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Representation and classification of color texture generate considerable interest within the field of computer vision. Texture classification is a difficult task that assigns unlabeled images or textures to the correct labeled class. Some key factors such as scaling and viewpoint variations and illumination changes make this task challenging. In this paper, we present a new feature extraction technique for color texture classification and recognition. The presented approach aggregates the features extracted from local binary patterns (LBP) and convolution neural network (CNN) to provide discriminatory information, leading to better texture classification results. Almost all of the CNN model cases classify images based on global features that describe the image as a whole to generalize the entire object. LBP classifies images based on local features that describe the image’s key points (image patches). Our analysis shows that using LBP improves the classification task when compared to using CNN only. We test the proposed approach experimentally over three challenging color image datasets (ALOT, CBT, and Outex). The results demonstrated that our approach improved up to 25% in the classification accuracy over the traditional CNN models. We identify optimal combinations for each dataset and obtain high classification rates. The proposed approach is robust, stable, and discriminatory among the three datasets and has shown enhancement in classification and recognition compared to the state-of-the-art method.

Graphical abstract, Orthogonal moments are used to represent digital images with minimum redundancy. Orthogonal moments with fractional-orders show better capabilities in digital image analysis than integer-order moments. In this work, the authors present new fractional-order shifted Gegenbauer polynomials. These new polynomials are used to define a novel set of orthogonal fractional-order shifted Gegenbauer moments (FrSGMs). The proposed method is applied in gray-scale image analysis and recognition. The invariances to rotation, scaling and translation (RST), are achieved using invariant fractional-order geometric moments. Experiments are conducted to evaluate the proposed FrSGMs and compare with the classical orthogonal integer-order Gegenbauer moments (GMs) and the existing orthogonal fractional-order moments. The new FrSGMs outperformed GMs and the existing orthogonal fractional-order moments in terms of image recognition and reconstruction, RST invariance, and robustness to noise.

A novel set of fractional orthogonal polar harmonic transforms for gray-scale and color image analysis are presented in this paper. These transforms are divided into two groups. The first group contains fractional polar complex exponential transforms (FrPCETs), fractional polar cosine transforms (FrPCTs), and fractional polar sine transforms (FrPSTs) for gray-scale images. The second group contains the fractional quaternion polar complex exponential transforms (FrQPCETs), fractional quaternion polar cosine transforms (FrQPCTs), and fractional quaternion polar sine transforms (FrQPSTs) for color images. All mathematical formulae for the basis functions, orthogonality relations and reconstruction forms are derived and their validity are proved. The required mathematical forms for invariance to rotation, scaling and translation (RST) are derived. A series of experiments is performed to test the validity of the proposed fractional polar harmonic transforms (FrPHTs) and the fractional quaternion polar harmonic transforms (FrQPHTs). The performances of the proposed FrPHTs and FrQPHTs are outperformed the classical polar harmonic transforms, the quaternion polar harmonic transforms and the existing fractional orthogonal transforms in terms of accuracy and numerical stability, digital image reconstruction, RST invariances, robustness to noise and computational efficiency.

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.

The diagnosis of COVID-19 is of vital demand. Several studies have been conducted to decide whether the chest X-ray and computed tomography (CT) scans of patients indicate COVID-19. While these efforts resulted in successful classification systems, the design of a portable and cost-effective COVID-19 diagnosis system has not been addressed yet. The memory requirements of the current state-of-the-art COVID-19 diagnosis systems are not suitable for embedded systems due to the required large memory size of these systems (e.g., hundreds of megabytes). Thus, the current work is motivated to design a similar system with minimal memory requirements. In this paper, we propose a diagnosis system using a Raspberry Pi Linux embedded system. First, local features are extracted using local binary pattern (LBP) algorithm. Second, the global features are extracted from the chest X-ray or CT scans using multi-channel fractional-order Legendre-Fourier moments (MFrLFMs). Finally, the most significant features (local and global) are selected. The proposed system steps are integrated to fit the low computational and memory capacities of the embedded system. The proposed method has the smallest computational and memory resources,less than the state-of-the-art methods by two to three orders of magnitude, among existing state-of-the-art deep learning (DL)-based methods.

Color image representation using quaternion moments has gained more interest during the last few years. In this paper, invariant color image representation using quaternion Legendre–Fourier moments (QLFMs) is presented. A new method for exact, fast and stable computation of QLFMs in polar coordinates is proposed. Explicit rotation, scaling and translation (RST) invariants of quaternion Legendre–Fourier are derived. Numerical experiments are performed to compare the performance of QLFMs with the existing quaternion moments. The comparison clearly shows the superiority of the proposed method over all existing quaternion moments in terms of image reconstruction capability, RST invariances and numerical stability.

In this paper, a new set of quaternion radial-substituted Chebyshev moments (QRSCMs) is proposed for color image representation and recognition. These new moments are circular moments defined over a unit disk by using a new set of orthogonal basis functions called radial-substituted Chebyshev functions. A new hybrid method is proposed for highly accurate computation of QRSCMs in polar coordinates. In this method, the angular kernel is exactly computed by analytical integration of Fourier function over circular pixels. The radial kernel is computed using a recurrence relation which completely eliminates the coefficient matrix associated with the radial-substituted Chebyshev functions. Rotation, scaling, and translation (RST) invariances for QRSCMs are proved. Numerical experiments were conducted where the results of these experiments show better performance of QRSCMs over existing quaternion moments in terms of image reconstruction capabilities, RST invariances, robust to different noises, and CPU elapsed times.

This paper proposes a geometrically invariant watermarking method based on highly accurate moments of Polar Harmonic Transforms (PHTs). Highly accurate, fast and numerically stable moments of PHTs are computed using a new simplified trigonometric formula. The proposed PHTs-based watermarking process is robust to geometric attacks. The proposed method consists of three main steps. In the first step, the Arnold scrambling algorithm is applied on a binary image. In the second step, accurate PHTs’ moments of the original host image are computed. In the third step, a digital watermark is embedded by performing the quantization of selected PHTs’ moments. The results of the numerical experiments ensure the validity of the proposed watermarking method. The proposed method shows a better visual imperceptibility and a better robustness to both geometric distortions and common signal processing attacks when compared with the existing moment-based watermarking methods.

Orthogonal moments were successfully used to extract features from gray-scale and color images. Recently, scientists show that orthogonal moments of fractional-orders have better capabilities to extract the fine features. In this work, novel orthogonal generic fractional-order Jacobi-Fourier moments are proposed for image processing, pattern recognition and computer vision applications. Novel orthogonal Jacobi-Fourier polynomials of fractional-order were derived and defined in polar coordinates. The mathematical equation for orthogonality was formulated and a three-term recurrence relation was derived for easier computation of these polynomials. The proposed orthogonal fractional-order Jacobi-Fourier moments are generic where other orthogonal fractional-order moments are derived as special cases by choosing different values of the controlling parameters. The invariance to geometric transformations, rotation, scaling and translations, is proved where the required mathematical formulae for these invariances are presented. The proposed new fractional-order moments were tested using different datasets of gray-scale and color images in terms of image reconstruction, invariance to geometric transformations, robustness to noise, image recognition, and computational times where their performance were compared with the recent existing orthogonal integer- and fractional-order moments. The proposed generic fractional-order Jacobi-Fourier moments outperformed all existing orthogonal moments.

Orthogonal moments enable computer-based systems to discriminate between similar objects. Mathematicians proved that the orthogonal polynomials of fractional-orders outperformed their corresponding counterparts in representing the fine details of a given function. In this work, novel orthogonal fractional-order Legendre-Fourier moments are proposed for pattern recognition applications. The basis functions of these moments are defined and the essential mathematical equations for the recurrence relations, orthogonality and the similarity transformations (rotation and scaling) are derived. The proposed new fractional-order moments are tested where their performance is compared with the existing orthogonal quaternion, multi-channel and fractional moments. New descriptors were found to be superior to the existing ones in terms of accuracy, stability, noise resistance, invariance to similarity transformations, recognition rates and computational times.

COVID-19 is a worldwide epidemic, as announced by the World Health Organization (WHO) in March 2020. Machine learning (ML) methods can play vital roles in identifying COVID-19 patients by visually analyzing their chest x-ray images. In this paper, a new ML-method proposed to classify the chest x-ray images into two classes, COVID-19 patient or non-COVID-19 person. The features extracted from the chest x-ray images using new Fractional Multichannel Exponent Moments (FrMEMs). A parallel multi-core computational framework utilized to accelerate the computational process. Then, a modified Manta-Ray Foraging Optimization based on differential evolution used to select the most significant features. The proposed method evaluated using two COVID-19 x-ray datasets. The proposed method achieved accuracy rates of 96.09% and 98.09% for the first and second datasets, respectively.

A new set of Gegenbauer moment invariants is proposed for pattern recognition applications. These moment invariants are expressed as a linear combination of geometric moment invariants where the later are invariants under translation, scaling and rotation of the image they describe. The invariance of Gegenbauer moments is tested by using different binary- and gray-level images. The obtained results show the accuracy of the new set of Gegenbauer moment invariants.

Pseudo Zernike moments are orthogonal moments used to represent digital images with minimum amount of information redundancy. Pseudo Zernike moment invariants are image features that are invariant to translation, scaling and rotation which play an essential role in discriminating and classifying similar images where the performance and robustness of the classifiers are highly dependent on the accuracy of these futures. In this work, a new method is presented for accurate computation of two-dimensional pseudo Zernike moment invariants. Approximation errors are removed by using exact geometric and radial geometric moments. Invariance to translation and scaling are computed, while the rotation invariance is directly achieved as direct property of pseudo Zernike moments. Numerical experiments are conducted on a set of standard images. The obtained results demonstrate the efficiency of the proposed method.

Gaussian-Hermite moments are orthogonal moments widely used in image processing and computer vision applications. Similar to the other families of orthogonal moments, highly computational demands represent the main challenging. In this work, an efficient method is proposed for fast computation of highly accurate Gaussian-Hermite moments for gray-level images. The proposed method achieves the accuracy through the integration of Gaussian-Hermite polynomials over the image pixels. To achieve the efficiency, the symmetry property of Gaussian-Hermite polynomials is employed where the computational complexity is reduced by 75%. Fast computational methodology is employed to significantly accelerate the computational process where the 2D Gaussian-Hermite moments are treated in a separated form. Numerical experiments are performed where the results are compared with the conventional method. The comparison of the obtained results clearly ensures the efficiency of the proposed method.

Comments on the recent work of Guo et al. [1] are presented, in order to correct the erroneous equations. The corrected equations of the Chebychev rational moments, for gray-level images, are presented. In addition, one numerical experiment is performed to ensure the validity of the corrected equations.

A new method is proposed for fast and low-complexity computation of exact 3D Legendre moments. The proposed method consists of three main steps. In the first step, the symmetry property is employed where the computational complexity is reduced by 87%. In the second step, exact values of 3D Legendre moments are obtained by mathematically integrating the Legendre polynomials over digital image voxels. An algorithm is employed to significantly accelerate the computational process. In this algorithm, the equations of 3D Legendre moments are treated in a separated form. The proposed method is applied to determine translation-scale invariance of 3D Legendre moments in a very simple way. Numerical experiments are performed where the results are compared with those of the existing methods. Complexity analysis and results of the numerical experiments clearly ensure the efficiency of the proposed method.

Image representation by using polynomial moments is an interesting theme. In this paper, image representation by using orthogonal Gegenbauer function is presented. A novel method for accurate and fast computation of orthogonal Gegenbauer moments is proposed. The accurate values of Gegenbauer moments are obtained by mathematically integrating Gegenbauer polynomials multiplied by their weight functions over the digital image pixels. A novel recurrence formula is derived for the kernel generation. The proposed method removes the numerical approximation errors involved in conventional method. A fast algorithm is proposed to accelerate the moment's computations. A comparison with the conventional method is performed. The obtained results explain the efficiency and the superiority of the proposed method.

A new method is proposed for fast and accurate computation of Zernike moments. This method presents a novel formula for computing exact Zernike moments by using exact complex moments where the exact values of complex moments are computed by mathematical integration of the monomials over digital image pixels. The proposed method is applicable to compute the full set of Zernike moments as well as the subsets of individual order, repetition and an individual moment. A comparison with other conventional methods is performed. The results show the superiority of the proposed method.

Orthogonal Legendre moments are used in several pattern recognition and image processing applications. Translation and scale Legendre moment invariants were expressed as a combination of the approximate original Legendre moments. The shifted and scaled Legendre polynomials were expressed in terms of the original Legendre polynomials according to complicated and time-consuming algebraic relations. In this paper, refined translation-scale Legendre moment invariants are obtained through the exact computation of original Legendre moments which completely remove approximation. Fast straightforward computation of central Legendre moments significantly reduces the computational time. According to the tremendous reduction of the computational complexity, the refined set of Legendre invariants is suitable for large size images. The performance of descriptors is evaluated by using a set of standard images.

Fast and accurate method is proposed for radial moment's computation. Exact radial moments are computed as a linear combination of exact geometric moments. The digital image is transformed to be inside the unit circle, where the transformed image is divided into four quadrants. Based on the symmetry property; only one quadrant of transformed image is needed to compute the whole set of moments. This leads to significant reduction in the computational complexity requirements. The proposed method completely removes the approximation errors and tremendously reduced the computational demands. Numerical experiments are performed, where the obtained results are compared with the approximated values. The obtained results clearly explained the efficiency of the proposed method.

Moment invariants are widely used in image processing, pattern recognition and computer vision. Several methods and algorithms have been proposed for fast and efficient calculation of moment's invariants where numerical approximation errors are involved in most of these methods. In this paper, an optimized set of moment invariants with respect to rotation, scaling and translation is presented. An accurate method is used for exact computation of moment invariants for gray level images. A fast algorithm is applied to accelerate the process of computation. Error analysis is presented and a comparison with other conventional methods is performed. The obtained results explain the superiority of the proposed method.

Affine moment invariants are widely used in pattern recognition and computer vision. The affine transform usually decomposed into a set of geometric transforms. The computation of these transforms relies on their relations with the geometric moments. Approximate computation of geometric moments produced a very large dynamic range that results in numerical instabilities. In this work, an exact method is used for the computation of affine moment invariants for gray level images, where the proposed method completely removes the approximation errors. Numerical experiments are performed to test the invariance of symmetric as well as asymmetric images subject to affine transformations. A comparison with the approximation method is made. The obtained results clearly explained the efficiency of the proposed method.

A novel method is proposed for exact Legendre moment computation for gray level images. A recurrence formula is used to compute exact values of moments by mathematically integrating the Legendre polynomials over digital image pixels. This method removes the numerical approximation errors involved in conventional methods. A fast algorithm is proposed to accelerate the moment's computations. A comparison with other conventional methods is performed. The obtained results explain the superiority of the proposed method.

Direct computation of Legendre orthogonal moments requires huge arithmetic operations, which is very time consuming. Many works have described methods for reducing the computations involved in evaluating Legendre moments. Nevertheless, reduction computational complexity is still an open problem and needs more investigation. Existing algorithms mainly focused on binary images and compute Legendre moments using a set of geometric moments. We propose a fast and efficient method for computation of Legendre moments for binary and gray level images. A recurrence formula of one-dimensional Legendre moments will be established using the recursive property of Legendre polynomials; then the method will be extended to calculate the two-dimensional Legendre moments. This method is completely independent on geometric moment. The complexity analysis shows that the proposed method computes Legendre moments more efficiently than the direct method and the other conventional methods.

Geometric moments are widely used in image processing and pattern recognition. While several methods have been proposed, exact geometric moment’s computation for gray level images is still unavailable. In this paper exact values of geometric moments are calculated using mathematical integration of the monomial terms over digital image pixels. This method removed the numerical approximation errors involved in conventional methods. A fast algorithm is proposed to accelerate the moment’s computations. The method is extended to compute the three-dimensional moments. A comparison with other conventional methods is performed. The obtained results explained the superiority of the proposed method.

Accurate reconstruction of noisy medical images is presented in this work. Speckle, additive white Gaussian and Rician noises are the most popular kinds of noise raised in medical imaging systems. Medical images contaminated with these noises were reconstructed herein by using Pseudo Zernike, Legendre, Gaussian-Hermite, and Krawtchouk moments. Numerical experiments were conducted and the moments' performance in reconstructing the noisy medical images was evaluated. The experiments have shown that the performance of Legendre moments is superior to all other moments in the case of speckle and Rician noises, while in the case of additive Gaussian noise, Legendre, Gaussian-Hermite and Krawtchouk moments presenting very similar performances.

An algorithm was proposed for very fast and low-complexity computation of three-dimensional Zernike moments. The 3D Zernike moments were expressed in terms of exact 3D geometric moments where the later are computed exactly through the mathematical integration of the monomial terms over the digital image/object voxels. A new symmetry-based method was proposed to compute 3D Zernike moments with 87% reduction in the computational complexity. A fast 1D cascade algorithm was also employed to add more complexity reduction. The comparison with existing methods was performed, where the numerical experiments and the complexity analysis ensured the efficiency of the proposed method especially with image and objects of large sizes.