In this paper, we present an in-depth study on the computational aspects of high-order discrete orthogonal Meixner polynomials (MPs) and Meixner moments (MMs). This study highlights two major problems related to the computation of MPs. The first problem is the overflow and the underflow of MPs values (“Nan” and “infinity”). To overcome this problem, we propose two new recursive Algorithms for MPs computation with respect to the polynomial order n and with respect to the variable x. These Algorithms are independent of all functions that are the origin the numerical overflow and underflow problem. The second problem is the propagation of rounding errors that lead to the loss of the orthogonality property of high-order MPs. To fix this problem, we implement MPs based on the following orthogonalization methods: modified Gram-Schmidt process (MGS), Householder method, and Givens rotation method. The proposed Algorithms for the stable computation of MPs are efficiently applied for the reconstruction and localization of the region of interest (ROI) of large-sized 1D signals and 2D/3D images. We also propose a new fast method for the reconstruction of large-size 1D signal. This method involves the conversion of 1D signal into 2D matrix, then the reconstruction is performed in the 2D domain, and a 2D to 1D conversion is performed to recover the reconstructed 1D signal. The results of the performed simulations and comparisons clearly justify the efficiency of the proposed Algorithms for the stable analysis of large-size signals and 2D/3D images.
相似文献In this article, we will present a new set of hybrid polynomials and their corresponding moments, with a view to using them for the localization, compression and reconstruction of 2D and 3D images. These polynomials are formed from the Hahn and Krawtchouk polynomials. The process of calculating these is successfully stabilized using the modified recurrence relations with respect to the n order, the variable x and the symmetry property. The hybrid polynomial generation process is carried out in two forms: the first form contains the separable discrete orthogonal polynomials of Krawtchouk–Hahn (DKHP) and Hahn–Krawtchouk (DHKP). The latter are generated as the product of the discrete orthogonal Hahn and Krawtchouk polynomials, while the second form is the square equivalent of the first form, it consists of discrete squared Krawtchouk–Hahn polynomials (SKHP) and discrete polynomials of Hahn–Krawtchouk squared (SHKP). The experimental results clearly show the efficiency of hybrid moments based on hybrid polynomials in terms of localization property and computation time of 2D and 3D images compared to other types of moments; on the other hand, encouraging results have also been shown in terms of reconstruction quality and compression despite the superiority of classical polynomials.
相似文献In this work, we propose new sets of 2D and 3D rotation invariants based on orthogonal radial dual Hahn moments, which are orthogonal on a non-uniform lattice. We also present theoretical mathematics to derive them. Thus, this paper presents in the first case new 2D radial dual Hahn moments based on polar representation of an image by one-dimensional orthogonal discrete dual Hahn polynomials and a circular function. The dual Hahn polynomials are general case of Tchebichef and Krawtchouk polynomials. In the second case, we introduce new 3D radial dual Hahn moments employing a spherical representation of volumetric image by one-dimensional orthogonal discrete dual Hahn polynomials and a spherical function, which are orthogonal on a non-uniform lattice. The 2D and 3D rotational invariants are extracts from the proposed 2D and 3D radial dual Hahn moments respectively. In order to test the proposed approach, three problems namely image reconstruction, rotational invariance and pattern recognition are attempted using the proposed moments. The result of experiments shows that the radial dual Hahn moments have performed better than the radial Tchebichef and Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial dual Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image and PSB database for 3D image.
相似文献Text summarization presents several challenges such as considering semantic relationships among words, dealing with redundancy and information diversity issues. Seeking to overcome these problems, we propose in this paper a new graph-based Arabic summarization system that combines statistical and semantic analysis. The proposed approach utilizes ontology hierarchical structure and relations to provide a more accurate similarity measurement between terms in order to improve the quality of the summary. The proposed method is based on a two-dimensional graph model that makes uses statistical and semantic similarities. The statistical similarity is based on the content overlap between two sentences, while the semantic similarity is computed using the semantic information extracted from a lexical database whose use enables our system to apply reasoning by measuring semantic distance between real human concepts. The weighted ranking algorithm PageRank is performed on the graph to produce significant score for all document sentences. The score of each sentence is performed by adding other statistical features. In addition, we address redundancy and information diversity issues by using an adapted version of Maximal Marginal Relevance method. Experimental results on EASC and our own datasets showed the effectiveness of our proposed approach over existing summarization systems.
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