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Properties of a general quaternion-valued gradient operator and its applications to signal processing

Frontiers of Information Technology & Electronic Engineering 2016年第2期17卷 83-95页

作者： Meng-di JIANG Yi LI Wei LIU Department of Electronic and Electrical Engineering University of Sheffield School of Mathematics and Statistics University of Sheffield

The gradients of a quaternion-valued function are often required for quaternionic signal processing *** HR gradient operator provides a viable framework and has found a number of ***,the applications so far have been limited to mainly real-valued quaternion functions and linear quaternionvalued *** generalize the operator to nonlinear quaternion functions,we define a restricted version of the HR operator,which comes in two versions,the left and the right *** then present a detailed analysis of the properties of the operators,including several different product rules and chain *** the new rules,we derive explicit expressions for the derivatives of a class of regular nonlinear quaternion-valued functions,and prove that the restricted HR gradients are consistent with the gradients in the real *** an application,the derivation of the least mean square algorithm and a nonlinear adaptive algorithm is *** results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the quaternion-valued signal model and the derived signal processing algorithm.

关键词： Quaternion gradient operator Signal processing Least mean square(LMS) algorithm Nonlinear adaptive filtering Adaptive beamforming

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Integral Theorems Based on a New gradient operator Derived from Biomembranes (Part I): Fundamentals

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Tsinghua Science and Technology 2005年第3期10卷 372-375页

作者：殷雅俊 Department of Engineering Mechanics School of Aerospace Tsinghua University Beijing 100084 China

A new gradient operator was derived in recent studies of topological structures and shape transi- tions in biomembranes. Because this operator has widespread potential uses in mechanics, physics, and biology, the operator’s general mathematical characteristics should be investigated. This paper explores the integral characteristics of the operator. The second divergence and the differential properties of the operator are used to demonstrate new integral transformations for vector and scalar fields on curved surfaces, such as the second divergence theorem, the second gradient theorem, the second curl theorem, and the second circulation theorem. These new theorems provide a mathematical basis for the use of this operator in many disciplines.

关键词： gradient operator integral theorem curved surfaces biomembranes

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Robust Visual Tracking Based on Convolutional Features with Illumination and Occlusion Handing

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Journal of Computer Science & Technology 2018年第1期33卷 223-236页

作者： Kang Li Fa-Zhi He Hai-Ping Yu State Key Laboratory of Software Engineering Wuhan University Wuhan 430072 China School of Computer Science Wuhan University Wuhan 430072 China School of Computer Science and Information Engineering Hubei University Wuhan 430062 China

Visual tracking is an important area in computer vision. How to deal with illumination and occlusion problems is a challenging issue. This paper presents a novel and efficient tracking algorithm to handle such problems. On one hand, a target＇s initial appearance always has clear contour, which is light-invariant and robust to illumination change. On the other hand, features play an important role in tracking, among which convolutional features have shown favorable performance. Therefore, we adopt convolved contour features to represent the target appearance. Generally speaking, first-order derivative edge gradient operators are efficient in detecting contours by convolving them with images. Especially, the Prewitt operator is more sensitive to horizontal and vertical edges, while the Sobel operator is more sensitive to diagonal edges. Inherently, Prewitt and Sobel are complementary with each other. Technically speaking, this paper designs two groups of Prewitt and Sobel edge detectors to extract a set of complete convolutional features, which include horizontal, vertical and diagonal edges features. In the first frame, contour features are extracted from the target to construct the initial appearance model. After the analysis of experimental image with these contour features, it can be found that the bright parts often provide more useful information to describe target characteristics. Therefore, we propose a method to compare the similarity between candidate sample and our trained model only using bright pixels, which makes our tracker able to deal with partial occlusion problem. After getting the new target, in order to adapt appearance change, we propose a corresponding online strategy to incrementally update our model. Experiments show that convolutional features extracted by well-integrated Prewitt and Sobel edge detectors can be eff^cient enough to learn robust appearance model. Numerous experimental results on nine challenging sequences show that our proposed

关键词： visual tracking convolutional feature gradient operator online learning particle filter

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Smoothness of the Functional Law Generated by a Nonlinear SPDE

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Chinese Annals of Mathematics,Series B 2008年第2期29卷 113-120页

作者： Marta SANZ-SOL Paul MALLIAVIN Facultat de Matemàtiques Universitat de BarcelonaGran Via 585E-08007 BarcelonaSpain. 10 rue Saint Louis-en-I'IleF-74004 ParisFrance

The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild *** is proved that the functional law of its solution is absolutely continuous and posses... 详细信息

关键词： Stochastic heat equation Probability law Absolute continuity Divergence operator gradient operator

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A New Corner Matching Algorithm Based on gradient

A New Corner Matching Algorithm Based on Gradient

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2008 9th International Conference on Signal Processing(ICSP’2008)

作者： Haiyan Yu Cuihua Ren Xiaolin Qiao School of Electronics and Information Technology Harbin Institute of Technology Harbin 150001 P.R.China

In this paper,a novel corner matching algorithm is *** operator in Harris corner detector is directly used to compute the similarity between *** initial matches are *** algorithm is contrasted with normalized *** computational complexity is reduced and matching speed is improved effectively because this method only adopts the addition and subtraction *** on several real images test the matching speed,the matching precision and matching rate of the *** results demonstrate that the algorithm not only have higher speed but also get higher matching precision and correct matching *** though the stereo image pairs have brightness differences,it still performs rather well.

关键词： corner matching gradient operator similarity

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