Bidimensional Empirical Mode Decomposition Method Research Articles

Bidimensional local characteristic-scale decomposition and its application in gear surface defect detection

Visual image-based inspection methods can directly reflect the type of defects on the surface of gears. However, these methods have many problems: firstly, as a two-dimensional signal, the data volume of images is large and the processing is relatively time-consuming. Although some existing image signal processing methods (e.g. bidimensional empirical mode decomposition (BEMD)) have good decomposition results, their decomposition speed is slow. The bidimensional local characteristic-scale decomposition (BLCD) method is proposed in this paper, which adaptively decomposes an image from high to low frequencies into several bidimensional intrinsic scale components. It is demonstrated that the BLCD method maintains the advantages of the BEMD method in terms of good decomposition ability and adaptive capability while significantly reducing the processing time and improving the computational efficiency. Secondly, in the running state of the gears, the obtained images sometimes contain noise, which is not convenient for detecting surface defect types. A gear surface defect detection method based on BLCD image denoising is proposed in this paper. Firstly, it uses the BLCD denoising module for preprocessing to provide high signal-to-noise ratio images for the subsequent detection module, and then uses the detection module for defect identification and classification. Experiments prove that the BLCD denoising module has excellent performance and it is well coupled with the detection module, giving the whole method higher accuracy and stability than other classification methods.

Noise suppression in the reconstructed image of digital holography based on the BEMDV method using improved particle swarm optimization.

In digital holography, the speckle noise caused by the coherent nature of the light source and the light scattering generated by the light path system degrade the quality of the reconstructed image seriously. Therefore, in this paper, we propose what we believe to be is a novel noise reduction method combining bidimensional empirical mode decomposition (BEMD) with the variational method, termed BEMDV. The reconstructed image is first decomposed into a series of bidimensional intrinsic mode function (BIMF) components with different frequencies using the BEMD method, and then a certain number of BIMF components are selected for noise reduction by the variational method. An improved particle swarm optimization algorithm is adopted to optimize the key parameters of the proposed method, so as to further improve its noise reduction performance. A reflective off-axis digital holographic imaging system is used to collect the holograms of the coin and optical resolution plate, and the experimental research on noise reduction is carried out. The results with qualitative and quantitative analyses show that the proposed method achieves a better performance on noise reduction and detail preservation than other general methods, enormously enhancing the image quality of holographic reconstruction.

Novel optimization-based bidimensional empirical mode decomposition

Despite its rapid advancement in the past two decades, bidimensional empirical mode decomposition (BEMD) still has several limitations in multi-scale feature description of input images. To ameliorate this issue, in this paper we present several optimization-based approaches to BEMD. First, we articulate an improved unconstrained optimization approach to BEMD (IUOA-BEMD). The essential idea is to formulate an optimization model to decompose an input image based on the Delaunay triangulation of its local maxima (minima). Second, we design a scale-guided optimization approach to BEMD (SGO-BEMD) so as to arrive at an improved modal image. SGO-BEMD uses the initial modal image (obtained from the aforementioned proposed IUOA-BEMD) as a necessary guide and can capture much clearer features at various spatial scales of the input image. In addition, an additional edge-preserving property can be obtained with the edge-aware decomposition if an edge-aware scale-guided optimization to BEMD (EASGO-BEMD) is used. The visualization and quantitative results for many artificial amplitude-modulated–frequency-modulated (AM-FM) images and real images have shown that the newly-proposed methods are very competitive with state-of-the-art BEMD methods. Moreover, we further evaluate the performance of BEMD methods according to their applications in image detail enhancement and image contrast & brightness enhancement. It may be noted that image contrast & brightness enhancement represents the first attempt to integrate BEMD with Retinex theory. Collectively, both types of enhancement validate the utility of the novel optimization-based approaches to BEMD proposed herein.

Effect of expansion on the wall heat flux in a supersonic turbulent boundary layer

Direct numerical simulation of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.25 and a friction Reynolds number of Reτ = 769 subjected to an expansion corner with a deflection angle of 12° is performed to investigate the effect of expansion on the characteristics of the wall heat flux (WHF). The effect of expansion on the statistical and structural properties of the fluctuating WHF is analyzed systematically in terms of probability density function, frequency spectra, and space-time correlations. Normalization using the local root mean square value yields good collapse of the probability density function curves. Unlike with wall pressure frequency spectra, it is found that expansion has little influence on the low-frequency components of the WHF spectrum. The correlation results show that the main effect of expansion is to increase the characteristic length scales and convection velocity of the WHF fluctuation in the post-expansion region. Furthermore, a direct comparison between the conditionally averaged flow fields and those presented in the authors' previous work [Tong et al., Phys. Fluids 34, 015127 (2022)] is performed to uncover the effect of expansion on the flow structures associated with extreme positive and negative WHF fluctuation events. We highlight that the extreme positive event emerges below a small hot spot under the action of a strong Q4 event, whereas the extreme negative event is relatively insensitive to expansion and still occurs between a pair of strong oblique vortices. In addition, we decompose the mean WHF into seven physics-informed contributions and quantify the effect of expansion on the dominating components with the aid of the bidimensional empirical mode decomposition method. The scale-decomposed results demonstrate quantitatively that expansion decreases the contribution of the large-scale structures in the outer region but the small-scale structures in the near-wall region contribute heavily to the mean WHF generation in the downstream region.

Phase retrieval for objects in rain based on a combination of variational image decomposition and variational mode decomposition in FPP.

As far as we know, there is no paper reported to retrieve the phase of an object in rain by the fringe projection profilometry (FPP) method. The fringe projection pattern taken in rain contains much rain noise, which makes it difficult to accurately retrieve the phase of the object. In this paper, we focus on the phase retrieval of the object in rain by the FPP method. We first decompose the original fringe projection pattern into a series of band-limited intrinsic mode functions by the two-dimensional variational mode decomposition (2D-VMD) method. Then we screen out fringe-associated modes adaptively based on mutual information and reconstruct the fringe projection pattern. Next, we decompose the reconstructed fringe projection pattern by the TGV-Hilbert-BM3D variational model to obtain the de-rained fringe component. Finally, we use the Fourier transform method, phase unwrapping method, and carrier-removal method to obtain the unwrapped phase. We test the proposed method on three fringe projection patterns taken in simulated rain weather, and we compare our proposed method with the phase-shifting method, windowed Fourier method, morphological operation-based bidimensional empirical mode decomposition method, 2D-VMD method, and the TGV-Hilbert-BM3D method. The experimental results demonstrate that, for the first time to our knowledge, our method can effectively retrieve the phase of an object in rain from a single fringe projection pattern.

Pre-stack gather optimization technology based on an improved bidimensional empirical mode decomposition method

This study proposes a pre-stack gather optimization technique based on the improved BEMD (bidimensional empirical mode decomposition) method with high stability and adaptability. An original gather signal was decomposed into different components with varying characteristics by the BEMD method, which combines morphological extremum point extraction and the bicubic spline interpolation method to obtain different-scale component signals. Then, wavelet threshold orthogonal filter was used to process the components, which correspond to noise, mostly in small-scale domain. Finally, correlation weighting reconstruction was performed on each component. The weight coefficient is determined according to the relationship between each component of the amplitude-preserving superposition gather and the original gather-preserving superposition gather. The testes on the data from Northeast Sichuan confirm that the method can optimize the pre-stack gather steadily and efficiently. The comparison of the AVO analysis results before and after optimization shows that the method is effective and feasible, which lays a good foundation for a prediction method based on pre-stack data.

Bidimensional Empirical Mode Decomposition-Based Diffusion Filtering for Image Denoising

In this paper, a new method is proposed for image denoising inspired by the bidimensional empirical mode decomposition algorithm and the diffusion-based filtering. In the bidimensional empirical mode decomposition technique, the noisy image is decomposed into its respective intrinsic mode functions and the high-frequency and the low-frequency noises are removed with the help of the proposed diffusion filtering method using its parameters such as connectivity, conductance function, gradient threshold and the number of iterations. The image is reconstructed with the help of these denoised intrinsic mode functions. Performance of the proposed technique is evaluated in terms of the peak signal-to-noise ratio, the structural similarity index, the mean square error and is then compared with the already existing techniques on the image denoising. From the experimentation and results obtained, it is clear that the bidimensional empirical mode decomposition method using the diffusion filtering algorithm is efficient for the denoising of the images both qualitatively and quantitatively.

A Novel Strategy to Image Decomposition for Wireless Capsule Endoscopy Images

Now a day wireless capsule endoscopy (WCE) is broadly used for detection of gastro internal organ diseases. WCE is produces quite 55000 images but still there is challenging task of it that captured noisy images. Removing noise from images is difficult aspiration for image denoising technique. Therefore, various redundant blur and amounts of remaining noise ought to be analysis to research the particular results of denoising method. In this research article, different methods are used for image denoising and evaluated performance for wireless capsule endoscopy images. The proposed approach is suggested Bidimensional Empirical Mode Decomposition (BEMD) for WCE images. Here evaluate performance of BEMD method and wavelet. Computer simulation proved that proposed technique offer considerable advantage than other method.

Enhancing chlorophyll fluorescence imaging under structured illumination with automatic vignetting correction for detection of chilling injury in cucumbers

Chlorophyll fluorescence imaging (CFI) is useful for detecting physiological disorders or defects for green-skinned horticultural products, because defective and normal plant tissues would have different responses to ultraviolet (UV) or short-wavelength visible excitation. This study was intended to evaluate the effectiveness of a new CFI approach by using structured illumination coupled with a proposed automated method for vignetting correction of chlorophyll fluorescence images, for enhanced detection of chilling injury in cucumbers. A CFI system with UV-blue light as an excitation source under structured illumination was assembled. Spectral images over the spectral region of 660–800 nm in 5 nm increments were first acquired from chilling-treated cucumbers under uniform UV-blue illumination to determine appropriate wavebands for implementation of CFI under structured illumination. Further experiment was conducted on a larger group of chilling treated cucumbers to acquire chlorophyll fluorescence images under structured illumination for two wavebands centered at 675 nm and 750 nm. An automatic method for vignetting correction of fluorescence images was proposed by using a modified bi-dimensional empirical mode decomposition (BEMD) technique. Results showed that the chlorophyll fluorescence spectra of cucumbers were characterized by two emission peaks around the regions of 685–690 nm and 740–745 nm respectively. The proposed BEMD method was effective for vignetting correction of fluorescence images, which eliminates the need of using a physical fluorescence target for image correction. Moreover, compared to uniform illumination, structured illumination was found to provide significantly better fluorescence images in terms of the image sharpness and contrast between the normal and chilling-injury tissues, which were inductive to enhancing the detection of chilling injury in cucumbers.

Feature extraction based on empirical mode decomposition for automatic mass classification of mammogram images

Breast cancer is one of the major health problems that leads to early mortality in women. To aid the radiologists, computer aided diagnosis provides a second opinion for the detection and classification of breast cancer. In this paper, two texture feature extraction methods using Empirical Mode Decomposition (EMD) have been proposed to classify the masses in mammogram images into benign or malignant. The first feature extraction method is based on Bi-dimensional Empirical Mode Decomposition (BEMD). On performing BEMD on Region of Interest (ROI) of mammogram image, the ROI is decomposed into a set of different frequency components called Bi-dimensional Intrinsic Mode Functions (BIMFs). Gray Level Co-occurrence Matrix (GLCM) and Gray Level Run Length Matrix (GLRM) features are extracted from these BIMFs and are given as input to the classifier for classification into benign or malignant. Due to the mode mixing problem that exists in BEMD, BIMFs obtained from BEMD are less orthogonal to each other. To overcome this drawback, the second feature extraction method called Modified Bi-dimensional Empirical Mode Decomposition (MBEMD) is proposed. The BIMFs are extracted by employing the proposed MBEMD on mammogram ROI. Features are extracted in a similar way as BEMD method. Support Vector Machine (SVM) and Linear Discriminant Analysis (LDA) classifiers are used for the classification of mammogram mass. The classification accuracy of 88.8%, 96.2% and Area Under the Curve (AUC) of Receiver Operating Characteristics (ROC) of 0.9, 0.96 are obtained with SVM classifier for BEMD, proposed MBEMD based features respectively. The results show that the proposed method yields consistent performance when applied across different databases.

Fast Bi-dimensional empirical mode decomposition(BEMD) based on variable neighborhood window method

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.

Fast Bi-dimensional empirical mode decomposition as an image enhancement technique for fruit defect detection

Image enhancement is critical to detection of fruit defects by imaging techniques. Vignetting and noise are major image artifacts, which can seriously affect image segmentation results, especially in inspecting the curved-surface objects like fruit. It is common to use a calibration object or a mathematic model to reduce the vignetting effect in defect detection, but the approach is often cumbersome, inflexible, and difficult to achieve desired results. In this study, a new image enhancement method based on bi-dimensional empirical mode decomposition (BEMD) of images was proposed to isolate and subsequently remove the effects of vignetting and noise by means of selective image reconstruction. The new BEMD method, along with three other BEMD methods, was first tested on decomposing a synthetic image with artificially added vignetting and noise. The BEMD was found to be the most efficient for image decomposition in terms of computation time, and also give high-quality reconstructed images. Experiments were further conducted by applying the BEMD to the direct and amplitude component images of apple samples with subsurface bruising and surface defects, which were acquired by using a structured-illumination reflectance imaging (SIRI) system. BEMD effectively reduced the image vignetting and greatly enhanced the defect features of the apples, based on both visual inspection and quantitative evaluation. BEMD offers an effective tool for enhancing SIRI images, and it is also promising for image enhancement with other imaging modalities for fruit defect detection.

Bidimensional empirical mode decomposition method for image processing in sensing system

Recent developments in image processing play a significant role in processing the images clearly. Undoubtedly, identifying the target against clutter is another challenging task in Ground Penetrating Radar (GPR) image processing. To successfully distinguish targets from surrounding clutter, a novel Bidimensional Empirical Mode Decomposition (BEMD) system is proposed. The overall process can be broken down into four steps. First, images are decomposed using BEMD arithmetic to extract the Intrinsic Mode Functions (IMFs). Then, these IMFs could be examined using gradual single frequency signals to bring out and highlight the physical meaning of instantaneous amplitudes and instantaneous frequencies. To find the best-fitting hyperbolas, the object position of the vertex is estimated using maximum point estimation method and velocity is estimated using a minimum entropy method. Finally, the location of reflection hyperbolas can be extracted clearly. The simulation and experimental images show the effectiveness of this method in identifying targets.

Computer-aided diagnosis of breast cancer using bi-dimensional empirical mode decomposition

Breast cancer is a serious disease for women in the world and ranks the second cancer for women in many countries. Computer-aided diagnosis provides a second view to aid for radiologists to detect and diagnose breast cancer. In this paper, we present a novel approach of textural features extraction from mammograms using bi-dimensional empirical mode decomposition (BEMD) method and classification for diagnosis of breast cancer. Preprocessing techniques such as noise removal, artifacts and background suppression and contrast enhancement are performed before features extraction stage. Gray-level co-occurrence matrices-based features are extracted from 2-D intrinsic mode functions obtained by applying BEMD method on mammographic images. Finally, these features are given as an input to least squares support vector machine for classification of mammogram as normal or abnormal. The experimental results show that the proposed method achieves 95% accuracy, which is better than as compared to other published methods in the Mini-MIAS database for diagnosis of breast cancer. The proposed method can be used as automatic, accurate and noninvasive method for breast cancer diagnosis and treatment.

Investigation of KDP crystal surface based on an improved bidimensional empirical mode decomposition method

Abstract This paper proposed a novel spatial frequency analysis method for the investigation of potassium dihydrogen phosphate (KDP) crystal surface based on an improved bidimensional empirical mode decomposition (BEMD) method. Aiming to eliminate end effects of the BEMD method and improve the intrinsic mode functions (IMFs) for the efficient identification of texture features, a denoising process was embedded in the sifting iteration of BEMD method. With removing redundant information in decomposed sub-components of KDP crystal surface, middle spatial frequencies of the cutting and feeding processes were identified. Comparative study with the power spectral density method, two-dimensional wavelet transform (2D-WT), as well as the traditional BEMD method, demonstrated that the method developed in this paper can efficiently extract texture features and reveal gradient development of KDP crystal surface. Furthermore, the proposed method was a self-adaptive data driven technique without prior knowledge, which overcame shortcomings of the 2D-WT model such as the parameters selection. Additionally, the proposed method was a promising tool for the application of online monitoring and optimal control of precision machining process.

Separating the gravity field of Iraq by using bidimensional empirical mode decomposition technique

Potential field is nonstationary and nonlinear data. The empirical mode decomposition (EMD) is considered as new data analysis method suitable for processing such type of data. EMD is a fully data driven technique to decompose signals into their natural scale components. It expresses the original signal as a sum of intrinsic mode functions (IMFs) whose characteristics are a reflection of the intrinsic physical meanings of the original signal. This research proposes the bidimensional empirical mode decomposition (BEMD) based on the calculation principle of empirical mode decomposition to be applied for separating the gravity field of Iraq. The method is compared with polynomial method to separate the same field. BEMD method shows a preference on the polynomial method in separating the gravity field into multi-scale components which reflects the anomaly source form from shallow to deep.

A Bidimensional Empirical Mode Decomposition Method for Fusion of Multispectral and Panchromatic Remote Sensing Images

This article focuses on the image fusion of high-resolution panchromatic and multispectral images. We propose a new image fusion method based on a Hue-Saturation-Value (HSV) color space model and bidimensional empirical mode decomposition (BEMD), by integrating high-frequency component of panchromatic image into multispectral image and optimizing the BEMD in decreasing sifting time, simplifying extrema point locating and more efficient interpolation. This new method has been tested with a panchromatic image (SPOT, 10-m resolution) and a multispectral image (TM, 28-m resolution). Visual and quantitative assessment methods are applied to evaluate the quality of the fused images. The experimental results show that the proposed method provided superior performance over conventional fusion algorithms in improving the quality of the fused images in terms of visual effectiveness, standard deviation, correlation coefficient, bias index and degree of distortion. Both five different land cover types WorldView-II images and three different sensor combinations (TM/SPOT, WorldView-II, 0.5 m/1 m resolution and IKONOS, 1 m/4 m resolution) validated the robustness of BEMD fusion performance. Both of these results prove the capability of the proposed BEMD method as a robust image fusion method to prevent color distortion and enhance image detail.

Image Decomposition Based on a Modified Bidimensional Empirical Mode Decomposition Method

This study introduces a modified bidimensional empirical mode decomposition method to deal with high resolution images. To avoid solving large linear equations and calculating large matrix, the images are split into several blocks, processed individually, and subsequently joined into one. Thus, the complexity of time and space is lowered efficiently.

Multivariate Gray Model-Based BEMD for Hyperspectral Image Classification

Bidimensional empirical mode decomposition (BEMD) has been one of the core activities in image processing due to its fully data-driven and self-adaptive nature. Unfortunately, this promising technique is sensitive to boundary effect. In this paper, a new method inspired by the multivariate gray model (MGM), namely ${\rm GM}(1, N)$ , is developed for boundary extension of the BEMD. Specifically, our contribution is threefold. First, focusing on evaluating the model coefficients and convolution integral, which are key elements in reducing the prediction error of the ${\rm GM}(1, N)$ , we replace the existing (composite) trapezoidal rule with (composite) Simpson rule and deduce an alternative MGM, termed as ${\rm S\hbox{-}GM}(1,N)$ . Second, the given image is extended by the GM(1, 3) or S-GM(1, 3) $(N=3)$ , whose characteristic data series and relative data series are, respectively, derived from the pixel values and coordinates of the image. Consequently, the extended image is decomposed into several bidimensional intrinsic mode functions (BIMFs) and a residue whose corresponding parts are extracted as the decomposition results of the original image. Finally, the proposed boundary effect mitigation methods are applied in the hyperspectral image classification. In greater detail, the BIMFs obtained by various BEMD methods are taken as features of the hyperspectral dataset whereas the widely used $k$ -nearest neighbors ( $k$ -NN) as well as the support vector machine, whose optimal parameters are selected by the genetic algorithm, are adopted as classifiers. Extensive experiments and comparisons with other generally acknowledged methods confirm that the proposed methods achieve promising improvement in the classification performance.

Engineering Surface Analysis by Bidimensional Empirical Mode Decomposition

It is well known that an engineering surface is composed of a large number of wavelengths of roughness that are superimposed on each other. Because these multi-scale features are related to different aspects of the processes the surface has undergone and closely related to the friction and wear properties of a surface, the analysis and characterization of these features becomes an important aspect of manufacture. The challenge is how to use them for acquiring knowledge and for aid to analysis. In this paper, a method for surface topography analysis is proposed based on bidimensional empirical mode decomposition (BEMD), which can provide good adaptive separation of surface texture into multiple hierarchical components known as bidimensional intrinsic mode functions (BIMFs). Applications are conducted by using a simulated surfaces to demonstrate the feasibility and applicability of using the bidimensional empirical mode decomposition method in the analysis of engineering surfaces.