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Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties. This study proposes a new fast recursive algorithm to compute Krawtchouk polynomial coefficients (KPCs). This algorithm is based on the symmetry property of KPCs along the primary and secondary diagonals of the polynomial array. The n−x plane of the KP array is partitioned into four triangles, which are symmetrical across the primary and secondary diagonals. The proposed algorithm computes the KPCs for only one triangle (partition), while the coefficients of the other three triangles (partitions) can be computed using the derived symmetry properties of the KP. Therefore, only N / 4 recursion times are required. The proposed algorithm can also be used to compute polynomial coefficients for different values of the parameter p in interval (0, 1). The performance of the proposed algorithm is compared with that in previous literature in terms of image reconstruction error, polynomial size, and computation cost. Moreover, the proposed algorithm is applied in a face recognition system to determine the impact of parameter p on feature extraction ability. Simulation results show that the proposed algorithm has a remarkable advantage over other existing algorithms for a wide range of parameters p and polynomial size N, especially in reducing the computation time and the number of operations utilized.

Abstract:The recent increase in the number of videos available in cyberspace is due to the availability of multimedia devices, highly developed communication technologies, and low-cost storage devices. These videos are simply stored in databases through text annotation. Content-based video browsing and retrieval are inefficient due to the method used to store videos in databases. Video databases are large in size and contain voluminous information, and these characteristics emphasize the need for automated video structure analyses. Shot boundary detection (SBD) is considered a substantial process of video browsing and retrieval. SBD aims to detect transition and their boundaries between consecutive shots; hence, shots with rich information are used in the content-based video indexing and retrieval. This paper presents a review of an extensive set for SBD approaches and their development. The advantages and disadvantages of each approach are comprehensively explored. The developed algorithms are discussed, and challenges and recommendations are presented.

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With the increasing growth of multimedia data, the current real-world video sharing websites are being huge in repository size, more specifically video databases. This growth necessitates to look for superior techniques in processing video because video contains a lot of useful information. Temporal video segmentation (TVS) is considered essential stage in content-based video indexing and retrieval system. TVS aims to detect boundaries between successive video shots. TVS algorithm design is still challenging because most of the recent methods are unable to achieve fast and robust detection. In this regard, this paper proposes a TVS algorithm with high precision and recall values, and low computation cost for detecting different types of video transitions. The proposed algorithm is based on orthogonal moments which are considered as features to detect transitions. To increase the speed of the TVS algorithm as well as the accuracy, fast block processing and embedded orthogonal polynomial algorithms are utilized to extract features. This utilization will lead to extract multiple local features with low computational cost. Support vector machine (SVM) classifier is used to detect transitions. Specifically, the hard transitions are detected by the trained SVM model. The proposed algorithm has been evaluated on four datasets. In addition, the performance of the proposed algorithm is compared to several state-of-the-art TVS algorithms. Experimental results demonstrated that the proposed algorithm performance improvements in terms of recall, precision, and F1score are within the ranges (1.31 -2.58), (1.53 -4.28), and (1.41 -3.03), respectively. Moreover, the proposed method shows low computation cost which is 2% of real-time.

Discrete orthogonal functions are important tools in digital signal processing. These functions received considerable attention in the last few decades. This study proposes a new set of orthogonal functions called discrete Krawtchouk-Tchebichef transform (DKTT). Two traditional orthogonal polynomials, namely, Krawtchouk and Tchebichef, are combined to form DKTT. The theoretical and mathematical frameworks of the proposed transform are provided. DKTT was tested using speech and image signals from a well-known database under clean and noisy environments. DKTT was applied in a speech enhancement algorithm to evaluate the efficient removal of noise from speech signal. The performance of DKTT was compared with that of standard transforms. Different types of distance (similarity index) and objective measures in terms of image quality, speech quality, and speech intelligibility assessments were used for comparison. Experimental tests show that DKTT exhibited remarkable achievements and excellent results in signal compression and speech enhancement. Therefore, DKTT can be considered as a new set of orthogonal functions for futuristic applications of signal processing.