Wavelet Moments Research Articles

An Approach for Observing and Modeling Errors in MEMS-Based Inertial Sensors Under Vehicle Dynamic

This paper studies the error behavior of low-cost inertial sensors in dynamic conditions. After proposing a method for error observations per sensor (i.e., gyroscope or accelerometer) and axes, their properties are estimated via the methodology of generalized method of wavelet moments. The developed model parameters are compared with those obtained under static conditions. Then, an attempt is presented to link the parameters of the established model to the dynamic of the vehicle. It is found that a linear relation explains a large portion of the exhibited variability. These findings suggest that the static methods employed for the calibration of inertial sensors could be improved when exploiting such a relationship.

Divergence-Free Wavelet Frames

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets retain the basic characteristics (decay rate and order of vanishing moments) of the initial wavelets. Since the Leray projector is also shift-invariant, it is defined as a Fourier multiplier, and our construction is implemented efficiently using the fast Fourier transform. In order to illustrate the practicality of the method, we present vector field denoising experiments.

A new method for on-line monitoring discharge pulse in WEDM-MS process

This paper presents a new method for on-line monitoring discharge pulse in wire electrical discharge machining-middle speed (WEDM-MS) process based on digital image processing and machine learning. Discharge pulse monitoring is a key aspect of the WEDM-MS control system, as it directly guides the direction and the speed of the machining. In the proposed system, the discharge pulse is captured using a high-bandwidth oscilloscope because the shortest period of discharge is less than 40 ms. The pro- posed system workflow consists of image reconstruction, pre-processing, feature extraction, and pulse classification. Wavelet moment analysis (WMA), Hu moment analysis (HMA), fractal dimension analysis (FDA), local geometric characteristics (LGC), and global geometric characteris- tics (GGC) are all applied in the image pre-processing to extract waveform image features and reduce image dimen- sion. These features are then used in a two-stage clas- sification technique that employs support vector machine (SVM) and random forests (RF) for pulse classification and

A Mellin transform approach to wavelet analysis

The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.

A fast and effective method of quantitative analysis of VB1, VB2 and VB6 in B-vitamins complex tablets based on three-dimensional fluorescence spectra

Scattering signals and partial overlapping of target peaks usually appear in fluorescence determination. In this study, the improved wavelet moment method was proposed and applied to the quantitative determination of multiple target components in real B-vitamins complex tablets based on three-dimensional (3D) fluorescence spectra. The correlation coefficients (R) were more than 0.9939, and the correlation coefficients of leave-one-out cross-validation (RLOO-cv) were more than 0.9376. The inter-day and intra-day variations were less than 5.8% and 6.1%, respectively. The recovery ranged from 97.6% to 109.4%. The limits of detection (LODs) and quantification (LOQs) were less than 0.07μgmL−1 and 0.13μgmL−1, respectively. All the statistical parameters indicated that the method was stable and reliable. The application to the practical samples confirmed that wavelet moment method effectively extracted the features of target components in 3D spectra and the proposed method could be applied to the analyses of food or other complex samples.

Fusing magnitude and phase of wavelet moments for content-based image retrieval

The wavelet moments (WMs) are capable to represent the variations in the images as they provide both time and frequency localisation. In this paper the image retrieval system is implemented using complex wavelet moments (CWMs). The magnitude of the WMs of image is rotation invariant, but the phase component changes with image rotation. The magnitude and phase of WMs are incorporated and used both real and imaginary components of WMs so as to make WMs complex to describe as image. The rotation invariance of real and imaginary component is achieved by correction and comparison of phases of WMs of two comparable images with suitable distance metric. The proposed algorithm is applied to USC Rotated Texture database and Colombia Object Image Library (COIL-100) database and detailed analysis is carried out and performance is compared with other orthogonal moments. In many cases the complex WMs produce excellent performance. The average retrieval accuracy for 13 textures, Bark, Brick, Bubble, Grass, Leather, Pigskin, Raffia, Sand, Straw, Water, Weave, Wood and Wool are 100, 85, 92, 99, 91, 92, 95, 97, 76, 94, 99, 74, and 95% respectively. Also, the experimental results on COIL-100 database reveals that the complex wavelet moment outperforms than complex Zernike moments and it is one of the useful descriptor for content-based image retrieval systems.

Gesture Recognition of Pigs Based on Wavelet Moment and Probabilistic Neural Network

For real-time monitoring the behavior of pigs in piggery, the method that combined the advantages of wavelet multi-scale analysis with invariant moments is proposed. Firstly, the original image is pre-processed by using ant colony algorithm to extract object contour. Then the target contour edge growth method and binary morphology are used, and the outlines of pigs are extracted by canny operator. Wavelet moment was used to get the global features of an image and increase the structural details of the image feature description. Finally, the neural network is applied to identify four behaviors including normal walking, walking down, looked up walking and lying of pigs. Experimental results show that the accuracy of the classification and identification of swine gesture reached more than 95%. This method has a better effect in the recognition of pigs and the noise resistance.

Content-based image retrieval using PSO and k-means clustering algorithm

In various application domains such as website, education, crime prevention, commerce, and biomedicine, the volume of digital data is increasing rapidly. The trouble appears when retrieving the data from the storage media because some of the existing methods compare the query image with all images in the database; as a result, the search space and computational complexity will increase, respectively. The content-based image retrieval (CBIR) methods aim to retrieve images accurately from large image databases similar to the query image based on the similarity between image features. In this study, a new hybrid method has been proposed for image clustering based on combining the particle swarm optimization (PSO) with k-means clustering algorithms. It is presented as a proposed CBIR method that uses the color and texture images as visual features to represent the images. The proposed method is based on four feature extractions for measuring the similarity, which are color histogram, color moment, co-occurrence matrices, and wavelet moment. The experimental results have indicated that the proposed system has a superior performance compared to the other system in terms of accuracy.

IMAGE RETRIEVAL USING CERTAIN BLOCK BASED DIFFERENCE OF INVERSE PROBABILITY AND CERTAIN BLOCK BASED VARIATION OF LOCAL CORRELATION COEFFICIENTS INTEGRATED WITH WAVELET MOMENTS

Content Based Image Retrieval (CBIR) is an evolving topic under image processing. Retrieval on medical images plays a vital role in saving mankind. Medical Content Based Image Retrieval (MCBIR) does not stop its work in displaying similar images; it also goes one step further for diagnosis to decide the method of therapy by comparing the query image and database image. Hence we believe that, our work is a mile stone in the medical imaging research and will gain an appreciable amount of demand in automatic diagnosis done through artificial intelligence. While handling a large amount of data base, retrieval naturally reduces the search area. Many research works were conducted on CBIR systems to yield better performance on retrieval of medical images. Here we propose a modified integrated approach which extracts low level image features: Color, intensity, shape and texture using Certain Block based Difference of Inverse Probability (CBDIP) and Certain Block based Variation of Local Correlation coefficients (CBVLC) for pre-processed images. Consequently wavelet moments are calculated on derived CBDIP and CBVLC values that leads to mining on medical images only with 48 feature vectors. Thereby greatly reducing total number of feature vectors used for similarity comparison for retrieval of similar images. To know the retrieval accuracy, precision and recall values are calculated for the mined 1000 images. It has been examined that this integrated approach shows an improvement in retrieval accuracy and the time taken for similarity comparison.

Generalized method of wavelet moments for inertial navigation filter design

The integration of observations issued from a satellite-based system (GNSS) with an inertial navigation system (INS) is usually performed through a Bayesian filter such as the extended Kalman filter (EKF). The task of designing the navigation EKF is strongly related to the inertial sensor error modeling problem. Accelerometers and gyroscopes may be corrupted by random errors of complex spectral structure. Consequently, identifying correct error-state parameters in the INS/GNSS EKF becomes difficult when several stochastic processes are superposed. In such situations, classical approaches like the Allan variance (AV) or power spectral density (PSD) analysis fail due to the difficulty of separating the error processes in the spectral domain. For this purpose, we propose applying a recently developed estimator based on the generalized method of wavelet moments (GMWM), which was proven to be consistent and asymptotically normally distributed. The GMWM estimator matches theoretical and sample-based wavelet variances (WVs), and can be computed using the method of indirect inference. This article mainly focuses on the implementation aspects related to the GMWM, and its integration within a general navigation filter alibration procedure. Regarding this, we apply the GMWM on error signals issued from MEMS-based inertial sensors by building and estimating composite stochastic processes for which classical methods cannot be used. In a first stage, we validate the resulting models using AV and PSD analyses and then, in a second stage, we study the impact of the resulting stochastic models design in terms of positioning accuracy using an emulated scenario with statically observed error signatures. We demonstrate that the GMWM-based calibration framework enables to estimate complex stochastic models in terms of the resulting navigation accuracy that are relevant for the observed structure of errors.

Estimation of Time Series Models via Robust Wavelet Variance

A robust approach to the estimation of time series models is proposed. Taking froma new estimation method called the Generalized Method of Wavelet Moments (GMWM)which is an indirect method based on the Wavelet Variance (WV), we replace the classicalestimator of the WV with a recently proposed robust M-estimator to obtain a robustversion of the GMWM. The simulation results show that the proposed approach can beconsidered as a valid robust approach to the estimation of time series and state-spacemodels.

A practical application of wavelet moment method on the quantitative analysis of Shuanghuanglian oral liquid based on three-dimensional fingerprint spectra

The overlapping and shifts of peaks and noise signals appear mostly in high performance liquid chromatography (HPLC) experiments. A practical application of wavelet moment method on the quantitative analysis of the main active components in Shuanghuanglian oral liquid samples was presented based on the determination of HPLC coupled with photodiode array detector (PAD). The wavelet moments were calculated from the divided regions in the grayscale images of three-dimensional (3D) HPLC-PAD fingerprint spectra according to the target peak(s), and then used to establish linear models, respectively. The correlation coefficients (R) were more than 0.9980 within the test ranges. The intra- and inter-day variations were less than 1.13% and 1.10%, respectively. The recovery ranged from 96.2% to 102.7%. The overall LODs and LOQs were less than 0.2μg/mL and 0.7μg/mL, respectively. Our study indicated that wavelet moment approach could defuse the overlapping and shifts of peaks and noise signals in the chromatographic determination owing to its multi-resolution and inherently invariance properties. Thus the analytical time was shortened, and the obtained results were reliable and accurate.

Wavelet moment invariants extraction of underwater laser vision image

Wavelet moment invariants are constructed for object recognition based on the global feature and local feature of target, which are brought for the simple background of the underwater objects, complex structure, similar form etc. These invariant features realize the multi-dimension feature extraction of local topology and invariant transform. Considering translation and scale invariant characteristics were ignored by conventional wavelet moments, some improvements were done in this paper. The cubic B-spline wavelets which are optimally localized in space-frequency and close to the forms of Li’s (or Zernike’s) polynomial moments were applied for calculating the wavelet moments. To testify superiority of the wavelet moments mentioned in this paper, generalized regression neural network (GRNN) was used to calculate the recognition rates based on wavelet invariant moments and conventional invariant moments respectively. Wavelet moments obtained 100% recognition rate for every object and the conventional moments obtained less classification rate. The result shows that wavelet moment has the ability to identify many types of objects and is suitable for laser image recognition.

RAMANUJAN SUMS FOR IMAGE PATTERN ANALYSIS

Ramanujan Sums (RS) have been found to be very successful in signal processing recently. However, as far as we know, the RS have not been applied to image analysis. In this paper, we propose two novel algorithms for image analysis, including moment invariants and pattern recognition. Our algorithms are invariant to the translation, rotation and scaling of the 2D shapes. The RS are robust to Gaussian white noise and occlusion as well. Our algorithms compare favourably to the dual-tree complex wavelet (DTCWT) moments and the Zernike's moments in terms of correct classification rates for three well-known shape datasets.

Aircraft recognition using modular extreme learning machine

In this paper, a novel recognition scheme is proposed for identifying the aircrafts of different types based on multiple modular neural network classifiers. Three moment invariants including Hu moments, Zernike moments and Wavelet moments are extracted from the characteristics exhibited by aircrafts and used as the input variables of each modular neural network respectively. Each modular neural network consists of multiple single-hidden layer feedforward networks which are trained using the extreme learning machine and different clustering data subsets. A clustering and selection method is used to get the classification rate of each modular neural network and then based on their weighted sum the final classification output is obtained. The proposed recognition scheme is finally evaluated by recognizing six different types of aircraft models and the simulation results show the superiority of the proposed method compared with the single ELM classifier and other classification algorithms.

An application of wavelet moments to the similarity analysis of three-dimensional fingerprint spectra obtained by high-performance liquid chromatography coupled with diode array detector

More and more the three-dimensional (3D) fingerprint spectra, which can be obtained by high performance liquid chromatography coupled with diode array detector (HPLC-DAD), are applied to the analysis of drugs and foods. A novel approach to the similarity analysis of traditional Chinese medicines (TCMs) was proposed based on the digital image processing using 3D HPLC-DAD fingerprint spectra. As the one of shape features of digital grayscale image, wavelet moments were employed to extract the shape features from the grayscale images of 3D fingerprint spectra of different Coptis chinensis samples, and used to the similarity analysis of these samples. Compared with the results obtained by traditional features including principal components and spectrum data under single-wavelength, our results represented the more reliable assessment. This work indicates that the better features of fingerprint spectra are more important than similarity evaluation methods. Wavelet moments, which possess multi-resolution specialty and the invariance property in image processing, are more effective than traditional spectral features for the description of the systemic characterisation of mixture sample.

Gesture Recognition System Based on Wavelet Moment

Vision-based gesturerecognition is a key technique to achieve a new generation of human-computerinteraction. As few text input search system by gesture recognition isdeveloped, based on the existing gesture recognition techniques, we use thegestures which are corresponding to the Chinese letters and numbers as inputgesture and use Microsoft kinect to obtain depth image to conduct hand gesturesegmentation. First, the edge of the gesture is extracted by Canny algorithm,and then the feature is extracted based on wavelet moment. Finally the gestureletters are obtained. Achieved the text input system based on gesturerecognition. Experiments show that the system is able to achieve Chinesecharacters accurately and effectively.

Decision Fusion Gait Recognition Based on Bayesian Rule and Support Vector Machine

To distinguish people’s identities, the information is normally included in one gait periodic sequence image. First, the gait energy image for feature extraction of wavelet moments was constructed. After boundary unwrapping, the gait silhouette boundary was extracted and principal component analysis (PCA) was use to obtain its compressed contour features. Then nearest neighbor classifier and support vector machines were applied for classification of these two features. Finally, support vector machine (SVM) on Bayesian rule were used to complete gait recognition with information fusion of different features. The method is evaluated on the National Laboratory of Pattern Recognition (NLPR) gait database and the correct recognition rate is relatively high. The experimental results show that the proposed method has good recognition performance.

Digital Image Zero-Watermarking Algorithm Based on Improved Wavelet Moment

Lots of anti-RST attacks watermarking algorithms have been proposed, but few solutions for local geometric attacks, in this paper it proposed a new algorithm combined with the the Wavelet Moment for an anti-geometric attacks. Since wavelet moment was proposed, it is widely used in the field of computer vision, image processing, but the large amount of computation must be improved to be applied to digital watermarking technology so that it can adapt to the real-time detection of digital watermarking. By image rotation, scaling, translation, shear, local distortions, filtering attack operations and so on, these attacks can be seen that the algorithm has good robustness, and the efficiency of watermark detection is relatively high. The experiments show that the algorithm is robustness, greatly accelerate the speed of operation, to unify the robust and efficient.

Determination of Dry Rubber Content in Natural Rubber Latex Based on Wavelet-Domain Fluorescence Image

Abstract A new method for determining the dry rubber content in natural rubber latex based on wavelet-domain fluorescence imaging is explained in this paper. A set of wavelet moment invariants, which are selected automatically based on the discrimination measures defined for the invariant features, are calculated and used to realize the quantitative analysis. Calibration is realized by calculating the standard template vectors of 31 classes of samples. According to the method of minimum distance classification and template matching, the dry rubber content of a tested sample can be determined.