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Efficient homography estimation using a recursive algorithm with a mixture of weighted Gaussian kernels

SIGNAL PROCESSING 2025年 231卷

作者： Hashemzadeh, F. Kumbasar, T. Univ Tabriz Fac Elect & Comp Engn Tabriz Iran Istanbul Tech Univ Control & Automat Engn Dept Istanbul Turkiye Istanbul Tech Univ AI & Intelligent Syst Lab Istanbul Turkiye

In this study, we propose an efficient recursive algorithm, named GK-RLS, defined with a mixture of weighted Gaussian kernels for efficient homography estimation. By defining the homography estimation problem as a least square problem and optimizing the estimation parameters based on minimizing expected estimation errors, GKRLS offers efficient incremental processing of feature points, rather than processing them as a batch like RANSAC, resulting in reduced computation time (CT) when handling a large number of paired features. To address real-world challenges such as noise and outliers commonly encountered in feature extraction and pairing, GKRLS incorporates a small-pass filter defined with Gaussian kernels to effectively attenuate their resulting large prediction errors, thus reducing outlier drawbacks. The algorithm's effective stopping criteria are established based on a concept akin to RANSAC, with termination occurring when the estimated homography matrix yields low geometric error for a predefined portion of paired feature points. The CT of the algorithm is crucial for online applications or scenarios requiring the sharing of feature data points within communication networks, such as between multiple drones or between drones and a ground station. Therefore, leveraging the iterative structure and effective stopping criteria of GK-RLS, it estimates the homography matrix using only a limited number of feature points, resulting in a smaller CT compared to RANSAC while having a similar estimation performance. Extensive evaluations, including sensitivity analysis, a drone simulation, and experimental implementation, demonstrate the superiority of GK-RLS over RANSAC, especially concerning the required CT. Overall, GK-RLS presents a promising solution for robust and efficient homography matrix estimation in various real-world scenarios that require process data in high sampling frequencies.

关键词： Homography Estimation recursive algorithm Gaussian kernels Computational time

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A recursive algorithm for dynamics of planar multibody systems with frictional unilateral constraints

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APPLIED MATHEMATICAL MODELLING 2025年 137卷

作者： Miao, Yangyang Rui, Xiaoting Wang, Pingxin Feng, Yu Li, Tang Zhang, Jianshu Nanjing Univ Sci & technol Inst Launch Dynam Nanjing Peoples R China Natl Key Lab Complex Multibody Syst Dynam Nanjing Peoples R China

The contact impact problem in planar multibody systems can be efficiently solved by formulating it as the linear complementarity problem, which requires a complex modeling process. To simplify the process, a recursive algorithm for the dynamics of planar multibody systems with frictional unilateral constraints is proposed based on the reduced multibody system transfer matrix method. Firstly, the contact forces of frictional unilateral constraints are integrated into the recurrence relations of system components using Lagrange multipliers. Subsequently, the relative motion equations of the contact positions are discretized in time, which are then utilized to describe the linear complementarity problem for systems. The dynamics of the system is solved by the Moreau time-stepping method with the recursive method. Finally, the proposed algorithm was validated using the woodpecker toy and used to model a slider-crank mechanism with clearance, which shows its characteristics of facilitating modeling, universal, and highly programmable. This recursive algorithm provides an effective tool for solving non-smooth planar multibody systems while extending the application of the multibody system transfer matrix method.

关键词： recursive algorithm Multibody system dynamics Frictional unilateral constraint Contact dynamics Coulomb friction Linear complementarity problem (LCP)

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A multi-cycle recursive clustering algorithm for the analysis of social media data streams

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PEER-TO-PEER NETWORKING AND APPLICATIONS 2025年第1期18卷 1-18页

作者： Ayorinde, Ayodeji O. Panneerselvam, John Yuan, Bo Liu, Lu Univ Leicester Sch Comp & Math Sci Leicester England Univ Exeter Dept Comp Sci Exeter England China Mobile Res Inst Artificial Intelligence & Intelligent Operat Ctr Beijing Peoples R China

Events are usually embedded in latent topics and the extraction of these latent topics are enabled by event detection algorithms. Unsupervised algorithms like Clustering algorithms are very useful for detecting events but with requirements which may not be relevant or easy to determine when using unstructured textual social media data. For instance, some algorithms are required to be used on specific data shapes, but determining the shape of an unstructured data may not be practical aside from the high level of noise in the data. Many of the existing algorithms work well with structured data, however, some of these algorithms can be adapted to unstructured data with the caveat that cluster formations may not contain consistent contextual information. We propose a novel Multi-Cycle recursive Clustering algorithm (MCRCA), able to sequentially eliminate noise, resulting in high homogeneous cluster formations. MCRCA does not require the initial specification of clusters numbers as the estimated number of clusters can be deduced at convergence. Our algorithm out-performs the classical LDA and K-Means algorithms in forming highly homogeneous clusters, context-wise.

关键词： Event detection recursive algorithm Likelihood ratio test Clustering Homogeneity

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recursive algorithm for real-time measurement of electrical variables in power systems

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IEEE TRANSACTIONS ON POWER DELIVERY 2006年第1期21卷 15-22页

作者： Lin, T Domijan, A Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Univ S Florida Dept Elect Engn Tampa FL 33620 USA

In this paper, a novel complex bandpass filter is presented which overcomes the pitfalls of the techniques in common use. This complex bandpass filter can correctly extract the phasor of the fundamental component and symmetrical components in voltage or current waveforms and then accurately estimate their instantaneous amplitude, phase angle, and frequency, even encountering various power disturbances. Further, a recursive algorithm is also developed for the complex bandpass filtering that updates current filtering output only using several previous sample values and filtering outputs. This attribute greatly reduces the computational complexity of complex bandpass filtering, which is the weakness of the continuous wavelet transform based on the well-known Morlet Wavelet. Thus, this recursive algorithm is highly desirable for real-time applications. The performance of the proposed technique is ascertained by using both simulated and practical power disturbance waveforms.

关键词： digital filter frequency estimation phasor measurement power system measurement recursive algorithm wavelet transform (WT)

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recursive algorithm for Sliding Walsh Hadamard Transform

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第11期62卷 2827-2836页

作者： Park, Chun-Su Sangmyung Univ Informat & Telecommun Engn Dept Cheonan South Korea

In this paper, a recursive sliding transform (RST) algorithm is proposed for the fast implementation of the Walsh Hadamard Transform (WHT) on sliding windows. The proposed RST algorithm accelerates the sliding WHT process by recursively reducing the order of WHT. Theoretical analysis shows that the proposed RST algorithm requires only 1.33 additions per sample for each WHT basis vector regardless of the size or dimension of the basis vector. The computational requirement of the proposed RST algorithm is the lowest among existing fast sliding WHT algorithms.

关键词： Block matching recursive algorithm sliding transform template matching Walsh Hadamard transform

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A recursive algorithm FOR FINDING THE MINIMUM NORM POINT IN A POLYTOPE AND A PAIR OF CLOSEST POINTS IN 2 POLYTOPES

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MATHEMATICAL PROGRAMMING 1993年第2期61卷 233-249页

作者： SEKITANI, K YAMAMOTO, Y 1. Institute of Socio-Economic Planning University of Tsukuba 305 Tsukuba Ibaraki Japan

For a given pair of finite point sets P and Q in some Euclidean space we consider two problems: Problem 1 of finding the minimum Euclidean norm point in the convex hull of P and Problem 2 of finding a minimum Euclidean distance pair of points in the convex hulls of P and Q. We propose a finite recursive algorithm for these problems. The algorithm is not based on the simplicial decomposition of convex sets and does not require to solve systems of linear equations.

关键词： MINIMUM NORM POINT MINIMUM DISTANCE PAIR OF POINTS recursive algorithm CONVEX QUADRATIC PROGRAM

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recursive algorithm for L1 Norm Estimation in Linear Models

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JOURNAL OF SURVEYING ENGINEERING 2011年第1期137卷 1-8页

作者： Khodabandeh, A. Amiri-Simkooei, A. R. Univ Tehran Dept Surveying & Geomat Engn Geodesy Div Fac Engn Tehran Iran Delft Univ Technol Delft Inst Earth Observat & Space Syst Fac Aerosp Engn NL-2629 HS Delft Netherlands Univ Isfahan Dept Surveying Engn Fac Engn Esfahan 81744 Iran

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which is based on Dikin's method. The method can be considered as an appropriate alternative for the classical simplex method, which is sometimes time-consuming. The proposed method, compared with the simplex method, is thus easier for implementation and faster in performance. Furthermore, a recursive form of the Dikin's method is derived, which resembles the recursive least-squares method. Two simulated numerical examples show that the proposed algorithm gives as accurate results as the simplex method but in considerably less time. When dealing with a large number of observations, this algorithm can thus be used instead of the iteratively reweighted least-squares method and the simplex method.

关键词： Iteratively reweighted least squares Linear programming problem Interior point methods Simplex method Affine method of Dikin Robust estimation L1 norm minimization recursive algorithm

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A recursive algorithm for ARMAX model identification in closed loop

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1999年第4期44卷 840-843页

作者： Landau, ID Karimi, A Univ Grenoble 1 ENSIEG Lab Automat Grenoble CNRSINPG F-38402 St Martin Dheres France Sharif Univ Technol Dept Elect Engn Tehran Iran

The joint problem of the recursive estimation of an optimal predictor for the closed-loop system and the unbiased parameter estimation of an ARMAX plant model in closed-loop operation is considered, A special reparameterized optimal predictor for the closed-loop is: introduced. This allows a parameter estimation algorithm for the plant model to be derived which is globally asymptotically stable in a deterministic environment and gives asymptotically unbiased parameters estimates under richness conditions.

关键词： ARMAX model closed-loop identification output error recursive algorithm

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recursive algorithm for the reliability of a connected-(1,2)-or-(2,1)-out-of-(m, n):F lattice system

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期188卷 854-864页

作者： Yamamoto, Hisashi Akiba, Tomoaki Nagatsuka, Hideki Moriyama, Yurie Yamagata Coll Ind & Technol Yamagata 9902473 Japan Tokyo Metropolitan Univ Fac Syst Design Tokyo 1910065 Japan Tokyo Metropolitan Inst Technol Prod Informat Syst Tokyo 1910065 Japan

The connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system is included by the connected-X-out-of-(m, n):F lattice system defined by Boehme et al. [Boehme, T.K., Kossow, A., Preuss, W., 1992. A generalization of consecutive-k-out-of-n:F system. IEEE Transactions on Reliability 41, 451-457]. This system fails if and only if at least one subset of connected failed components occurs which includes at least a (1, 2)-matrix (that is, a row and two columns) or a (2, 1)-matrix(that is, two rows and a column) of failed components. This system is applied to two-dimensional network problems with adjacent constraints, and various systems, for example, a supervision system, etc. In this paper, we propose a new recursive algorithm for evaluating of the reliability of a connected-(1, 2)-or-(2, 1)-out-of-(m,n):F lattice system. We calculate the orders of the computing time and memory size of the our algorithm. We perform a numerical experiment in order to compare our proposed algorithm with the algorithm in the previous studies. A numerical experiment shows that the proposed algorithm is more efficient than the other algorithms for evaluating the reliability of the a connected-(1,2)-or-(2, 1)-out-of-(m,n):F lattice system when n is large. (C) 2007 Published by Elsevier B.V.

关键词： reliability recursive algorithm connected-(1,2)-or-(2,1)-out-of-(m, n): F lattice system connected-X-out-of-(m, n): F lattice system

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recursive algorithm for efficient representation of ECG signals

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ELECTRONICS LETTERS 1998年第6期34卷 526-528页

作者： Paul, JS Reddy, MRS Kumar, VJ Indian Inst Technol Madras 600036 Tamil Nadu India

A method is presented for representing signals made up of discrete component waves separated by iso-electric regions such as electrocardiogram (EGG), respiratory and blood pressure signals. The computational complexity is minimised by treating the discrete cosine transform of a group of component waves to be the sum of a finite number of biphasic rational functions.

关键词： discrete component wave Electrodiagnostics and other electrical measurement techniques medical signal processing biphasic rational function signal representation blood pressure signal computational complexity iso-electric region recursive functions discrete cosine transform electrocardiogram Integral transforms recursive algorithm Bioelectric signals respiratory signal ECG signal representation Signal processing and detection discrete cosine transforms Bioelectricity electrocardiography

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