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Numeral recognition is considered an essential preliminary step for optical character recognition, document understanding, and others. Although several handwritten numeral recognition algorithms have been proposed so far, achieving adequate recognition accuracy and execution time remain challenging to date. In particular, recognition accuracy depends on the features extraction mechanism. As such, a fast and robust numeral recognition method is essential, which meets the desired accuracy by extracting the features efficiently while maintaining fast implementation time. Furthermore, to date most of the existing studies are focused on evaluating their methods based on clean environments, thus limiting understanding of their potential application in more realistic noise environments. Therefore, finding a feasible and accurate handwritten numeral recognition method that is accurate in the more practical noisy environment is crucial. To this end, this paper proposes a new scheme for handwritten numeral recognition using Hybrid orthogonal polynomials. Gradient and smoothed features are extracted using the hybrid orthogonal polynomial. To reduce the complexity of feature extraction, the embedded image kernel technique has been adopted. In addition, support vector machine is used to classify the extracted features for the different numerals. The proposed scheme is evaluated under three different numeral recognition datasets: Roman, Arabic, and Devanagari. We compare the accuracy of the proposed numeral recognition method with the accuracy achieved by the state-of-the-art recognition methods. In addition, we compare the proposed method with the most updated method of a convolutional neural network. The results show that the proposed method achieves almost the highest recognition accuracy in comparison with the existing recognition methods in all the scenarios considered. Importantly, the results demonstrate that the proposed method is robust against the noise distortion and outperforms the convolutional neural network considerably, which signifies the feasibility and the effectiveness of the proposed approach in comparison to the state-of-the-art recognition methods under both clean noise and more realistic noise environments.

Tchebichef polynomials (TPs) play a crucial role in various fields of mathematics and applied sciences, including numerical analysis, image and signal processing, and computer vision. This is due to the unique properties of the TPs and their remarkable performance. Nowadays, the demand for high-quality images (2D signals) is increasing and is expected to continue growing. The processing of these signals requires the generation of accurate and fast polynomials. The existing algorithms generate the TPs sequentially, and this is considered as computationally costly for high-order and larger-sized polynomials. To this end, we present a new efficient solution to overcome the limitation of sequential algorithms. The presented algorithm uses the parallel processing paradigm to leverage the computation cost. This is performed by utilizing the multicore and multithreading features of a CPU. The implementation of multithreaded algorithms for computing TP coefficients segments the computations into sub-tasks. These sub-tasks are executed concurrently on several threads across the available cores. The performance of the multithreaded algorithm is evaluated on various TP sizes, which demonstrates a significant improvement in computation time. Furthermore, a selection for the appropriate number of threads for the proposed algorithm is introduced. The results reveal that the proposed algorithm enhances the computation performance to provide a quick, steady, and accurate computation of the TP coefficients, making it a practical solution for different applications.

The property of rotation, scaling and translation invariant has a great important in 3D image classification and recognition. Tchebichef moments as a classical orthogonal moment have been widely used in image analysis and recognition. Since Tchebichef moments are represented in Cartesian coordinate, the rotation invariance can’t easy to realize. In this paper, we propose a new set of 3D rotation scaling and translation invariance of radial Tchebichef moments. We also present a theoretical mathematics to derive them. Hence, this paper we present a new 3D radial Tchebichef moments using a spherical representation of volumetric image by a one-dimensional orthogonal discrete Tchebichef polynomials and a spherical function. They have better image reconstruction performance, lower information redundancy and higher noise robustness than the existing radial orthogonal moments. At last, a mathematical framework for obtaining the rotation, scaling and translation invariants of these two types of Tchebichef moments is provided. Theoretical and experimental results show the superiority of the proposed methods in terms of image reconstruction capability and invariant recognition accuracy under both noisy and noise-free conditions. The result of experiments prove that the Tchebichef moments have done better than the Krawtchouk moments with and without noise. Simultaneously, the reconstructed 3D image converges quickly to the original image using 3D radial Tchebichef moments and the test images are clearly recognized from a set of images that are available in a PSB database.

The species abundance distribution (SAD) depicts the relative abundance of species within a community, which is a key concept in ecology. Here, we test whether SADs are more likely to either follow a lognormal‐like or follow a logseries‐like distribution and how that may change with spatial scale. Our results show that the shape of SADs changes from logseries‐like at small, plot scales to lognormal‐like at large, landscape scales. However, the rate at which the SAD's shape changes also depends on species traits linked to the spatial distribution of individuals. Specifically, we show for oligophagous and small macro‐moth species that a logseries distribution is more likely at small scales and a lognormal distribution is more likely at large scales, whereas the logseries distribution fits well at both small and large scales for polyphagous and large species. We also show that SAD moments scale as power laws as a function of spatial scale, and we assess the performance of Tchebichef moments and polynomials to reconstruct SADs at the landscape scale from information at local scales. Overall, the method performed well and reproduced the shapes of the empirical distributions.

The wireless capsule endoscopy (WCE) invented by Given Imaging has been gradually used in hospitals due to its great breakthrough that it can view the entire small bowel for gastrointestinal diseases. However, a tough problem associated with this new technology is that too many images to be examined by eyes cause a huge burden to physicians, so it is significant if we can help physicians do diagnosis using computerized methods. In this paper, a new method aimed for bleeding and ulcer detection in WCE images is proposed. This new approach mainly focuses on color feature, also a very powerful clue used by physicians for diagnosis, to judge the status of gastrointestinal tract. We propose a new idea of chromaticity moment as the features to discriminate normal regions and abnormal regions, which make full use of the Tchebichef polynomials and the illumination invariant of HSI color space, and we verify performances of the proposed features by employing neural network classifier. Experimental results on our present image data of bleeding and ulcer show that it is feasible to exploit the proposed chromaticity moments to detect bleeding and ulcer for WCE images.

Orthogonal Tchebichef moments of fractional order (FrTMs) serve as descriptors for signals and images. Many fields, including signal analysis and watermarking, have relied heavily on such moments. This study addresses three critical limitations in existing approaches: the computational burden of higher-order moment calculations, numerical instability affecting reconstruction accuracy, and orthogonality deterioration in large-scale signal processing. Furthermore, using the QR decomposition approach is crucial to maintain the orthogonality of the higher-order moments. We introduce an improved computational framework with three main scientific contributions as development of an optimized set of three interrelated second-order recurrence equations for normalized FrTMs, implementation of the Schwarz-Rutishauser algorithm as an alternative to classical QR decomposition methods, maintaining orthogonality with substantially lower computational overhead; and integration of these innovations into a comprehensive system for biomedical signal reconstruction and watermarking. The method in question was tested on two benchmark datasets the MIT-BIH arrhythmia and CHB-MIT Scalp EEG. The findings indicate that the proposed methodology exhibits significantly higher performance levels than current methodologies, with a 64.3% improvement in PSNR (reaching 147.08 dB compared to 89.74 dB in existing approaches), 89.7% reduction in MSE (0.0092 versus 0.09 average), and 84.1% decrease in bit error rate (0.25 versus 1.57) for watermarking applications. Processing time was also reduced by 64.3% compared to competing methods, making this approach substantially more efficient for implementation in Internet of Healthcare Things (IoHT) contexts.

One of the major application areas of the fractional-order discrete transform (FrDTs) is in signal and information security, particularly in signal and image/video encryption. Recently, many researchers proposed techniques that implemented not only the fractional transforms, but also various randomized versions of the FrDTs, which add more security features to signal’s encryption. In this paper, we propose a new image/video encryption scheme based on fractional-order discrete Tchebichef transform (FrDTT) using singular value decomposition. The FrDTTs are derived algebraically using the spectral decomposition of discrete Tchebichef polynomials, then the singular value decomposition technique in order to build a basic set of orthonormal eigenvectors which help to develop FrDTTs. Finally, we implement and apply the scheme proposed in this paper for encrypting test images and video sequences. Moreover, we methodically perform the security evaluation in terms of brute force and statistical attacks as well as comparisons with the existing methods in terms of secret key sensitivity and space. The promising experiment results demonstrate the effectiveness and efficiency of our proposed FrDTTs based image encryption techniques.

In digital pathology, accurate diagnosis and prognosis critically depend on robust feature representation of Whole Slide Images (WSIs). While deep learning offers powerful solutions, its “black box” nature presents significant challenges to clinical interpretability and widespread adoption. Handcrafted features offer interpretability, yet orthogonal moments, particularly Tchebichef moments (TMs), remain underexplored for WSI analysis. This study introduces TMs as interpretable, efficient, and scalable handcrafted descriptors for WSIs, alongside a novel two-dimensional digital filter architecture designed to enhance numerical stability and hardware compatibility during TM computation. We conducted a comprehensive reconstruction analysis using H&E-stained WSIs from the MIDOG++ dataset to evaluate TM effectiveness. Our results demonstrate that lower-order TMs accurately reconstruct both square and rectangular WSI patches, with performance stabilising beyond a threshold moment order, confirmed by SNIRE, SSIM, and BRISQUE metrics, highlighting their capacity to retain structural fidelity. Furthermore, our analysis reveals significant computational efficiency gains through the use of pre-computed polynomials. These findings establish TMs as highly promising, interpretable, and scalable feature descriptors, offering a robust alternative for computational pathology applications that prioritise both accuracy and transparency.

The research focuses on the analysis of seismic data, specifically targeting the detection, edge segmentation, and classification of seismic images. These processes are fundamental in image processing and are crucial in understanding the stratigraphic structure and identifying oil and natural gas resources. However, there is a lack of sufficient resources in the field of seismic image detection, and interpreting 2D seismic image slices based on 3D seismic data sets can be challenging. In this research, image segmentation involves image preprocessing and the use of a U-net network. Preprocessing techniques, such as Gaussian filter and anisotropic diffusion, are employed to reduce blur and noise in seismic images. The U-net network, based on the Canny descriptor is used for segmentation. For image classification, the ResNet-50 and Inception-v3 models are applied to classify different types of seismic images. In image detection, Tchebichef invariants are computed using the Tchebichef polynomials’ recurrence relation. These invariants are then used in an optimized multi-class SVM network for detecting and classifying various types of seismic images. The promising results of the SVM model based on Tchebichef invariants suggest its potential to replace Hu moment invariants (HMIs) and Zernike moment invariants (ZMIs) for seismic image detection. This approach offers a more efficient and dependable solution for seismic image analysis in the future.

This article proposes a new method for the fast and efficient calculation of 3D Tchebichef moments,which are an essential tool for the characterization and analysis of 3D objects. This method integrates the Kronecker tensor product to the computation of 3D Tchebichef moments for higher orders with the advantage of being parallelizable. The experimental results clearly show the benefits and efficacy of the proposed method compared to existing methods.