Stationary Wavelet Transform Research Articles

Development & Analysis of 2D Medical Image Fusion Using Wavelets

Abstract: Medical image fusion is the technique of integrating two or more images from various imaging modalities/scans to get a fused image with information having the details of anatomical information combined from all the modalities for accurate diagnosis and further treatment. This paper performs the analysis of various wavelet functions for decomposition and synthesis. PET (Positron Emission Tomography) and MRI (Magnetic Resonance Imaging) scans of Brain and chest are used and compared using Stationary Wavelet Transform (SWT) and Discrete wavelet Transform (DWT). Entropy is calculated which is a measure of information acquired after the fusion process. Keywords: Wavelet transform, Fusion, Stationary Wavelet Transform, Discrete, Medical image

Applicability of Continuous, Stationary, and Discrete Wavelet Transforms in Engineering Signal Processing

AbstractWavelet-based signal processing techniques are widely applied in multiple disciplines. However, few studies consider the applicability of different wavelet transforms in engineering signal ...

EffCDNet: Transfer learning with deep attention network for change detection in high spatial resolution satellite images

High spatial resolution satellite (HRS) images are being extensively utilized for the detection of changes like urban dynamics, infrastructure surveillance, disaster management, and topographic map-making applications. The enormous information and challenging data are important for the change detection (CD) in these images. However, lack of training data and an excessive amount of information, which discourage the researcher from developing a deep-learning-based efficient algorithm for CD. Therefore we want to develop an efficient algorithm in terms of accuracy and speed. Hence, we gain attention on designing an optimized Convolution Neural Network (CNN) while maintaining the speed and segmentation accuracy of the network. We develop an optimized architecture called as EffCDNet which adopts a siamese-based pre-trained encoder with an Attention-based UNet decoder for semantic segmentation. The network is built with pre-trained EfficientNet architecture with shared weights for strong feature extraction and to overcome the limitations caused by insufficient training data. The attention-based UNet decoder uses the attention-gate layer mechanism right before concatenation operation. This obtains more discriminative relevant features for improving the segmentation performance. Also, it is used for the reconstruction of fine-grained feature maps with significant use of context information. For improvement in the change map, we used the Undecimated Discrete Wavelet Transform (UDWT) fusion as a post-processing technique for spatial and temporal analysis of multi-resolution images to obtain a much more enhanced information difference map. The resulting image is less affected by noise, shift-invariable, and overcomes the mixed pixel problem to detect small possible changes. Experimental results on LEVIR-CD, SZATKI AirChange (AC), and Onera Satellite Change Detection (OSCD) benchmark datasets proved that the proposed approach outperforms its superiority in terms of Intersection over Union (IoU) and inference time over the existing methods.

Adaptive clustering-based approach for forgery detection in images containing similar appearing but authentic objects

Copy-move forgery is one of the well-known image forgery technique which exploits regions of the same image to create forged image by replicating or hiding authentic content of the original image. Original images can also contain similar looking but authentic objects. In such cases, identification of authentic and tampered images is a complicated task. To tackle this problem, we propose a method in which Stationary Wavelet Transform (SWT) and spatial-constrained edge preserving watershed segmentation are applied over input image in preprocessing step. Keypoint extraction and descriptor computation are performed using Cascaded Features from Accelerated Segment Test (Cascaded FAST) and Binary Robust Invariant Scalable Keypoint (BRISK) descriptor, respectively. Approximate nearest neighbor search is performed using Random Binary Search Tree (RBST) method. For keypoint clustering, Adaptive Density Peak Clustering (ADPC) technique is employed. Outlier removal is performed using Random Sample Consensus (RANSAC) technique. Further, forged regions are localized using correlation map generation. Experimental results display that the proposed approach can effectively distinguish between forged and original images containing similar appearing but authentic objects. It is also able to detect forged images sustaining different post-processing attacks. For COVERAGE dataset, proposed technique achieves high F-Measure = 86.901% and low False Positive Rate (FPR) = 15.241% in comparison to state-of-the-art techniques.

Underwater Acoustic Image Denoising Using Stationary Wavelet Transform and Various Shrinkage Functions

Underwater acoustic images are captured by sonar technology which uses sound as a source. The noise in the acoustic images may occur only during acquisition. These noises may be multiplicative in nature and cause serious effects on the images affecting their visual quality. Generally image denoising techniques that remove the noise from the images can use linear and non-linear filters. In this paper, wavelet based denoising method is used to reduce the noise from the images. The image is decomposed using Stationary Wavelet Transform (SWT) into low and high frequency components. The various shrinkage functions such as Visushrink and Sureshrink are used for selecting the threshold to remove the undesirable signals in the low frequency component. The high frequency components such as edges and corners are retained. Then the inverse SWT is used for reconstruction of denoised image by combining the modified low frequency components with the high frequency components. The performance measure Peak Signal to Noise Ratio (PSNR) is obtained for various wavelets such as Haar, Daubechies,Coiflet and by changing the thresholding methods.

Multi Sensor Image Fusion Using Stationary Wavelet Transform and Feature Extraction from Gabor Filter and GLCM Texture

Image Fusion is a process of adding information obtained from various sensors and intelligent systems. This provides an image which containing complete information. In this process we fuse images of the same scene one is Infrared Image and other is visible image to produce an image that contains more information. In this the Infrared which are low resolution and noisy nature of image and visual image fused using Stationary wavelet transfer algorithm. In this we have used Gabor filter and GLCM to extract feature and compared the two feature extraction method using quality matrix parameters and found which method is the best method of fusion. The fusion is used in satellite image fusion which mostly used in maps also for decision-making process involved in interpreting images from multi sensor data. Images of several different targets (a military vehicle, a wood chipper, a pickup truck, and people) were used to assess how human subjects view and interpret different types of images. The premise is that combining complementing data from several sensors will result in more accurate findings for data processing difficulties. Although significant progress has been achieved in this sector, complete modeling of the human brain remains a distant objective.

GPR clutter reduction by multi-resolution based tensor RPCA

ABSTRACT A new clutter reduction method which utilizes the multi-resolution and multi-directional information of the ground-penetrating radar (GPR) image is proposed. Sub-images obtained by stationary wavelet transform (SWT) or nonsubsampled counterlet transform (NSCT) are cast into a tensor structure presenting higher information compared to the spatial input data. A tensor-robust principal component analysis (TRPCA) algorithm is used for low-rank and sparse decomposition (LRSD) followed by inverse transform of the sparse tensor component to provide the clutter reduction results. The proposed methods TRPCA-SWT and TRPCA-NSCT are compared both visually and quantitatively to robust principal component analysis (RPCA) and TRPCA-bandpass filter (TRPCA-BPF), which employ the spatial raw GPR data and outputs of simple low-pass and high-pass filters respectively. Visual and quantitative results demonstrate that the clutter reduction performance increases when a higher number of scales and directions are used prior to the LRSD decomposition. Moreover, one of the proposed methods, TRPCA-NSCT, removes the background noise more efficiently due to its higher multi-resolution and multi-direction investigation capability, increasing the performance of the target detection algorithms.

Energy management system for microgrids using weighted salp swarm algorithm and hybrid forecasting approach

The concept of a microgrid (MG) has been introduced to integrate the conventional generators, different renewable energy resources and energy storage systems (ESS) to meet the specific load demand. However, the intermittent nature of renewable energy resources produces a variable output, which drives an imbalance between power generation and demand in MG. The ESS is utilized to makes a balance between power generation and demand. When several renewable energy resources and ESS are available in MG as energy resources, then an energy management system (EMS) is required that can handle the stochastic nature of renewable energy resources, schedule the power of renewable energy resources and ESS for managing the power flow among MG resources and main grid while ensuing cost-effective operation. Therefore, this paper proposed an optimum EMS that aims to minimize the overall operating cost of grid-connected MG along with the short-term forecasting of PV power and load demand. The proposed EMS consists of four modules: forecasting, scheduling, data acquisition (DAQ), and human–machine interface (HMI) modules. An improved hybrid forecasting approach that combines a 3-level stationary wavelet transform (SWT) and grey wolf optimization-based least-square support vector machine (GWO-LSSVM) is proposed in the forecasting module to achieve day-ahead forecasting of PV power and load demand. In the scheduling module, the weighted salp swarm algorithm-based scheduling is applied to achieve the optimum power flow of grid-connected MG. Then, the DAQ and HMI module is used to monitor, analyze, and modified the input variables of the forecasting and scheduling module. The MATLAB/Simulink environment is then used to simulate the proposed EMS for grid-connected MG. Finally, numerical results demonstrate the efficiency of the proposed EMS for grid-connected MG with commercial load demand over the existing competitive approaches.

An assessment of noise variance estimations in Bayes threshold denoising under stationary wavelet domain on brain lesions and tumor MRIs

PurposeA major key success factor regarding proficient Bayes threshold denoising refers to noise variance estimation. This paper focuses on assessing different noise variance estimations in three Bayes threshold models on two different characteristic brain lesions/tumor magnetic resonance imaging (MRIs).Design/methodology/approachHere, three Bayes threshold denoising models based on different noise variance estimations under the stationary wavelet transforms (SWT) domain are mainly assessed, compared to state-of-the-art non-local means (NLMs). Each of those three models, namely D1, GB and DR models, respectively, depends on the most detail wavelet subband at the first resolution level, on the entirely global detail subbands and on the detail subband in each direction/resolution. Explicit and implicit denoising performance are consecutively assessed by threshold denoising and segmentation identification results.FindingsImplicit performance assessment points the first–second best accuracy, 0.9181 and 0.9048 Dice similarity coefficient (Dice), sequentially yielded by GB and DR; reliability is indicated by 45.66% Dice dropping of DR, compared against 53.38, 61.03 and 35.48% of D1 GB and NLMs, when increasing 0.2 to 0.9 noise level on brain lesions MRI. For brain tumor MRI under 0.2 noise level, it denotes the best accuracy of 0.9592 Dice, resulted by DR; however, 8.09% Dice dropping of DR, relative to 6.72%, 8.85 and 39.36% of D1, GB and NLMs is denoted. The lowest explicit and implicit denoising performances of NLMs are obviously pointed.Research limitations/implicationsA future improvement of denoising performance possibly refers to creating a semi-supervised denoising conjunction model. Such model utilizes the denoised MRIs, resulted by DR and D1 thresholding model as uncorrupted image version along with the noisy MRIs, representing corrupted version ones during autoencoder training phase, to reconstruct the original clean image.Practical implicationsThis paper should be of interest to readers in the areas of technologies of computing and information science, including data science and applications, computational health informatics, especially applied as a decision support tool for medical image processing.Originality/valueIn most cases, DR and D1 provide the first–second best implicit performances in terms of accuracy and reliability on both simulated, low-detail small-size region-of-interest (ROI) brain lesions and realistic, high-detail large-size ROI brain tumor MRIs.

A denoising performance comparison based on ECG Signal Decomposition and local means filtering

The electrocardiogram (ECG) signal is popular and extensively used as a diagnostic tool for revealing several diseases related to the heart. Unfortunately, its sensitive to noises from various sources. Denoising these noises remains a hard and major challenge task, although there are some existing methods for denoising, they remain limited to a few types of noises with significant distortion after the filtering process. In this paper, we investigated a hybrid system that can deal with different types of noises, with different levels of SNR, conserving all the signal features with the minimum distortion. The hybrid system consists of a decomposition method followed by local means (LM) filtering. The best candidates used for the signal decomposition are the Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), Discrete Wavelet Transform (DWT), and Stationary Wavelet Transform (SWT). To demonstrate the effectiveness of the proposed method, several real ECG recordings and synthetic ECG infected by a different type of noise (i.e., baseline wander, muscle artifacts, electrode motion, mix noise, white noise, colored noise) with different levels of signal to noise ratios (24, 18, 6, 0, −6) dB are used in our numerical analysis. The performance evaluation of our proposed system is made using the following metrics: SNR improvement, signal-to-noise and distortion ratio (SINAD), the approximate entropy, and the fuzzy entropy. The experimental results emphasized that the Ensemble Empirical Mode Decomposition (EEMD) followed by local means (LM) outperforms all the comparison methods, in terms of all the metrics used, with few exceptions where the Empirical Mode Decomposition (EMD) followed by local means (LM) and Discrete Wavelet Transform (DWT) followed by local means (LM) performed well.

Single and multiple regions duplication detections in digital images with applications in image forensic

‘With the help of powerful image editing software, various image modifications are possible which are known as image forgeries. Copy-move is the easiest way of image manipulation, wherein an area of the image is copied and replicated in the same image. The major reason for performing this forgery is to conceal undesirable contents of the image. Thus, means are required to unveil the presence of duplicated areas in an image. In this article, an effective and efficient approach for copy-move forgery detection (CMFD) is proposed, which is based on stationary wavelet transform (SWT), speeded-up robust features (SURF), and a novel scaled density-based spatial clustering of applications with noise (sDBSCAN) clustering. The SWT allows the SURF descriptor to extract only energy-rich features from the input image. The SURF features can detect the tampered regions even under post-processing attacks like contrast adjustment, scaling, and affine transformation on the images. On the extracted features, a novel scaled density-based spatial clustering of applications with noise (sDBSCAN) clustering algorithm is applied to detect forged regions with high accuracy as it can easily identify the clusters of arbitrary shapes and sizes and can filter the outliers. For performance evaluation, three publicly available datasets namely MICC-F220, MICC-F2000, and image manipulation dataset (IMD) are employed. The qualitative and quantitative analysis demonstrates that the proposed approach outperforms state-of-the-art CMFD approaches in the presence of different post-processing attacks.

Radar Life Signal Processing Algorithm Based on Improved EEMD

Non-contact measurement of human vital signs is of great significance to the construction of smart homes and hospitals. The vital signal extracted from the FMCW radar contains a lot of noise. In order to reduce the noise impact and improve the life signal detection results accuracy, Ensemble Empirical Mode Decomposition (EEMD) algorithm is studied, and a new method based on the combination of EEMD and Translation Invariant Wavelet Transform (TIWT) is proposed. This method firstly decomposes the original signal using EEMD to obtain several Intrinsic Mode Function (IMF) components, and then changes the arrangement order of IMF by Translation Invariant Wavelet Transform to change the position of the singularity in the whole signal to reduce or eliminate the oscillations. Finally, signal screening is completed and life signals are reconstructed. Experiments show that, the proposed method has better detection accuracy in detecting vital signs collected by radar.

A dissection and enhancement technique for combined damage characterisation in composite laminates using laser-line scanning thermography

Impact induced combined damage in composite laminates attracts great attention due to its significant degradation of the structural integrity. However, the provision of the quantitative analysis of each damage portion is challenging due to its bare visibility and structural mixture complexity, so-called barely visible impact damage (BVID), which is referred to as inter-laminar delamination, and is inherently coupled with in-plane transverse and matrix damage also known as combined damage. Instead of focusing on one type of damage in most of the existing studies, this paper proposes a decomposition and targeted enhancement technique based on Stationary Wavelet Transform (SWT) for such coupled BVID in composite laminates using laser-line scanning thermography. Firstly, a combined damage model composed of in-plane damage and inter-laminar delamination is established by finite element numerical modelling to predict the thermal response pattern in the laser scanning thermography. Then, a feature separation and targeted enhancement strategy based on SWT in the frequency domain is proposed to improve the contrast of the matrix crack and delamination in combined damage scenarios induced by low-velocity rigid impact via drop-tower tests, meanwhile eliminating noise and suppressing the laser pattern background. The enhanced images of in-plane damage and delamination are furtherly processed by Random Sample Consensus (RANSAC) method and confidence map algorithms to calibrate the damage profile. The proposed technique is validated through inspecting a group of unidirectional carbon fibre-reinforced polymer composite samples, impacted by a variety of energy levels, in fibre-parallel (0°), 45° and orthogonal scanning modes. The results demonstrate that the proposed technique can pertinently isolate, enhance and characterise the inspected in-plane crack and inter-laminates delamination in a flexible manner. The proposed methodology paves the way towards automated infrared thermography data analysis for quantitative dissection of actual combined damage in composite laminates.

Statistical image watermark decoder based on local frequency-domain Exponent-Fourier moments modeling

There are three indispensable, yet contrasting requirements for a watermarking scheme: perceptual transparency, watermark capacity, and robustness against attacks. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. In this paper, we propose a statistical image watermark decoder based on the local frequency-domain Exponent-Fourier moments modeling, which can achieve the tradeoff among imperceptibility, robustness and data payload. The frequency-domain EFMs magnitudes are first generated by combining stationary wavelet transform (SWT) and Exponent-Fourier moments (EFMs). We divide the target region to select local frequency-domain EFMs magnitudes, which are planned to embed watermarks, statistical modeling, and extract watermarks. In order to achieve an accurate modeling process, we conduct the comprehensive statistical analyses of local frequency-domain EFMs magnitudes and establish the powerful Beta Generalized Weibull mixtures-based hidden Markov tree (BGW-HMT) model, which can take into account the non-Gaussian distribution characteristic and the interscale dependency at the same time. The Expectation/Conditional Maximisation Either (ECME) algorithm and upward–downward algorithm are successfully applied to estimate the parameters of BGW-HMT model. At the receiver, the BGW-HMT model is used in the design process of watermark decoder. The decoder structure is developed by using the maximum likelihood decision. In order to prove the effectiveness of proposed watermarking scheme, multi-angle performance tests are performed, including imperceptibility, robustness, watermark capacity and time complexity. The corresponding experimental results from the above four perspectives are inspiring. Compared with the state-of-the-art schemes, our statistical decoder is significantly superior to other statistical decoders.

Image resolution and contrast enhancement with optimal brightness compensation using wavelet transforms and particle swarm optimization

Improving the image resolution and contrast along with uniform brightness distribution over the entire image helps to retrieve the vital realistic information necessary for human perception and interpretation. A new procedure to improve these parameters is implemented and tested. Initially, the image is super resolute using discrete wavelet transform (DWT), stationary wavelet transform (SWT) image decomposition and bicubic interpolation. The resolute image is used for contrast enhancement by using SWT and contrast limited adaptive histogram equalization (CLAHE) approach. The optimized brightness compensation technique, which uses particle swarm optimization (PSO), is applied to the resolution and contrast-enhanced image to obtain uniform brightness distribution over the entire image. The proposed approach is tested on three data sets of images and it is found that the visual results, as well as the resolution and contrast levels of the tested images, are significantly superior to subjective and objective results.

Bayesian damage recognition in document images based on a joint global and local homogeneity model

Physical damages (such as torn-offs and scratches) are commonly seen in historical documents. Recognition of such damages is currently absent in digitization-and-information-extraction (DIE) systems but crucial for automatic document comprehension and exploitation. In this paper we propose a generic damage recognition (DR) method based on a joint global and local modeling of the text homogeneity (TH) pattern exhibited in document images. More specifically, a connected component (CC) based formulation is developed as a global homogeneity measure, where TH is characterized using a probabilistic graph model for a coarse recognition of damaged regions. A multi-resolution analysis (MRA) of TH is further developed for a granular within-CC recognition of damage pixels, where the disparity between damage and text pixels is characterized by exploiting neighborhood transitions. This enables the formulation of a local homogeneity measure, where the neighborhood transition around an individual pixel is modeled using the propagation of the approximation coefficients of a stationary wavelet transform (SWT). The proposed global and local homogeneity measures are integrated as a joint likelihood in a Bayesian model with a Markov random field (MRF) prior, where DR is formulated as a maximum a posterior (MAP) inference which is addressed using Markov Chain Monte Carlo (MCMC) sampling. The resulting algorithm is tested on a set of real-life historical newspaper images containing damages of varying size and shape. The performance of the algorithm is evaluated using both F-measures and the Intersection-over-Union (IoU) metric, where test results demonstrate the promising potential of the proposed method.

A Multi-Objective Enhanced Fruit Fly Optimization (MO-EFOA) Framework for Despeckling SAR Images using DTCWT based Local Adaptive Thresholding

ABSTRACT The importance of Satellite Aperture Radar (SAR) imagery systems is increasing day-by-day in various field such as earth observation, hi-technology war mechanisms, etc. The images captured by SAR imagery systems are mainly used to detect and classify objects captured in the images. Due to the complexity of the image capturing process, SAR images can be highly noisy – often consisting of multiplicative noise, also known as speckle. To detect or classify objects in SAR images, speckle noise must be removed from images. During despeckling process, the preservation of important information in the SAR images while removing noise such as edge or patterns is a crucial task. Despeckling methods are liable to compromise on edge preservation ability while aspiring for good quality denoised images. Many researchers have proposed wavelet transform based despeckling approaches such as Discrete Wavelet Transform (DWT), Undecimated Wavelet Transform (UDWT), Dual Tree Complex Wavelet Transform (DTCWT). In these approaches, finding the best values of the coefficients plays an important role in yielding excellent denoised images with preserved edges. In this paper, we have proposed a novel optimization framework that optimizes thresholding coefficients of DTCWT despeckling method for SAR images. The proposed optimization framework is based on Fruit Fly Optimization (FOA) algorithm. The approach is a multi-objective optimization algorithm that is used to find maximum values for Peak Signal-to-Noise Ratio (PSNR), Mean Structural Similarity Index (MSSIM) and Equivalent number of look (ENL). The maximum value of MSSIM indicates high edge preservation capacity, whereas maximum PSNR value indicates good quality denoising of images. The maximum ENL value represents a good speckle-noise smoothing capability. We have applied our framework over some classical images as well as over SAR images of MSTAR dataset. In our experiments, we found that our proposed framework results in the excellent PSNR 36.87 dB, 35.4 dB and 37.8 dB, MSSIM values 0.92, 0.93 and 0.92, respectively, in the case of lena image, MSTAR dataset image and TerraSAR-X dataset image.

Short duration Vectorcardiogram based inferior myocardial infarction detection: class and subject-oriented approach.

Myocardial infarction (MI) happens when blood stops circulating to an explicit segment of the heart causing harm to the heart muscles. Vectorcardiography (VCG) is a technique of recording direction and magnitude of the signals that are produced by the heart in a 3-lead representation. In this work, we present a technique for detection of MI in the inferior portion of heart using short duration VCG signals. The raw signal was pre-processed using the median and Savitzky-Golay (SG) filter. The Stationary Wavelet Transform (SWT) was used for time-invariant decomposition of the signal followed by feature extraction. The selected features using minimum-redundancy-maximum-relevance (mRMR) based feature selection method were applied to the supervised classification methods. The efficacy of the proposed method was assessed under both class-oriented and a more real-life subject-oriented approach. An accuracy of 99.14 and 89.37% were achieved respectively. Results of the proposed technique are better than existing state-of-art methods and used VCG segment is shorter. Thus, a shorter segment and a high accuracy can be helpful in the automation of timely and reliable detection of MI. The satisfactory performance achieved in the subject-oriented approach shows reliability and applicability of the proposed technique.

Source Localization of EEG Brainwaves Activities via Mother Wavelets Families for SWT Decomposition.

A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

A secure and sensitive wavelet transform based technique for stator fault detection in the cases of line‐connected and inverter‐fed induction machines

Here a new sensitive fault detection criterion is proposed, based on the stationary wavelet transform (SWT) decomposition components of the stator currents, for the online detection of stator winding turn-to-turn faults at an early stage of development. The energies of the desired detail components are calculated and the normalized Euclidean distance of the energy differences between the three phases is used as a new fault detection criterion. The robustness of the proposed technique against the presence of rotor turn-to-turn faults and loading variations is demonstrated. In addition, an adaptive threshold level as a function of the voltage unbalance factor is proposed to guarantee the robustness of the diagnostic technique against unbalanced voltage sources. Experimental results demonstrate the effectiveness and sensitivity of the proposed diagnostic approach for the detection of stator faults in line-connected and inverter-fed motors.