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A NATURAL GRADIENT ALGORITHM FOR THE SOLUTION OF LYAPUNOV EQUATIONS BASED ON THE geodesic distance

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Journal of Computational Mathematics 2014年第1期32卷 93-106页

作者： Xiaomin Duan Huafei Sun Zhenning Zhang School of Mathematics Bcijing Institute of Technology Beijing 100081 China School of Science Dalian Jiaotong University Dalian 116028 China College of Applied Scienees Beijing University of Technology Beijing 100123 China

A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as the objective function. Moreover, a gradient descent algorithm based on the classical Euclidean distance is provided to compare with this natural gradient descent algorithm. Furthermore, the behaviors of two proposed algorithms and the conventional modified conjugate gradient algorithm are compared and demonstrated by two simulation examples. By comparison, it is shown that the convergence speed of the natural gradient descent algorithm is faster than both of the gradient descent algorithm and the conventional modified conjugate gradient algorithm in solving the Lyapunov equation.

关键词： Lyapunov equation geodesic distance Natural gradient descent algorithm.

Image recoloring using geodesic distance based color harmonization

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Computational Visual Media 2015年第2期1卷 143-155页

作者： Xujie Li Hanli Zhao Guizhi Nie Hui Huang Intelligent Information Systems Institute Wenzhou University

In this paper, we present a computationally simple yet effective image recoloring method based on color harmonization. Our method permits the user to obtain recolored results interactively by rotating a harmonious template after completing color harmonization. Two main improvements are made in this paper. Firstly, we give a new strategy for finding the most harmonious scheme, in terms of finding the template which best matches the hue distribution of the input image. Secondly, in order to achieve spatially coherent harmonization, geodesic distances are used to move hues lying outside the harmonious sectors to inside them. Experiments show that our approach can produce higher-quality visually pleasing recolored images than existing methods. Moreover, our method is simple and easy to implement, and has good runtime performance.

关键词： image editing color harmonization geodesic distance

Detection of Foreign Particles in Medical Solution Using Modified Affinity Propagation

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Chinese Journal of Electronics 2018年第1期27卷 140-149页

作者： PENG Hanghang XU Xuemei LI Lixian YIN linzi School of Physics and Electronics Central South University

A new detection method based on modified affinity propagation is proposed for detecting foreign particles in medical solution. The captured sequential images are used to generate moving tra jectories of possible foreign particles. The external disturbances and background are almost removed by using a series of simple and effective image processing. The extracted potential targets,including foreign particles and possible residual noises, are partitioned into a number of valid clusters by modified affinity propagation clustering, in which the new similarity measure can better reflect the intrinsic link of linearstructured datasets and the temporal constraint enforces the temporal continuity of data points. The foreign particles can be easily recognized by analyzing the cluster structure according to the continuity and smoothness of moving targets tra jectory. This algorithm combines modified affinity propagation method with the moving characteristics of different particles, and can achieve accurate partitions efficiently even though the clusters are badly adjacent. The experimental results indicate that the proposed algorithm can detect foreign particles effectively with high detection speed and accuracy.

关键词： Foreign particle detection Affinity propagation geodesic distance Modified affinity propagation

Optimal control on special Euclidean group via natural gradient algorithm

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Science China(Information Sciences) 2016年第11期59卷 63-72页

作者： Chunhui LI Erchuan ZHANG Lin JIU Huafei SUN School of Mathematics and Statistics Beijing Institute of Technology School of Mathematics and Statistics University of Western Australia Department of Mathematics Tulane University School of Mathematics and Statistics and Beijing Key Laboratory on MCAACI Beijing Institute of Technology

Considering the optimal control problem about the control system of the special Euclidean group whose output only depends on its input is meaningful in practical applications. The optimal control considered here is described as the output matrix is as close as possible to the target matrix by adjusting the system *** geodesic distance is adopted as the measure of the difference between the output matrix and the target matrix, and the trajectory of the control input obtained in the process is achieved. Furthermore, some numerical simulations are shown to illustrate our outcomes based on the natural gradient descent algorithm for optimizing the control system of the special Euclidean group.

关键词： system control natural gradient special Euclidean group geodesic distance numerical simulation

Stochastic Contrast Measures for SAR Data: A Survey

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雷达学报（中英文） 2019年第6期8卷 758-781页

作者： Alejandro C.Frery La CCAN–Laboratório de Computa??o Científica e Análise Numérica Universidade Federal de Alagoas

“Contrast”is an generic denomination for“difference”.Measures of contrast are a powerful tool in image processing and analysis,e.g.,in denoising,edge detection,segmentation,classification,parameter estimation,change detection,and feature *** present a survey on techniques that aim at measuring the contrast between(i)samples of SAR imagery,and(ii)samples and models,with emphasis on those that employ the statistical properties of the data.

关键词： Contrast Divergence Entropy geodesic distance Statistics Synthetic Aperture Radar(SAR)

The Fermat-Torricelli problem on surfaces

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 362-366页

作者： CHEN Zhi-guo Department of Mathematics Zhejiang University

In this note a simple proof of the famous Fermat-Torricelli problem is given. For the vertices of a given triangle, Fermat asks for a fourth point such that the sum of its Euclidean distances to the three given points is minimized. Many authors present geometric approaches to the Fermat-Torricelli problem. We solve the problem by analytic and geometrical method and extend it to the sphere, we also characterize the median point P on the general regular surface.

关键词： Fermat-Torricelli problem median point geodesic distance regular surface

Topological distance-constrained feature descriptor learning model for vessel matching in coronary angiographies

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Virtual Reality & Intelligent Hardware 2021年第4期3卷 287-301页

作者： Xiaojiao SONG Jianjun ZHU Jingfan FAN Danni AI Jian YANG Beijing Engineering Research Center of Mixed Reality and Advanced Display School of Optics and PhotonicsBeijing Institute of TechnologyBeijing 100081China

Background Feature matching technology is vital to establish the association between virtual and real objects in virtual reality and augmented reality ***,it provides them with the ability to match a dynamic *** image matching methods,of which most are deep learning-based,have been proposed over the past few ***,vessel fracture,stenosis,artifacts,high background noise,and uneven vessel gray-scale make vessel matching in coronary angiography extremely *** matching methods perform poorly in this *** In this study,a topological distance-constrained feature descriptor learning model is *** model regards the topology of the vasculature as the connection relationship of the *** topological distance combines the geodesic distance between the input patches and constrains the descriptor network by maximizing the feature difference between connected and unconnected patches to obtain more useful potential feature *** Matching patches of different sequences of angiographic images are generated for the *** matching accuracy and stability of the proposed method is superior to those of the existing *** The proposed method solves the problem of matching coronary angiographies by generating a topological distance-constrained feature descriptor.

关键词： Vessel matching Deep learning Feature descriptor Coronary angiographies geodesic distance Topological distance-constrained

Generation of Performance-Driven Facial Expressions

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Computer Aided Drafting,Design and Manufacturing 2009年第2期19卷 56-62页

作者： GOU Ye WANG Xiao-kan School of Electronic and Information Engineering Beijing University of Aeronautics and Astronautics Beijing 100191 China

Coordinates of the key facial feature points can be captured by motion capture system OPTOTRAK with real-time character and high accuracy. The facial model is considered as an undirected weighted graph. By iteratively subdividing the related triangle edges, the geodesic distance between points on the model surface is finally obtained. The RBF （Radial Basis Functions） interpolation technique based on geodesic distance is applied to generate deformation of the facial mesh model. Experimental results demonstrate that the geodesic distance can explore the complex topology of human face models perfectly and the method can generate realistic facial expressions.

关键词： facial expression performance-driven RBF geodesic distance