Fast Computation of Hahn Polynomials for High Order Moments

Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction. Commonly, DHPs are used as object representation; however, they suffer from the problem of numerical instability when the moment order becomes large. In this paper, an operative method to compute the Hahn orthogonal basis is proposed and applied to high orders. This paper developed a new mathematical model for computing the initial value of the DHP and for different values of DHP parameters (α and β). In addition, the proposed method is composed of two recurrence algorithms with an adaptive threshold to stabilize the generation of the DHP coefficients. It is compared with state-of-the-art algorithms in terms of computational cost and the maximum size that can be correctly generated. The experimental results show that the proposed algorithm performs better in both parameters for wide ranges of parameter values α and β, and polynomial sizes

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision. Racah polynomials were originally introduced by Wilson and later modified by Zhu to be orthogonal on a discrete set of samples. However, when the degree of the polynomial is high, it encounters numerical instability issues. In this paper, we propose a novel algorithm called Improved Stabilization (ImSt) for computing DRP coefficients. The algorithm partitions the DRP plane into asymmetric parts based on the polynomial size and DRP parameters. We have optimized the use of stabilizing conditions in these partitions. To compute the initial values, we employ the logarithmic gamma function along with a new formula. This combination enables us to compute the initial values efficiently for a wide range of DRP parameter values and large polynomial sizes. Additionally, we have derived a symmetry relation for the case when the Racah polynomial parameters are zero ( a=0 , =0 ). This symmetry makes the Racah polynomials symmetric about the main diagonal, and we present a different algorithm for this specific scenario. We have demonstrated that the ImSt algorithm works for a broader range of parameters and higher degrees compared to existing algorithms. A comprehensive comparison between ImSt and the existing algorithms has been conducted, considering the maximum polynomial degree, computation time, restriction error analysis, and reconstruction error. The results of the comparison indicate that ImSt outperforms the existing algorithms for various values of Racah polynomial parameters

Abstract Pattern Image Generation using Generative Adversarial Networks

Abstract pattern is very commonly used in the textile and fashion industry. Pattern design is an area where designers need to come up with new and attractive patterns every day. It is very difficult to find employees with a sufficient creative mindset and the necessary skills to come up with new unseen attractive designs. Therefore, it would be ideal to identify a process that would allow for these patterns to be generated on their own with little to no human interaction. This can be achieved using deep learning models and techniques. One of the most recent and promising tools to solve this type of problem is Generative Adversarial Networks (GANs). In this paper, we investigate the suitability of GAN in producing abstract patterns. We achieve this by generating abstract design patterns using the two most popular GANs, namely Deep Convolutional GAN and Wasserstein GAN. By identifying the best-performing model after training using hyperparameter optimization and generating some output patterns we show that Wasserstein GAN is superior to Deep Convolutional GAN

Plain, Edge, and Texture Detection Based on Orthogonal Moment

Image pattern classification is considered a significant step for image and video processing. Although various image pattern algorithms have been proposed so far that achieved adequate classification, achieving higher accuracy while reducing the computation time remains challenging to date. A robust image pattern classification method is essential to obtain the desired accuracy. This method can be accurately classify image blocks into plain, edge, and texture (PET) using an efficient feature extraction mechanism. Moreover, to date, most of the existing studies are focused on evaluating their methods based on specific orthogonal moments, which limits the understanding of their potential application to various Discrete Orthogonal Moments (DOMs). Therefore, finding a fast PET classification method that accurately classify image pattern is crucial. To this end, this paper proposes a new scheme for accurate and fast image pattern classification using an efficient DOM. To reduce the computational complexity of feature extraction, an election mechanism is proposed to reduce the number of processed block patterns. In addition, support vector machine is used to classify the extracted features for different block patterns. The proposed scheme is evaluated by comparing the accuracy of the proposed method with the accuracy achieved by state-of-the-art methods. In addition, we compare the performance of the proposed method based on different DOMs to get the robust one. The results show that the proposed method achieves the highest classification accuracy compared with the existing methods in all the scenarios considered

Performance enhancement of high order Hahn polynomials using multithreading

Orthogonal polynomials and their moments have significant role in image processing and computer vision field. One of the polynomials is discrete Hahn polynomials (DHaPs), which are used for compression, and feature extraction. However, when the moment order becomes high, they suffer from numerical instability. This paper proposes a fast approach for computing the high orders DHaPs. This work takes advantage of the multithread for the calculation of Hahn polynomials coefficients. To take advantage of the available processing capabilities, independent calculations are divided among threads. The research provides a distribution method to achieve a more balanced processing burden among the threads. The proposed methods are tested for various values of DHaPs parameters, sizes, and different values of threads. In comparison to the unthreaded situation, the results demonstrate an improvement in the processing time which increases as the polynomial size increases, reaching its maximum of 5.8 in the case of polynomial size and order of 8000 × 8000 (matrix size). Furthermore, the trend of continuously raising the number of threads to enhance performance is inconsistent and becomes invalid at some point when the performance improvement falls below the maximum. The number of threads that achieve the highest improvement differs according to the size, being in the range of 8 to 16 threads in 1000 × 1000 matrix size, whereas at 8000 × 8000 case it ranges from 32 to 160 threads

Speech Enhancement Algorithm Based on Super-Gaussian Modeling and Orthogonal Polynomials

Different types of noise from the surrounding always interfere with speech and produce annoying signals for the human auditory system. To exchange speech information in a noisy environment, speech quality and intelligibility must be maintained, which is a challenging task. In most speech enhancement algorithms, the speech signal is characterized by Gaussian or super-Gaussian models, and noise is characterized by a Gaussian prior. However, these assumptions do not always hold in real-life situations, thereby negatively affecting the estimation, and eventually, the performance of the enhancement algorithm. Accordingly, this paper focuses on deriving an optimum low-distortion estimator with models that fit well with speech and noise data signals. This estimator provides minimum levels of speech distortion and residual noise with additional improvements in speech perceptual aspects via four key steps. First, a recent transform based on an orthogonal polynomial is used to transform the observation signal into a transform domain. Second, noise classification based on feature extraction is adopted to find accurate and mutable models for noise signals. Third, two stages of nonlinear and linear estimators based on the minimum mean square error (MMSE) and new models for speech and noise are derived to estimate a clean speech signal. Finally, the estimated speech signal in the time domain is determined by considering the inverse of the orthogonal transform. The results show that the average classification accuracy of the proposed approach is 99.43%. In addition, the proposed algorithm significantly outperforms existing speech estimators in terms of quality and intelligibility measures

3D Object Recognition Using Fast Overlapped Block Processing Technique

Three-dimensional (3D) image and medical image processing, which are considered big data analysis, have attracted significant attention during the last few years. To this end, efficient 3D object recognition techniques could be beneficial to such image and medical image processing. However, to date, most of the proposed methods for 3D object recognition experience major challenges in terms of high computational complexity. This is attributed to the fact that the computational complexity and execution time are increased when the dimensions of the object are increased, which is the case in 3D object recognition. Therefore, finding an efficient method for obtaining high recognition accuracy with low computational complexity is essential. To this end, this paper presents an efficient method for 3D object recognition with low computational complexity. Specifically, the proposed method uses a fast overlapped technique, which deals with higher-order polynomials and high-dimensional objects. The fast overlapped block-processing algorithm reduces the computational complexity of feature extraction. This paper also exploits Charlier polynomials and their moments along with support vector machine (SVM). The evaluation of the presented method is carried out using a well-known dataset, the McGill benchmark dataset. Besides, comparisons are performed with existing 3D object recognition methods. The results show that the proposed 3D object recognition approach achieves high recognition rates under different noisy environments. Furthermore, the results show that the presented method has the potential to mitigate noise distortion and outperforms existing methods in terms of computation time under noise-free and different noisy environments

Low-cost autonomous car level 2: Design and implementation for conventional vehicles

Modern cars are equipped with autonomous systems to assist the driver and improve driving experience. Driving assist system (DAS) is one of the most significant components of a self-driving vehicle (SDV), used to overcome non-autonomous driving challenges. However, most conventional cars are not equipped with DAS, and high-cost systems are required to equip these vehicles with DAS. Moreover, the design of DAS is very complex outside of the industry while it requires going through the Electronic Control Unit (ECU), which has a high level of security. Therefore, a basic system needs be installed in conventional cars which makes driving more efficient in terms of driver assistance. In this paper, an intelligent DAS is presented for real-time prediction of steering angle using deep learning (DL) and raw dataset collected from a real environment. Furthermore, an object detection model is deployed to assist and warn the driver of various types of objects along with corresponding distance measurement based on DL. Outputs from DL models are fed into the steering control system, which has Electronic Power Steering (EPS). The steering angle is measured in real time using an angle sensor and is posted back to the steering control system to make automated adjustments accordingly. Real-time tests are conducted on a 2009 Toyota Corolla equipped with a digital camera to capture live video stream, Controller Area Network (CAN-BUS) messages, and a steering angle sensor. The performance evaluation of the proposed system indicates intelligent steering control and driver assistance when evaluated in a real-time environment

Fast and efficient computation of high‐order Tchebichef polynomials

Discrete Tchebichef polynomials (DTPs) and their moments are effectively utilized in different fields such as video and image coding due to their remarkable performance. However, when the moments order becomes large (high), DTPs prone to exhibit numerical instabilities. In this paper, a computationally efficient and numerically stable recurrence algorithm is proposed for high order. The proposed algorithm is based on combining two recurrence algorithms. In addition, an adaptive threshold is used to stabilize the generation of the DTP coefficients. The designed algorithm can generate the DTP coefficients for high order and large signal size. To evaluate the performance of the proposed algorithm, a comparison study is performed with state-of-the-art algorithms in terms of computational cost and capability of generating DTPs with large size and high order. The results show that the proposed algorithm has a remarkable low computation cost and numerically stable compared to other algorithms. The improvement shows that the computation of the polynomial for a limited order is 27x times faster than the efficient algorithm