Bidimensional Intrinsic Mode Functions Research Articles

Prediction of Soil Nutrients Based on Topographic Factors and Remote Sensing Index in a Coal Mining Area, China

(1) Background: Coal mining operations caused severe land subsidence and altered the distributions of soil nutrients that influenced by multiple environmental factors at different scales. However, the prediction performances for soil nutrients based on their scale-specific relationships with influencing factors remains undefined in the coal mining area. The objective of this study was to establish prediction models of soil nutrients based on their scale-specific relationships with influencing factors in a coal mining area. (2) Methods: Soil samples were collected based on a 1 × 1 km regular grid, and contents of soil organic matter, soil available nitrogen, soil available phosphorus, and soil available potassium were measured. The scale components of soil nutrients and the influencing factors collected from remote sensing and topographic factors were decomposed by two-dimensional empirical mode decomposition (2D-EMD), and the predictions for soil nutrients were established using the methods of multiple linear stepwise regression or partial least squares regression based on original samples (MLSROri or PLSROri), partial least squares regression based on bi-dimensional intrinsic mode function (PLSRBIMF), and the combined method of 2D-EMD, PLSR, and MLSR (2D-EMDPM). (3) Results: The correlation types and correlation coefficients between soil nutrients and influencing factors were scale-dependent. The variances of soil nutrients at smaller scale were stochastic and non-significantly correlated with influencing factors, while their variances at the larger scales were stable. The prediction performances in the coal mining area were better than those in the non-coal mining area, and 2D-EMDPM had the most stable performance. (4) Conclusions: The scale-dependent predictions can be used for soil nutrients in the coal mining areas.

Image Processing Algorithm Based on Bi-dimensional Local Mean Decomposition

Because images contain rich characteristic information, adaptive image decomposition algorithms are necessary to achieve multi-scale extraction of image information in multi-scale image decomposition processing. For this reason, based on local mean decomposition (LMD), which has good self-adaptive characteristics, this paper proposes a new adaptive image processing algorithm, bi-dimensional local mean decomposition (BLMD). BLMD can decompose the original image into multiple bi-dimensional product functions (BPFs). Aiming at the decomposition of BLMD, this paper proposes targeted solutions and designs for the extraction of extremum points, screening process interpolation methods, and decomposition and stop conditions involved in BLMD. After fully recognizing the self-adaptive and multi-scale characteristics of BLMD, this paper proposes a variable neighborhood window method to obtain the extreme points in the decomposition process and uses fractal theory to interpolate the image and obtain the corresponding mean surface and other information. Then, the number of non-coincident extreme points on the zero-valued plane projection between adjacent surfaces in the screening process is counted and analyzed, and a stop condition that matches the characteristics of the image is given to ensure the BPF component obtained by decomposition accurately reflects certain feature information of an image. Finally, the BLMD proposed in this paper is formed. Empirical analysis shows this method can quickly decompose and maintain the characteristics of data-drivenness, adaptability and scale consistency of LMD; it can also avoid the disadvantages of other adaptive processing algorithms, such as the bi-dimensional intrinsic mode function obtained by the decomposition of bi-dimensional empirical mode decomposition and the residual failing to completely contain the feature information of the original image.

Text line segmentation and binarization of handwritten historical documents using the fast and adaptive bidimensional empirical mode decomposition

Text line segmentation is a basic step that can be used to serve several processes in the recognition stage. Image segmentation is thus inevitable. A necessary step for text line segmentation is the image binarization. However, it is challenging due to complex background in such images. In this paper, we present a new text line segmentation and banarization method based on fast and adaptive bidimensional empirical mode decomposition (FABEMD). To achieve this, we use the FABEMD method to decompose each image into two components. The binarization threshold is calculated taking into account the characteristics of each component. The inspiration for the new binarization method was drawn from the standard Niblack's and Sauvola's Algorithms. Then the text line segmentation is performed after eliminating the BIMF1 (bidimensional intrinsic mode functions) which could disrupt the segmentation process. The results show that the proposed approach is less sensitive to noise and provides improved text line segmentation and binarization compared to iterative methods.

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.

Bidimensional Empirical Mode Decomposition for SAR Image Feature Extraction With Application to Target Recognition

This study introduces a target recognition algorithm for synthetic aperture radar (SAR) images based on the features extracted by bidimensional empirical mode decomposition (BEMD). BEMD provides an adaptive and empirical way to process signals, which generates bidimensional intrinsic mode functions (BIMFs) to describe the details of SAR images. Therefore, the generated BIMFs are complementary to the original image and their joint use could probably improve the recognition performance. In order to fully exploit the discrimination of these components, the joint sparse representation (JSR) is employed during the classification. JSR operates as multi-task learning algorithm, which represents each component numerically while considering their inner correlations. The original image together with the generated BIMFs are simultaneously represented by JSR to determine the target label according to the output reconstruction errors. Experimental results on the Moving and Stationary Target Acquisition and Recognition (MSTAR) data set demonstrate the validity of the proposed method under different operating conditions. In comparison with some baseline algorithms, the superiority of the proposed method is furtherly validated.

Medical Image Fusion using bi-dimensional empirical mode decomposition (BEMD) and an Efficient Fusion Scheme.

Background: Medical image fusion is being widely used for capturing complimentary information from images of different modalities. Combination of useful information presented in medical images is the aim of image fusion techniques, and the fused image will exhibit more information in comparison with source images.Objective: In the current study, a BEMD-based multi-modal medical image fusion technique is utilized. Moreover, Teager-Kaiser energy operator (TKEO) was applied to lower BIMFs. The results were compared to six routine methods.Material and Methods: In this study, which is of experimental type, an image fusion technique using bi-dimensional empirical mode decomposition (BEMD), Teager-Kaiser energy operator (TKEO) as a local feature selection and Hierarchical Model And X (HMAX) model is presented. BEMD fusion technique can preserve much functional information. In the process of fusion, we adopt the fusion rule of TKEO for lower bi-dimensional intrinsic mode functions (BIMFs) of two images and HMAX visual cortex model as a fusion rule for higher BIMFs, which are verified to be more appropriate for human vision system. Integrating BEMD and this efficient fusion scheme can retain more spatial and functional features of input images.Results: We compared our method with IHS, DWT, LWT, PCA, NSCT and SIST methods. The simulation results and fusion performance show that the presented method is effective in terms of mutual information, quality of fused image (QAB/F), standard deviation, peak signal to noise ratio, structural similarity and considerably better results compared to six typical fusion methods.Conclusion: The statistical analyses revealed that our algorithm significantly improved spatial features and diminished the color distortion compared to other fusion techniques. The proposed approach can be used for routine practice. Fusion of functional and morphological medical images is possible before, during and after treatment of tumors in different organs. Image fusion can enable interventional events and can be further assessed.

BEMD image fusion based on PCNN and compressed sensing

Bidimensional empirical mode decomposition (BEMD) is a new method for multi-scale image decomposition. In order to forbid useless information to cause an adverse impact on results and make the process have a better self-adaptability, this paper presents a new multi-scale image fusion method, which combines pulse coupled neural network (PCNN) and compressed sensing, and uses them in the BEMD. At first, BEMD processes the original images decomposed into multiple bidimensional intrinsic mode function (BIMFs) and a residual image. Then after doing compression measurement on each layer of BIMFS, we can get compression measurement coefficients. The coefficients at the same layer do the PCNN image fusion, and we can get measurement sampling BIMFs. And then after measurement sampling BIMFs reconstructed, we can get the final BIMFs. The residual images do the fusion based on entropy weight to get the final residual image. At last, after BEMD inverse transform, the final BIMFs and the final residual image get the result image. Experimental studies have shown that compared with other multi-scale decompositions-based image fusion algorithms, the algorithm in this paper has a better performance in terms of objective criteria and visual appearance.

A multi scale guided filter for illumination estimation in retinex algorithm

The method of illumination estimation for images affects the effect of retinex algorithm and causes information loss and halo artefact. A multi scale guided filter is proposed to estimate the illumination. In this method, bidimensional empirical mode decomposition is combined with guided filter. Firstly, the image is decomposed into multiple bidimensional intrinsic mode functions and a trend function by bidimensional empirical mode decomposition. Secondly, we use guided filter to estimate illumination information of each bidimensional intrinsic mode functions. Then illuminance component is formed by combining the illuminance information and the trend function. Finally, guided filter is again used to achieve a more accurate illuminance component. The simulation results show that multi scale guided filter can estimate the illumination component deeply and ensure the integrity of the reflection component. In the effect image of retinex algorithm, the contrast is raised by 1, the luminance is raised by 1, the information entropy is raised by 0.18, the clarity is raised by 0.001, and the visual effect is improved as a whole.

Bi-dimensional empirical mode decomposition (BEMD) and the stopping criterion based on the number and change of extreme points

In the bi-dimensional empirical mode decomposition, the determination of the stopping criterion is an important reason for obtaining a complete bi-dimensional intrinsic mode function. An excellent stopping criterion can adapt the image characteristics to stop the decomposition. This paper first analyzes the number and distribution of extreme points reflecting the physical state of the mean surface during the sieving process. Then, bi-dimensional empirical mode decomposition and the stopping criterion based on the number and change of extreme points is proposed. In order to verify the adaptability, effectiveness and reliability of the criterion, the relevant examples were subjected to bi-dimensional empirical mode decomposition experiments under the conditions of the traditional stopping criterion, the GRILL stopping criterion and the stopping criterion proposed in this paper. The results show that the intrinsic mode function obtained by the stop criterion proposed in this paper is more in line with the physical characteristics, more reflective of the original image feature information and with higher accuracy.

Image fusion method based on regional feature and improved bidimensional empirical mode decomposition

The decomposition of multiple source images using bidimensional empirical mode decomposition (BEMD) often produces mismatched bidimensional intrinsic mode functions, either by their number or their frequency, making image fusion difficult. A solution to this problem is proposed using a fixed number of iterations and a union operation in the sifting process. By combining the local regional features of the images, an image fusion method has been developed. First, the source images are decomposed using the proposed BEMD to produce the first intrinsic mode function (IMF) and residue component. Second, for the IMF component, a selection and weighted average strategy based on local area energy is used to obtain a high-frequency fusion component. Third, for the residue component, a selection and weighted average strategy based on local average gray difference is used to obtain a low-frequency fusion component. Finally, the fused image is obtained by applying the inverse BEMD transform. Experimental results show that the proposed algorithm provides superior performance over methods based on wavelet transform, line and column-based EMD, and complex empirical mode decomposition, both in terms of visual quality and objective evaluation criteria.

Automatic fringe enhancement with novel bidimensional sinusoids-assisted empirical mode decomposition.

Fringe-based optical measurement techniques require reliable fringe analysis methods, where empirical mode decomposition (EMD) is an outstanding one due to its ability of analyzing complex signals and the merit of being data-driven. However, two challenging issues hinder the application of EMD in practical measurement. One is the tricky mode mixing problem (MMP), making the decomposed intrinsic mode functions (IMFs) have equivocal physical meaning; the other is the automatic and accurate extraction of the sinusoidal fringe from the IMFs when unpredictable and unavoidable background and noise exist in real measurements. Accordingly, in this paper, a novel bidimensional sinusoids-assisted EMD (BSEMD) is proposed to decompose a fringe pattern into mono-component bidimensional IMFs (BIMFs), with the MMP solved; properties of the resulted BIMFs are then analyzed to recognize and enhance the useful fringe component. The decomposition and the fringe recognition are integrated and the latter provides a feedback to the former, helping to automatically stop the decomposition to make the algorithm simpler and more reliable. A series of experiments show that the proposed method is accurate, efficient and robust to various fringe patterns even with poor quality, rendering it a potential tool for practical use.

SAR image change detection algorithm based on stationary wavelet and bi-dimensional intrinsic mode function

Speckle noise in synthetic aperture radar (SAR) image is produced by the coherent imaging mechanism, which brings a great impact on the change information acquisition of multi-temporal SAR images. Two-dimensional stationary wavelet transform (SWT) and bi-dimensional empirical mode decomposition (BEMD) are the non-stationary signal processing theory of multi-scale transform. According to their implementation process and SAR image characteristic, this paper proposed a new multi-temporal SAR image change detection method based on the combination of the stationary wavelet transform and the bi-dimensional intrinsic mode function (BIMF) features, called SWT-BIMF algorithm. The contribution of the new algorithm includes two aspects. One is the design of the two selections of decomposition features, that is, the speckle noise filtering; another is the selected features to perform the enhance processing, so more effective change information will obtain. The feasibility of the SWT-BIMF algorithm is verified by the measured SAR image data, and good experimental results are obtained.

Multi-focus image fusion based on window empirical mode decomposition

In order to improve multi-focus image fusion quality, a novel fusion algorithm based on window empirical mode decomposition (WEMD) is proposed. This WEMD is an improved form of bidimensional empirical mode decomposition (BEMD), due to its decomposition process using the adding window principle, effectively resolving the signal concealment problem. We used WEMD for multi-focus image fusion, and formulated different fusion rules for bidimensional intrinsic mode function (BIMF) components and the residue component. For fusion of the BIMF components, the concept of the Sum-modified-Laplacian was used and a scheme based on the visual feature contrast adopted; when choosing the residue coefficients, a pixel value based on the local visibility was selected. We carried out four groups of multi-focus image fusion experiments and compared objective evaluation criteria with other three fusion methods. The experimental results show that the proposed fusion approach is effective and performs better at fusing multi-focus images than some traditional methods.

A novel oil spill detection method from synthetic aperture radar imageries via a bidimensional empirical mode decomposition

Oil spills pose a major threat to ocean ecosystems and their health. Synthetic aperture radar (SAR) sensors can detect oil spills on the sea surface. These oil spills appear as dark spots in SAR images. However, dark formations can be caused by a number of phenomena. It is aimed to distinguishing oil spills or look-alike objects. A novel method based on a bidimensional empirical mode decomposition is proposed. The selected dark formations are first decomposed into several bidimensional intrinsic mode functions and the residue. Subsequently, 64 dimension feature sets are calculated using the Hilbert spectral analysis and five new features are extracted with a relief algorithm. Mahalanobis distances are then used for classification. Three data sets containing oil spills or look-alikes are used to test the accuracy rate of the method. The accuracy rate is more than 90%. The experimental results demonstrate that the novel method can detect oil spills validly and accurately.

Multispectral image fusion for illumination-invariant palmprint recognition.

Multispectral palmprint recognition has shown broad prospects for personal identification due to its high accuracy and great stability. In this paper, we develop a novel illumination-invariant multispectral palmprint recognition method. To combine the information from multiple spectral bands, an image-level fusion framework is completed based on a fast and adaptive bidimensional empirical mode decomposition (FABEMD) and a weighted Fisher criterion. The FABEMD technique decomposes the multispectral images into their bidimensional intrinsic mode functions (BIMFs), on which an illumination compensation operation is performed. The weighted Fisher criterion is to construct the fusion coefficients at the decomposition level, making the images be separated correctly in the fusion space. The image fusion framework has shown strong robustness against illumination variation. In addition, a tensor-based extreme learning machine (TELM) mechanism is presented for feature extraction and classification of two-dimensional (2D) images. In general, this method has fast learning speed and satisfying recognition accuracy. Comprehensive experiments conducted on the PolyU multispectral palmprint database illustrate that the proposed method can achieve favorable results. For the testing under ideal illumination, the recognition accuracy is as high as 99.93%, and the result is 99.50% when the lighting condition is unsatisfied.

Iteration-Free Bi-Dimensional Empirical Mode Decomposition and Its Application

A bi-dimensional empirical mode decomposition (BEMD) is one of the powerful methods for decomposing non-linear and non-stationary signals without a prior function. It can be applied in many applications such as feature extraction, image compression, and image filtering. Although modified BEMDs are proposed in several approaches, computational cost and quality of their bi-dimensional intrinsic mode function (BIMF) still require an improvement. In this paper, an iteration-free computation method for bi-dimensional empirical mode decomposition, called iBEMD, is proposed. The locally partial correlation for principal component analysis (LPC-PCA) is a novel technique to extract BIMFs from an original signal without using extrema detection. This dramatically reduces the computation time. The LPC-PCA technique also enhances the quality of BIMFs by reducing artifacts. The experimental results, when compared with state-of-the-art methods, show that the proposed iBEMD method can achieve the faster computation of BIMF extraction and the higher quality of BIMF image. Furthermore, the iBEMD method can clearly remove an illumination component of nature scene images under illumination change, thereby improving the performance of text localization and recognition.

Hyperspectral Image Classification Using Fast and Adaptive Bidimensional Empirical Mode Decomposition With Minimum Noise Fraction

The scattered pixel problem in hyperspectral images caused by atmospheric noises and incomplete classification can lead to unsatisfactory classification; this problem remains to be solved. This letter reports the application of minimum noise fractions (MNFs) combined with fast and adaptive bidimensional empirical mode decomposition (FABEMD) as a two-step process to improve the classification accuracy of airborne visible–infrared imaging spectrometer hyperspectral image of the Indian Pine data set. With dimensional reduction by using MNF, FABEMD, considered as a low-pass filter, decomposes a hyperspectral image into several bidimensional intrinsic mode functions (BIMFs) and a residue image. The first four BIMFs are removed and the remainder BIMFs are integrated to reconstruct informative images that are subsequently classified through a support vector machine classifier (SVM). The classification results show that the proposed approach can effectively eliminate noise effects and can obtain higher accuracy than does traditional MNF SVM.

Analysis of fMRI images with bi-dimensional empirical mode decomposition based-on Green's functions

Abstract We present a new method for decomposing two-dimensional data arrays with empirical mode decomposition (EMD). It performs envelope surface interpolation based on Green's functions in tension (GiT) to extract bi-dimensional intrinsic mode functions (BIMFs). The new method is called GiT-BEMD and outperforms existing bi-dimensional ensemble EMD (BEEMD) variants in terms of computational costs and quality of extracted intrinsic modes. More specifically, it is easy to implement, much faster than BEEMD, very robust and free from processing artifacts. GiT-BEMD is applied to fMRI data recorded during a contour integration task. Features extracted from resulting volume intrinsic mode functions (VIMFs) achieve higher classification accuracy compared to the canonical BEEMD. The new method thus provides a valuable alternative to existing mode decomposition methods for analyzing images.

A green’s function-based Bi-dimensional empirical mode decomposition

Bidimensional Empirical Mode Decomposition(BEMD) interprets an image as a superposition of Bidimensional Intrinsic Mode Functions (BIMFs). They are extracted by a process called sifting, which encompasses two-dimensional surface interpolations connecting a set of local maxima or minima to form corresponding envelope surfaces. Existing surface interpolation schemes are computationally very demanding and often induce artifacts in the extracted modes. This paper suggests a novel method of envelope surface interpolation based on Green’s functions. Including surface tension greatly improves the stability of the new method which we call Green’s function in tension-based BEMD (GiT-BEMD). Simulation results, using toy images with various textures, facial images and functional neuroimages, demonstrate the superior performance of the new method when compared to its canonical BEMD counterpart. GiT-BEMD strongly speeds up computations and achieves a higher quality of the extracted BIMFs. Furthermore, GiT-BEMD can be extended simply to an ensemble-based variant (GiT-BEEMD), if needed. In summary, the study suggests the new variant GiT-BEMD as a highly competitive, fast and stable alternative to existing BEMD techniques for image analysis.

A new multi‐focus image fusion algorithm based on BEMD and improved local energy

A multi‐focus image fusion method, which is based on bidimensional empirical mode decomposition (BEMD) and improved local energy algorithm, is presented in this paper. First, the source image is decomposed by BEMD. Then maximum criterion combined with weighted average fusion rule based on local energy is applied to bidimensional intrinsic mode function components of the corresponding frequency segment. If the phase of the bidimensional intrinsic mode function coefficients decomposed by BEMD on two source images is the same, the local energy maximum criterion is used in the frequency coefficients of the fused image; else, if the corresponding phase is opposite, bidimensional intrinsic mode function coefficients of the fused image is determined by a weighted average method based on local energy. Finally, the fusion result is obtained by the inverse BEMD transformation on the fusion coefficient. Simulation shows that the proposed algorithm significantly outperforms traditional methods such as the maximum criterion, weighted average, and wavelet fusion rules. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.