Digital topology, crucial for image analysis, tackles identifying connected components and holes in digital images using homology groups (Betti numbers). These invariants are essential in machine learning and biomedic...
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Digital topology, crucial for image analysis, tackles identifying connected components and holes in digital images using homology groups (Betti numbers). These invariants are essential in machine learning and biomedical image analysis, requiring accurate and efficient computation. This study introduces a novel algorithm for computing homology groups and Euler characteristics of 2D digital images. Using digital simplicial complexes and 8-adjacency, the method achieves computational efficiency, with a time complexity of O(k2.1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(k<^>{2.1})$$\end{document}, surpassing traditional persistent homology methods (O(n3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n<^>3)$$\end{document}). A significant contribution is the proof that higher-dimensional homology groups (Hn8(X)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_n<^>8(X) = 0$$\end{document} for n >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 2$$\end{document}) vanish in 2D digital images, ensuring consistency with classical topology. Extensive evaluations confirmed the algorithm's scalability with pixel density, accurately computing Betti numbers (beta 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage
In recent years, reservoir models based on the Connection Element Method (CEM) have gained extensive application in reservoir development. This mesh-free modeling approach effectively captures all flow paths and flow-...
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In recent years, reservoir models based on the Connection Element Method (CEM) have gained extensive application in reservoir development. This mesh-free modeling approach effectively captures all flow paths and flow-splitting coefficients between nodes, providing a clear view of flow interactions and accurately identifying primary connectivity pathways between injection and production wells. However, the traditional approach of traversing flow paths and splitting coefficients imposes a significant computational load, particularly when applied to large reservoirs with numerous virtual wells. To enhance simulation efficiency, this paper introduces a novel method leveraging the Ant Colony Optimization (ACO) algorithm to efficiently identify the path with the highest splitting coefficient between well pairs. This approach rapidly calculates and filters the dominant connectivity paths between injection and production wells in CEM models. A comparative analysis shows that, while the ACO algorithm provides limited benefit with a small number of connectivity paths, it significantly outperforms the conventional depth-first search algorithm as the number of experimental wells increases.
The algorithm is becoming more and more complex because of complicated and uncertain model. Actually, a part of control rules could not be used usually and the scope of many parameters is defined more widely. The abov...
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ISBN:
(纸本)9781424427239
The algorithm is becoming more and more complex because of complicated and uncertain model. Actually, a part of control rules could not be used usually and the scope of many parameters is defined more widely. The above control modes may lead to wasting of much computer system resource and decreasing system running efficiency. A new degenerating algorithm is presented in this paper. Those unusual control modes can be founded by the degenerating mechanism. Those unchanged or changed little parameters are also remembered in the algorithm. The insensitive parameters or the scope of parameters which are changed little can be saved as a common control pattern. The adjustment control parameters in the single algorithm or switching between different controlling algorithms are degenerated to coordinate a small amount of parameters in narrow space. A real control example about logistics is illuminated in the paper. The sensitive parameters scope in common control mode is gained. The parameter database is built to save insensitive running parameters for control objects. The adaptive adjusting process for parameters can be completed in a short time according to sensitive parameters areas. The algorithm efficiency can be increased by simulation analyzing. At the same time, the system robustness is strengthened by the degenerating Mechanism.
The algorithm is becoming more and more complex because of complicated and uncertain ***,a part of control rules could not be used usually and the scope of many parameters is defined more *** above control modes may l...
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The algorithm is becoming more and more complex because of complicated and uncertain ***,a part of control rules could not be used usually and the scope of many parameters is defined more *** above control modes may lead to wasting of much computer system resource and decreasing system running efficiency.A new degenerating algorithm is presented in this *** unusual control modes can be founded by the degenerating *** unchanged or changed little parameters are also remembered in the *** insensitive parameters or the scope of parameters which are changed little can be saved as a common control *** adjustment control parameters in the single algorithm or switching between different controlling algorithms are degenerated to coordinate a small amount of parameters in narrow space.A real control example about logistics is illuminated in the *** sensitive parameters scope in common control mode is *** parameter database is built to save insensitive running parameters for control *** adaptive adjusting process for parameters can be completed in a short time according to sensitive parameters *** algorithm efficiency can be increased by simulation *** the same time,the system robustness is strengthened by the degenerating Mechanism.
A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter,...
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A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second-order polynomial with respect to the state vector components. The algorithm efficiency is illustrated by three examples of navigation data processing. It is shown that the polynomial filter provides accuracy close to the best potential one calculated using the particle filter. At the same time, the amount of computation required to implement this algorithm is much smaller than that for the particle filter. In addition, the polynomial filter provides a consistent calculated accuracy characteristic.
The paper compares two fast algorithms, the normalized correlation algorithm and the generalized phase correlation algorithm, used for images superposition in aircraft map-matching navigation systems. It is shown that...
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ISBN:
(纸本)9781538654385
The paper compares two fast algorithms, the normalized correlation algorithm and the generalized phase correlation algorithm, used for images superposition in aircraft map-matching navigation systems. It is shown that the normalized correlation algorithm appears to be more resistant to various geometry and brightness distortions.
Traditionally, individual location has been difficult to utilize, due to a lack of precise positioning technologies. Now, with location-aware technologies integrated into lightweight mobile devices such as sensor node...
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ISBN:
(纸本)9781467355018;9781467354998
Traditionally, individual location has been difficult to utilize, due to a lack of precise positioning technologies. Now, with location-aware technologies integrated into lightweight mobile devices such as sensor nodes, location-based services are becoming a phenomenon in mobile services. These nodes, however, can potentially reveal sensitive and private information about individuals. In most location-aware applications such as personal navigations, location privacy is an issue. In this paper, new finding about generating efficient navigation instruction for imprecise location known as imprecise navigation is discussed. An algorithm called privacy-aware personal navigation algorithm is introduced and two types of navigational directions (relative and cardinal direction) are used for comparison. The efficiency of the algorithms has been analyzed based on its navigational performance and privacy protection. Hence, this research has the potential to support both protecting location privacy and generating better navigational instruction for imprecise navigation.
This article proposes an enhanced switching stabilization of Takagi-Sugeno fuzzy systems by developing a new fuzzy switching controller. A distinctive feature of the proposed approach is the enhanced ability to utiliz...
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This article proposes an enhanced switching stabilization of Takagi-Sugeno fuzzy systems by developing a new fuzzy switching controller. A distinctive feature of the proposed approach is the enhanced ability to utilize the updated information of the normalized fuzzy weighting functions at each sampling point. Compared with those recent results in the literature, two key performance indexes, i.e., reducing the conservatism and alleviating the online computational burden, can be improved together while the off-line computational burden increases as a tradeoff but is still affordable from the point of algorithmic complexity. As a result, the efficiency of fuzzy stabilization is enhanced and thus its scope of application can be enlarged much more than before. Finally, the superiority of the proposed approach is illustrated by some simulation comparisons.
This paper presents a new algorithm for calculating azimuth and altitude of the Sun from its ecliptic coordinates. The equations of the new procedure are not based on spherical trigonometry, like the procedure current...
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This paper presents a new algorithm for calculating azimuth and altitude of the Sun from its ecliptic coordinates. The equations of the new procedure are not based on spherical trigonometry, like the procedure currently used for computing the solar vector, but on analytic geometry enriched by matrix algebra. Our proposal allows the horizontal coordinates of the Sun to be determined with a significantly higher computational efficiency than the classic algorithm without any loss in accuracy. (C) 2008 Elsevier Ltd. All rights reserved.
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