed an accuracy and specificity of 99% each, and a sensitivity and precision of 90% each. Six statistical features are retrieved from 150 enhanced images using wavelet packet coefficients at level 4 of the Daubechies 4 wavelet function. These features are used to develop the classifier model using ensemble learning to create a model with training and testing accuracy of 96.7% and 76.7%, respectively. When this model is applied to classify twelve detected tumor images, the accuracy is 75%; there are three misclassified images, all of which belong to the pituitary disease group. Conclusion: Based on the research, it appears that the proposed approach could lead to the development of computer-aided diagnosis (CADx) software that physicians can use as a reference for the treatment of rain tumor.

This study describes an automated detection of polyp type as it is very important to determine the existence of dysplasia—a stage leading to the development of gastrointestinal cancer. The polyp-type classification is performed by a multiclass support vector machine from feature-fusion of bi-dimensional empirical mode decomposition (BEMD) and convolutional neural network (CNN). An extensive experiment is performed using standard datasets by extracted features from the individual technique as well as a fusion of features from BEMD and CNN. The fusion technique confirms satisfactory performance compared to other techniques with an accuracy of 98.94%. Moreover, it shows potentiality in precisely classifying some challenging polyps even though these are somehow confusing for human experts.

Empirical mode decomposition (EMD) based methods have been widely used in fringe pattern analysis, including denoising, detrending, normalization, etc. The common problem of using EMD and Bi-dimensional EMD is the mode mixing problem, which is generally caused by uneven distribution of extrema. In recent years, we have proposed some algorithms to solve the mode mixing problem and further applied these methods in fringe analysis. In this paper, we introduce the development of these methods and show the successful results of two most recent algorithms.

This paper proposed a novel multiresolution image fusion approach, which is based on bidimensional empirical mode decomposition (BEMD). The BEMD image is different from the former multi-scale image fusion algorithms which need predetermined filters or wavelet functions. This letter made research on several key issues relevant to the 2D image decomposition and proposed a BEMD image fusion rule to 2D Intrinsic Mode Functions (2D IMF) and residue image of BEMD. The experiments showed the improved performance of this novel algorithm compared with the discrete wavelet transform (DWT).