Krawtchouk Moments Research Articles

Quantitative analysis of multicomponent mixtures of rubber and additives based on terahertz time-domain spectroscopy and Krawtchouk moments

This paper presents a quantitative analytical method based on terahertz time-domain spectroscopy and chemometrics, which was used to detect the content of diphenyl-p-phenylenediamine in a five-component mixture comprising tire rubber and additives. We separately extracted the features of the spectra by using principal component analysis and Krawtchouk moments, and then used partial least squares regression and support vector regression to develop quantitative analysis models. The experimental results show that support vector regression outperforms partial least squares regression in the quantitative analysis of multicomponent mixtures, and the Krawtchouk moments method effectively enhances the prediction accuracy of the model. The Krawtchouk moment combined with support vector regression model shows excellent predictive ability. The correlation coefficient and root mean square error of Krawtchouk moment combined with support vector regression model for the calibration set were 0.9749 and 1.7256%, respectively, and for the prediction set were 0.9669 and 1.9777%, respectively. The results demonstrate that terahertz time-domain spectroscopy combined with Krawtchouk moments and support vector regression is an effective method for determining the antioxidant content in rubber and additive compounds.

Optimal image 2D/3D by Krawtchouk moments and ABC algorithm

In our research, we provide an enhanced and effective Krawtchouk moments parameter p optimization approach using the Artificial Bee Colony (ABC) algorithm optimization technique for the purpose of completing tasks including the reconstruction and classification of 3D and 2D images with high quality. The proposed method, which uses the ABC algorithm to generate a suitable parameter based on Krawtchouck moments, aims to accurately characterize the image as a vector known as the descriptor vector of moments, which is then used to reconstruct the image for each order. The simulation and analysis of the findings demonstrate the high level of quality and effectiveness of the suggested KM-ABC approach for image reconstruction, as well as its excellent accuracy in images with and without noise.

Octonion-based transform moments for innovative stereo image classification with deep learning

Recent advances in imaging technologies have led to a significant increase in the adoption of stereoscopic images. However, despite this proliferation, in-depth research into the complex analysis of the visual content of these stereoscopic images is still relatively rare. The advent of stereoscopic imaging has brought a new dimension to visual content. These images offer a higher level of visual detail, making them increasingly common in a variety of fields, including medicine and industrial applications. However, exploiting the full potential of stereoscopic images requires a deeper understanding. By exploiting the capabilities of octonion moments and the power of artificial intelligence, we aim to break new ground by introducing a novel method for classifying stereoscopic images. The proposed method is divided into two key stages: The first stage involves data preprocessing, during which we strive to construct a balanced database divided into three distinct categories. In addition, we extract the stable Octonion Krawtchouk moments (SOKM) for each image, leading to a database of moment images with dimensions of 128 × 128 × 1. In the second step, we train a convolutional neural network (CNN) model using this database, with the aim of discriminating between different categories. Standard measures such as precision, accuracy, recall, F1 score, and ROC curves are used to assess the effectiveness of our method. These measures provide a quantitative assessment of the performance of our object classification approach for stereoscopic images.

Robust face recognition using convolutional neural networks combined with Krawtchouk moments

<span lang="EN-US">Face recognition is a challenging task due to the complexity of pose variations, occlusion and the variety of face expressions performed by distinct subjects. Thus, many features have been proposed, however each feature has its own drawbacks. Therefore, in this paper, we propose a robust model called Krawtchouk moments convolutional neural networks (KMCNN) for face recognition. Our model is divided into two main steps. Firstly, we use 2D discrete orthogonal Krawtchouk moments to represent features. Then, we fed it into convolutional neural networks (CNN) for classification. The main goal of the proposed approach is to improve the classification accuracy of noisy grayscale face images. In fact, Krawtchouk moments are less sensitive to noisy effects. Moreover, they can extract pertinent features from an image using only low orders. To investigate the robustness of the proposed approach, two types of noise (salt and pepper and speckle) are added to three datasets (YaleB extended, our database of faces (ORL), and a subset of <a name="_Hlk128818620"></a>labeled faces in the wild (LFW)). Experimental results show that KMCNN is flexible and performs significantly better than using just CNN or when we combine it with other discrete moments such as Tchebichef, Hahn, Racah moments in most densities of noises.</span>

Machine learning analysis of wing venation patterns accurately identifies Sarcophagidae, Calliphoridae and Muscidae fly species.

In medical, veterinary and forensic entomology, the ease and affordability of image data acquisition have resulted in whole-image analysis becoming an invaluable approach for species identification. Krawtchouk moment invariants are a classical mathematical transformation that can extract local features from an image, thus allowing subtle species-specific biological variations to be accentuated for subsequent analyses. We extracted Krawtchouk moment invariant features from binarised wing images of 759 male fly specimens from the Calliphoridae, Sarcophagidae and Muscidae families (13 species and a species variant). Subsequently, we trained the Generalized, Unbiased, Interaction Detection and Estimation random forests classifier using linear discriminants derived from these features and inferred the species identity of specimens from the test samples. Fivefold cross-validation results show a 98.56 ± 0.38% (standard error) mean identification accuracy at the family level and a 91.04 ± 1.33% mean identification accuracy at the species level. The mean F1-score of 0.89 ± 0.02 reflects good balance of precision and recall properties of the model. The present study consolidates findings from previous small pilot studies of the usefulness of wing venation patterns for inferring species identities. Thus, the stage is set for the development of a mature data analytic ecosystem for routine computer image-based identification of fly species that are of medical, veterinary and forensic importance.

Orthogonal-Moment-Based Attraction Measurement With Ocular Hints in Video-Watching Task

Pupil dilation and eye movements are closely related to human emotional and cognitive processes. Visual stimulus, especially video clips, is widely used in computer-assisted experimental paradigms as emotional inducers. However, the level of attraction as a critical factor to such visual stimulus still needs comprehensive investigation. This article conducts a novel study of attraction assessment with pupil diameter and eye movements. We collected high temporal resolution ocular variation data from 50 subjects while they viewed a variety of emotional video stimuli. Besides, this article proposes two orthogonal-moment-based feature extraction methods for emotion classification, i.e., Legendre moment and Krawtchouk moment. The results of experiments show that our proposed feature sets achieve better classification performance compared with conventional time-or frequency-domain feature sets. The accuracy of predicting attraction level reached 87.4% and 91.0% when new features were used alone and combined with conventional features, respectively. Compared with the conventional features with an accuracy of 86.6%, our proposed features can improve the accuracy by 4.4%.This study conducts a ground investigation of quantitative attraction assessment for video clips, which might provide reference for paradigm design of affective computing research.

Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm

Krawtchouk polynomials (KPs) are discrete orthogonal polynomials associated with the Gauss hypergeometric functions. These polynomials and their generated moments in 1D or 2D formats play an important role in information and coding theories, signal and image processing tools, image watermarking, and pattern recognition. In this paper, we introduce a new four-term recurrence relation to compute KPs compared to their ordinary recursions (three-term) and analyse the proposed algorithm speed. Moreover, we use Clenshaw’s technique to accelerate the computation procedure of the Krawtchouk moments (KMs) using a fast digital filter structure to generate a lattice network for KPs calculation. The proposed method confirms the stability of KPs computation for higher orders and their signal reconstruction capabilities as well. The results show that the KMs calculation using the proposed combined method based on a four-term recursion and Clenshaw’s technique is reliable and fast compared to the existing recursions and fast KMs algorithms.

Copyright protection of multiple CT images using Octonion Krawtchouk moments and grey Wolf optimizer

This paper proposes a novel Octonion Krawtchouk Moments (OKMs) transform to deal with a set of images in a compact manner, and based on this transform, a local zero-watermarking scheme is proposed to protect the copyright of CT medical images. The scheme first annotates regions of interest (ROIs) on seven medical images and then uses the OKMs of these ROIs to construct a single feature image called zero-watermark. This scheme adopts the gray Wolf Optimizer (GWO) algorithm to have a blind nature and to improve robustness against common image processing manipulations and attacks (zero-watermarking requirements). In addition, our scheme uses the trained U-net (R231) model to reduce the search space for the GWO algorithm and prevent this algorithm from getting stuck in a local optimal solution. The experimental results show that the proposed method is very robust against common image processing manupilations and attacks and has superiority compared with superb other zero-watermarking methods.

Local Orthogonal Moments for Local Features.

By introducing parameters with local information, several types of orthogonal moments have recently been developed for the extraction of local features in an image. But with the existing orthogonal moments, local features cannot be well-controlled with these parameters. The reason lies in that zeros distribution of these moments' basis function cannot be well-adjusted by the introduced parameters. To overcome this obstacle, a new framework, transformed orthogonal moment (TOM), is set up. Most existing continuous orthogonal moments such as Zernike moments, fractional-order orthogonal moments (FOOMs), etc. are all special cases of TOM. To control the basis function's zeros distribution, a novel local constructor is designed, and local orthogonal moment (LOM) is proposed. Zeros distribution of LOM's basis function can be adjusted with parameters introduced by the designed local constructor. Consequently, locations, where local features extracted from by LOM, are more accurate than those by FOOMs. In comparison with Krawtchouk moments and Hahn moments etc., the range, where local features are extracted from by LOM, is order insensitive. Experimental results demonstrate that LOM can be utilized to extract local features in an image.

Krawtchouk moments and support vector machines based coal and rock interface cutting thermal image recognition

Research on precise identification technology of coal and rock interfaces is carried out to resolve the problem of interface recognition of coal and rock in the intelligent mining of coal-firing equipment. Krawtchouk moment has been implemented in the extract of coal and rock's thermal infrared image, according to the highly recognized degree of Krawtchouk and its convenient operation. The invariant moment Krawtchouk and the vector support wavelet are proposed to identify the interfaces between charcoal and rock. The invariable time of Krawtchouk and the moments from Krawtchouk coal and rock infrastructure are calculated using thermal imaging cloud images from coal and rock cutting experiments in order to build the images of the coal and rock. The image is generated by thermal imaging. Then the vector support algorithms are built on the basis of the building of the self-vectors to recognize images of coal and rock. Results show that invariants in the Krawtchouk time used as the infrarouge image feature on the interface between coal and rock can better identify the image and significantly increase the recognition rate.

An Energy-Efficient Compression Algorithm of ECG Signals in Remote Healthcare Monitoring Systems

Remote Healthcare Monitoring Systems (RHMs) that use ECG signals are very effective tools for the early diagnosis of various heart conditions. However, these systems are still confronted with a problem that reduces their efficiency, such as energy consumption in wearable devices because they are battery-powered and have limited storage. This paper presents a novel algorithm for the compression of ECG signals to reduce energy consumption in RHMs. The proposed algorithm uses discrete Krawtchouk moments as a feature extractor to obtain features from the ECG signal. Then the accelerated Ant Lion Optimizer (AALO) selects the optimum features that achieve the best-reconstructed signal. Our proposed algorithm is extensively validated using two benchmark datasets: MIT-BIH arrhythmia and ECG-ID. The proposed algorithm provides the average values of compression ratio (CR), percent root mean square difference (PRD), signal to noise ratio (SNR), Peak Signal to noise ratio (PSNR), and quality score (QS) are 15.56, 0.69, 44.52, 49.04 and 23.92, respectively. The comparison demonstrates the advantages of the proposed compression algorithm on recent algorithms concerning the mentioned performance metrics. It also tested and compared against other existing algorithms concerning Processing Time, compression speed and computational efficiency. The obtained results show that the proposed algorithm extremely outperforms in terms of (Processing Time = 6.89 s), (compression speed = 4640.19 bps) and (computational efficiency = 2.95). The results also indicate that the proposed compression algorithm reduces energy consumption in a wearable device by decreasing the wake-up time by 3600 ms.

On the classification of simple and complex biological images using Krawtchouk moments and Generalized pseudo-Zernike moments: a case study with fly wing images and breast cancer mammograms.

In image analysis, orthogonal moments are useful mathematical transformations for creating new features from digital images. Moreover, orthogonal moment invariants produce image features that are resistant to translation, rotation, and scaling operations. Here, we show the result of a case study in biological image analysis to help researchers judge the potential efficacy of image features derived from orthogonal moments in a machine learning context. In taxonomic classification of forensically important flies from the Sarcophagidae and the Calliphoridae family (n = 74), we found the GUIDE random forests model was able to completely classify samples from 15 different species correctly based on Krawtchouk moment invariant features generated from fly wing images, with zero out-of-bag error probability. For the more challenging problem of classifying breast masses based solely on digital mammograms from the CBIS-DDSM database (n = 1,151), we found that image features generated from the Generalized pseudo-Zernike moments and the Krawtchouk moments only enabled the GUIDE kernel model to achieve modest classification performance. However, using the predicted probability of malignancy from GUIDE as a feature together with five expert features resulted in a reasonably good model that has mean sensitivity of 85%, mean specificity of 61%, and mean accuracy of 70%. We conclude that orthogonal moments have high potential as informative image features in taxonomic classification problems where the patterns of biological variations are not overly complex. For more complicated and heterogeneous patterns of biological variations such as those present in medical images, relying on orthogonal moments alone to reach strong classification performance is unrealistic, but integrating prediction result using them with carefully selected expert features may still produce reasonably good prediction models.

An intrusive method for estimating speech intelligibility from noisy and distorted signals.

An objective metric that predicts speech intelligibility under different types of noise and distortion would be desirable in voice communication. To date, the majority of studies concerning speech intelligibility metrics have focused on predicting the effects of individual noise or distortion mechanisms. This study proposes an objective metric, the spectrogram orthogonal polynomial measure (SOPM), that attempts to predict speech intelligibility for people with normal hearing under adverse conditions. The SOPM metric is developed by extracting features from the spectrogram using Krawtchouk moments. The metric's performance is evaluated for several types of noise (steady-state and fluctuating noise), distortions (peak clipping, center clipping, and phase jitters), ideal time-frequency segregation, and reverberation conditions both in quiet and noisy environments. High correlation (0.97-0.996) is achieved with the proposed metric when evaluated with subjective scores by normal-hearing subjects under various conditions.

Orthogonal single-pixel imaging using an adaptive under-Nyquist sampling method

Single-pixel imaging (SPI) recently has made significant progress, however, it is still an open issue to adaptively tradeoff its imaging fidelity and speed. Here, we present an adaptive sampling method for SPI to reduce the sampling rate for improving the imaging speed adaptively, sacrificing as little as possible of its imaging fidelity. The proposed method only requires setting an error band to realize adaptive under-Nyquist sampling, based upon the fact that the coefficient matrix consisted of the frequency components obtained by the orthogonal transforms is sparse. First, an appropriately elaborated sampling path, which can be divided into multiple segments, can be set according to this coefficient matrix measured by a single-pixel detector. Then the variance of each segment is calculated and expressed in logarithmic form for the real-time polynomial curve fitting. When the variation of the curve’s slope is small enough and reaches an error band, the sampling is adaptively stopped. Finally, the object image can be reconstructed via the adaptive sampling method following the elaborated sampling path for improving the imaging speed adaptively. The effectiveness of the adaptive sampling SPIs based on the orthogonal transforms, such as Hadamard transform, discrete cosine transform, Fourier transform, and Krawtchouk moments transform, is theoretically and experimentally demonstrated. It should be noted the proposed method can be also applied in SPIs using other orthogonal transforms, in which only an error band is set by the users.

New Set of Invariant Quaternion Krawtchouk Moments for Color Image Representation and Recognition

One of the most often used techniques to represent color images is quaternion algebra. This study introduces the quaternion Krawtchouk moments, QKrMs, as a new set of moments to represent color images. Krawtchouk moments (KrMs) represent one type of discrete moments. QKrMs use traditional Krawtchouk moments of each color channel to describe color images. This new set of moments is defined by using orthogonal polynomials called the Krawtchouk polynomials. The stability against the translation, rotation, and scaling transformations for QKrMs is discussed. The performance of the proposed QKrMs is evaluated against other discrete quaternion moments for image reconstruction capability, toughness against various types of noise, invariance to similarity transformations, color face image recognition, and CPU elapsed times.

Identification of systolic and diastolic heart failure progression with Krawtchouk moment feature-aided Harris hawks optimized support vector machine

Identification of systolic and diastolic heart failure progression with Krawtchouk moment feature-aided Harris hawks optimized support vector machine

Robust anaglyph 3D video watermarking based on cyan mosaic generation and DCT insertion in Krawtchouk moments

Robust anaglyph 3D video watermarking based on cyan mosaic generation and DCT insertion in Krawtchouk moments

Real-time Computation of Krawtchouk Moments on Gray Images Using Block Representation

Real-time Computation of Krawtchouk Moments on Gray Images Using Block Representation

Artificial intelligent classification of biomedical color image using quaternion discrete radial Tchebichef moments

In this work, we propose a new set of an intelligent classifier of biomedical color images using Quaternion Discrete Radial Tchebichef Moments (QRTM). This moment has shown very high robustness in terms of color image representation. Thus, we propose a new approach for the fast and accurate reconstruction of multi-level and color images. This approach based on the reconstruction of color images by applying matrix computation. In the second step, we propose a new method for the extraction of Quaternion Discrete Radial Tchebichef Moments invariant (QRTMI). This method based on the representation of the extraction of these invariants. The performance of the invariance of these moments under the three types of geometrical transformations (Rotation, translation, scale) are very important. Finally, we present a new model based on a Multilayer perceptron (MLP) for the classification of biomedical color images. The experimental results show that the QRTMI very powerful compared with radial Legendre - Fourier and Quaternion discrete radial Krawtchouk moments invariant for the biomedical colors images using the BreaKHis Database (Breast Tumor).

Color image analysis of quaternion discrete radial Krawtchouk moments

In this work, we suggest a new set of quaternion discrete radial Krawtchouk moments (QDRKMs) for color image reconstruction and classification. These new discrete moments are represented over a disk by using discrete orthogonal radial Krawtchouk moments. The use of Quaternion discrete moments for color image eliminates the discretization errors produced when the Quaternion continuous moments are used. Furthermore, this approach is suggested for highly accurate calculation of QDRKMs in polar coordinates where the kernel is exactly calculated by over circular color pixels. The translation, scaling, and rotation (TSR) invariances for QDRKMs are proved. Theoretical analysis and numerical experiments investigation were shown in terms of the performance description of TSR invariances, classification and robustness to different noises of the QDRKMs compared with continuous quaternion Legendre–Fourier moments using COIL 100 database.