Two-dimensional Wavelet Decomposition Research Articles

Orthogonalized layer features with wavelet for multi-object tracking

Abstract Multi-object tracking (MOT) in crowded scenes presents challenges such as target occlusion and interference from similar objects. The detection models that rely on the target center as positive samples often struggle with noise introduced by ambiguous data annotations. To address these issues, we propose to segregate the target features of distinct frequency tiers by leveraging wavelet decomposition. Features obtained from two-dimensional wavelet decomposition can exhibit orthogonality and complementarity along the horizontal and vertical directions. Low-frequency components are usually related to visible targets, while high-frequency energy often emanates from targets undergoing occlusion, enabling discrimination between multi-layered objectives. Experimental evaluations are conducted on the MOT17 and MOT20 benchmarks (motchallenge.net), which demonstrate that our approach has better competitive performance compared to the current state-of-the-art methods.

Multi-Scale Analysis of Surface Building Density and Land Subsidence Using a Combination of Wavelet Transform and Spatial Autocorrelation in the Plains of Beijing

Land subsidence is a major issue in the Beijing Plain in China, caused by the construction of new buildings and infrastructure combined with groundwater extraction. This study employs a multi-level two-dimensional wavelet decomposition to decompose land subsidence into high- and low-frequency components, and Moran’s I index to analyze the spatial distribution of land subsidence and its main influencing factors. By comparing the spatial distributions of the high- and low-frequency components, we estimate the correlation between land subsidence and influencing factors at different scales. Utilizing a combination of wavelet decomposition and Moran’s I analysis, our study establishes a clear spatial correlation between continuously varying factors such as groundwater and clay layer thickness, and the low-frequency components of land subsidence, allowing for a focused analysis of the relationship between surface building density and the high-frequency components of land subsidence. Quantitatively, the study identifies a significant correlation at specific granularities, particularly at 480 m and 960 m, underscoring the nuanced interaction between urban development and land subsidence patterns. These insights into the spatial distribution of land subsidence and its contributing factors can inform the development of effective strategies to address this issue.

Source Edge Detection of Potential Field Data Using Wavelet Decomposition

Edge detection of the sources of potential field anomaly is an important step in the interpretation of subsurface source geometries. The conventional methods based on calculation of horizontal or vertical derivatives identify the edges or center of sources by minima, maxima, or zero values in the transformed data. We present a wavelet source edge detector method (WSED) using wavelet multiresolution analysis to identify potential field sources boundaries. The two-dimensional wavelet decomposition is an effective method to understand the frequency components of the signal in different directions. We use a 2D-discrete wavelet transform using Haar wavelets in resolving lateral edges for source edge detection. We test the method on synthetic magnetic anomalies due to sources of complex geometries generated using prismatic sources. We investigated the robustness of the method on the magnetic data of the Bishop model and found the results useful in resolving the edges. We applied the method to gravity data of the north Delhi fold belt, India, to identify boundaries of different geological formations. Our results indicate distinct properties of the source edges in the wavelet domain, which is for the first time reported for the interpretation of the potential field anomalies.

Ensemble Learning Approaches to Data Imbalance and Competing Objectives in Design of an Industrial Machine Vision System

Numerous industrial applications of machine learning feature critical issues that need to be addressed. This work proposes a framework to deal with these issues, such as competing objectives and class imbalance in designing a machine vision system for the in-line detection of surface defects on glass substrates of thin-film transistor liquid crystal displays (TFT-LCDs). The developed inspection system composes of (i) feature engineering: extraction of only the defect-relevant features from images using two-dimensional wavelet decomposition and (ii) training ensemble classifiers (proof of concept with a C5.0 ensemble, random forests (RF), and adaptive boosting (AdaBoost)). The focus is on cost sensitivity, increased generalization, and robustness to handle class imbalance and address multiple competing manufacturing objectives. Comprehensive performance evaluation was conducted in terms of accuracy, sensitivity, specificity, and the Matthews correlation coefficient (MCC) by calculating their 12,000 bootstrapped estimates. Results revealed significant differences (p < 0.05) between the three developed diagnostic algorithms. RFR (accuracy of 83.37%, sensitivity of 60.62%, specificity of 89.72%, and MCC of 0.51) outperformed both AdaBoost (accuracy of 81.14%, sensitivity of 69.23%, specificity of 84.48%, and MCC of 0.50) and the C5.0 ensemble (accuracy of 78.35%, sensitivity of 65.35%, specificity of 82.03%, and MCC of 0.44) in all the metrics except sensitivity. AdaBoost exhibited stronger performance in detecting defective TFT-LCD glass substrates. These promising results demonstrated that the proposed ensemble approach is a viable alternative to manual inspections when applied to an industrial case study with issues such as competing objectives and class imbalance.

Application of Machine Learning Methods for Biometric Identification by Iris

The paper is devoted to the application of machine learning methods for biometric identification of the iris. for biometric identification of a person by iris recognition. In order to investigate the possibilities of machine learning for the iris recognition, the UBIRIS database was used in this work. A distinctive feature of this database is that the task of identification is complicated by the registration of images in non-ideal conditions. This approach is aimed at developing algorithms for automatic iris recognition under limited conditions for obtaining high-quality images, remote registration, noise, and in the absence of cooperation by the subject. Glare from light sources, differences in lighting conditions, closure of part of the eye by the eyelids complicate the recognition process due to the significant fluctuation of features for different images of the iris of one person. The purpose of this work is to identify and compare the informative features of the iris obtained in different coordinate bases, as well as to choose the classification method that provides the highest accuracy in the identification of the person on the iris. Comparison of the use in iris recognition such features as the coefficients of two-dimensional discrete Fourier transform, the coefficients of discrete cosine transform, as well as the approximation coefficients of the 3rd and 4th levels of two-dimensional wavelet transform is considered. The accuracy of a number of classifiers using these feature sets is determined. Based on this, a combination of features and classifiers are proposed that provides the highest accuracy of person identification based on the iris recognition. The highest classification accuracy of the iris recognition was 98.5% using the approximation coefficients of the 4th level of two-dimensional wavelet decomposition and a classifier implementing the linear discriminant method. The use of two-dimensional discrete Fourier transform coefficients for iris recognition yielded 97.5% correctly identified individuals in the case of machine learning method based on the k-nearest neighbor ensemble. This algorithm also made it possible to obtain maximum classification accuracy (94.5%) for the coefficients of the discrete cosine transformation. The use of wavelet coefficients can significantly reduce the dimensionality of the data for classification compared to the use of Fourier transform coefficients or discrete cosine transform. Applying of vertical, horizontal and diagonal wavelet coefficients of detail as features for iris recognition gives lower accuracy compared to the use of wavelet coefficients of approximation of the same level.

Spatial Multiresolution Analysis of the Effect of PM2.5 on Birth Weights.

Fine particulate matter (PM2.5) measured at a given location is a mix of pollution generated locally and pollution traveling long distances in the atmosphere. Therefore, the identification of spatial scales associated with health effects can inform on pollution sources responsible for these effects, resulting in more targeted regulatory policy. Recently, prediction methods that yield high-resolution spatial estimates of PM2.5 exposures allow one to evaluate such scale-specific associations. We propose a two-dimensional wavelet decomposition that alleviates restrictive assumptions required for standard wavelet decompositions. Using this method we decompose daily surfaces of PM2.5 to identify which scales of pollution are most associated with adverse health outcomes. A key feature of the approach is that it can remove the purely temporal component of variability in PM2.5 levels and calculate effect estimates derived solely from spatial contrasts. This eliminates the potential for unmeasured confounding of the exposure - outcome associations by temporal factors, such as season. We apply our method to a study of birth weights in Massachusetts, U.S.A from 2003-2008 and find that both local and urban sources of pollution are strongly negatively associated with birth weight. Results also suggest that failure to eliminate temporal confounding in previous analyses attenuated the overall effect estimate towards zero, with the effect estimate growing in magnitude once this source of variability is removed.

A Five-Level Wavelet Decomposition and Dimensional Reduction Approach for Feature Extraction and Classification of MR and CT Scan Images

This paper presents a two-dimensional wavelet based decomposition algorithm for classification of biomedical images. The two-dimensional wavelet decomposition is done up to five levels for the input images. Histograms of decomposed images are then used to form the feature set. This feature set is further reduced using probabilistic principal component analysis. The reduced set of features is then fed into either K nearest neighbor algorithm or feed-forward artificial neural network, to classify images. The algorithm is compared with three other techniques in terms of accuracy. The proposed algorithm has been found better up to 3.3%, 12.75%, and 13.75% on average over the first, second, and third algorithm, respectively, using KNN and up to 6.22%, 13.9%, and 14.1% on average using ANN. The dataset used for comparison consisted of CT Scan images of lungs and MR images of heart as obtained from different sources.

Variability Evaluation of Signal in Two-dimensional Wavelet Decomposition Using Fractal Dimension

The paper presents the possibilities of using the fractal dimension to evaluate the signals in wavelet decomposition process. The tests have been carried out on samples produced by face milling process for the six types of materials. It has been shown that the fractal dimension enables characterize signal irregularities in quantitatively and qualitatively way.

Quality inspection guided laser processing of irregular shape objects by stereo vision measurement: application in badminton shuttle manufacturing

The quality inspection process is usually carried out after first processing of the raw materials such as cutting and milling. This is because the parts of the materials to be used are unidentified until they have been trimmed. If the quality of the material is assessed before the laser process, then the energy and efforts wasted on defected materials can be saved. We proposed a new production scheme that can achieve quantitative quality inspection prior to primitive laser cutting by means of three-dimensional (3-D) vision measurement. First, the 3-D model of the object is reconstructed by the stereo cameras, from which the spatial cutting path is derived. Second, collaborating with another rear camera, the 3-D cutting path is reprojected to both the frontal and rear views of the object and thus generates the regions-of-interest (ROIs) for surface defect analysis. An accurate visual guided laser process and reprojection-based ROI segmentation are enabled by a global-optimization–based trinocular calibration method. The prototype system was built and tested with the processing of raw duck feathers for high-quality badminton shuttle manufacture. Incorporating with a two-dimensional wavelet-decomposition–based defect analysis algorithm, both the geometrical and appearance features of the raw feathers are quantified before they are cut into small patches, which result in fully automatic feather cutting and sorting.

The Study of a Fast Sub-Pixel Registration Method for Remote Sensing Image

We put forward a fast and efficiently sub-pixel registration method for solving the classical methods’ problems of low efficiency, and use efficiently sub-images instead of original image to sub-pixel registration based on the Fourier transform phase correlation and matrix Fourier transform method. Effective sub-images are selected from the total size of the high-frequency energy after two-dimensional wavelet decomposition, then we use the phase correlation to calculate the pixel displacement and matrix Fourier transform to calculate the sub-pixel displacement. Not only the improved method is inherited the advantage of matrix Fourier transform sub-pixel registration, but also the registration speed is greatly improved. This is more applicable to massive remote sensing data. Through simulation and engineering practice, composited registration accuracy and speed, proved that the improved method is more efficient compared with the classical methods, and it’s more suitable for real remote sensing image registration.

Digital Watermark Based on W-SVD Method in Copyright Protection of E-Service

Abstract In order to solve digital products copyright problem, this paper uses the good mathematical properties of singular value decomposition and combines with two-dimensional wavelet decomposition, chaotic Logistic sequence and template scrambling to product a high security digital watermark. The statistic analysis indicates this method has good security and robust, which can be used widely in the e-service area.

A Face Recognition Algorithm Based on Block PCA and Wavelet Transform

As the most successful method of linear distinguish, principal component analysis(PCA) method is widely used in identify areas, such as face recognition. But traditional PCA is influenced by light conditions, facial expression and it extracts the global features of the image, so the recognition rate is not very high. In order to improve more accurately identify facial features and extract local features which account for a larger contribution to the identification. This paper brings up a method of a block face recognition based on wavelet transform (WT-BPCA). In the algorithm, face images are done two-dimensional wavelet decomposition, then from which extract low frequency sub-images. According to different face area makes different contribution to recognition, we use sub-block PCA method. According to the contribution of the block recognition results generate weighting factors, the face recognition rate based on PCA is effectively improved. Finally we construct classification to recognite. Do experiments in the ORL face database. Results show that this method is superior to the method of the traditional PCA.

Multiresolution analysis of density fluctuation in supersonic mixing layer

Due to the difficulties in measuring supersonic density field, the multiresolution analysis of supersonic mixing layer based on experimental images is still a formidable challenge. By utilizing the recently developed nanoparticle based planar laser scattering method, the density field of a supersonic mixing layer was measured at high spatiotemporal resolution. According to the dynamic behavior of coherent structures, the multiresolution characteristics of density fluctuation signals and density field images were studied based on Taylor’s hypothesis of space-time conversion and wavelet analysis. The wavelet coefficients reflect the characteristics of density fluctuation signals at different scales, and the detailed coefficients reflect the differences of approximation at adjacent levels. The density fluctuation signals of supersonic mixing layer differ from the periodic sine signal and exhibit similarity to the fractal Koch signal. The similarity at different scales reveals the fractal characteristic of mixing layer flowfield. The two-dimensional wavelet decomposition and reconstruction of density field images extract the approximate and detailed signals at different scales, which effectively resolve the characteristic structures of the flowfield at different scales.

Wavelet-based analysis of enstrophy transfers in two-dimensional turbulence

Two-dimensional turbulence admits two different ranges of scales: a direct enstrophy cascade from the injection scale to the small scales and an inverse energy cascade at large scales. It has already been shown in previous papers that vortical structures are responsible for the transfers of energy upscale while filamentary structures are responsible for the forward transfer of the enstrophy. Here we propose an original mathematical tool, the interaction function, for studying the space localization of the enstrophy fluxes. It is defined using an orthogonal two-dimensional wavelet decomposition.

Wavelet Analysis of Soil Mass Images for Particle Size Determination

A method for determination of average grain size from images of fairly uniform particle size soil masses is presented. The procedure utilizes two-dimensional wavelet decomposition of gray scale images. Earlier attempts to quantify grain sizes based on the statistics of co-occurrence matrices suffered from dependence on the illumination intensity and soil color. By normalizing the energy distribution from wavelet decomposition the effects of these previously problematic factors have been eliminated. A general relationship between the center of area beneath the normalized energy distribution and the perceived particle size in pixels per diameter (PPD) is established. A sample problem demonstrates that the proposed wavelet decomposition method provides accurate grain sizes for a wide range of magnification levels as long as the resulting PPD is between approximately 1 and 50.

Wavelet-based compression of medical images: filter-bank selection and evaluation

Wavelet-based image coding algorithms (lossy and lossless) use a fixed perfect reconstruction filter-bank built into the algorithm for coding and decoding of images. However, no systematic study has been performed to evaluate the coding performance of wavelet filters on medical images. We evaluated the best types of filters suitable for medical images in providing low bit rate and low computational complexity. In this study a variety of wavelet filters are used to compress and decompress computed tomography (CT) brain and abdomen images. We applied two-dimensional wavelet decomposition, quantization and reconstruction using several families of filter banks to a set of CT images. Discreet Wavelet Transform (DWT), which provides efficient framework of multi-resolution frequency was used. Compression was accomplished by applying threshold values to the wavelet coefficients. The statistical indices such as mean square error (MSE), maximum absolute error (MAE) and peak signal-to-noise ratio (PSNR) were used to quantify the effect of wavelet compression of selected images. The code was written using the wavelet and image processing toolbox of the MATLAB (version 6.1). This results show that no specific wavelet filter performs uniformly better than others except for the case of Daubechies and bi-orthogonal filters which are the best among all. MAE values achieved by these filters were 5 x 10(-14) to 12 x 10(-14) for both CT brain and abdomen images at different decomposition levels. This indicated that using these filters a very small error (approximately 7 x 10(-14)) can be achieved between original and the filtered image. The PSNR values obtained were higher for the brain than the abdomen images. For both the lossy and lossless compression, the 'most appropriate' wavelet filter should be chosen adaptively depending on the statistical properties of the image being coded to achieve higher compression ratio.