projection equations
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2020 ◽  
Vol 12 (3) ◽  
pp. 556 ◽  
Author(s):  
Shanshan Feng ◽  
Yun Lin ◽  
Yanping Wang ◽  
Yanhui Yang ◽  
Wenjie Shen ◽  
...  

Digital elevation model (DEM) generation using multi-aspect synthetic aperture radar (SAR) imagery applying radargrammetry has become a hotspot. The traditional radargrammetric method is to solve the rigorous radar projection equations to obtain the three dimensional coordinates of targets. In this paper, we propose a new DEM generation method based on the offset between multi-aspect images formed on ground plane. The ground object will be projected to different positions from different viewing aspect angles if the height of object is not equal to the height of imaging plane. The linear relationship between the offset of imaging positions and height of the object is derived and scale factor is obtained finally. Height information can be retrieved from offset of imaging positions directly through the DEM extraction model presented in this paper. Thus the solution to nonlinear equations point by point can be avoided. Real C band airborne circular SAR images is used to verify the proposed approach. When extracted DEM applied in multi-aspect imaging process, superimposition of multi-aspect images will no longer be defocusing and can achieve finer observation of the scanned scene.


Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 198
Author(s):  
Kyung Kim

In this manuscript, we study a system of extended general variational inequalities (SEGVI) with several nonlinear operators, more precisely, six relaxed ( α , r ) -cocoercive mappings. Using the projection method, we show that a system of extended general variational inequalities is equivalent to the nonlinear projection equations. This alternative equivalent problem is used to consider the existence and convergence (or approximate solvability) of a solution of a system of extended general variational inequalities under suitable conditions.


2016 ◽  
Vol 23 (2) ◽  
pp. 606-616 ◽  
Author(s):  
Zhiting Liang ◽  
Yong Guan ◽  
Gang Liu ◽  
Xiangyu Chen ◽  
Fahu Li ◽  
...  

The `missing wedge', which is due to a restricted rotation range, is a major challenge for quantitative analysis of an object using tomography. With prior knowledge of the grey levels, the discrete algebraic reconstruction technique (DART) is able to reconstruct objects accurately with projections in a limited angle range. However, the quality of the reconstructions declines as the number of grey levels increases. In this paper, a modified DART (MDART) was proposed, in which each independent region of homogeneous material was chosen as a research object, instead of the grey values. The grey values of each discrete region were estimated according to the solution of the linear projection equations. The iterative process of boundary pixels updating and correcting the grey values of each region was executed alternately. Simulation experiments of binary phantoms as well as multiple grey phantoms show that MDART is capable of achieving high-quality reconstructions with projections in a limited angle range. The interesting advancement of MDART is that neither prior knowledge of the grey values nor the number of grey levels is necessary.


Robotica ◽  
2014 ◽  
Vol 33 (6) ◽  
pp. 1325-1350 ◽  
Author(s):  
Yunong Zhang ◽  
Weibing Li ◽  
Zhijun Zhang

SUMMARYIn order to resolve the redundancy of a wheeled mobile redundant manipulator comprising a two-wheel-drive mobile platform and a 6-degree-of-freedom manipulator, a physical-limits-constrained (PLC) minimum velocity norm (MVN) coordinating scheme (termed as PLC-MVN-C scheme) is proposed and investigated. Such a scheme can not only coordinate the mobile platform and the manipulator to fulfill the end-effector task and to achieve the desired optimal index (i.e., minimizing the norm of the rotational velocities of the wheels and the joint velocities of the manipulator) but also consider the physical limits of the robot (i.e., the joint-angle limits and joint-velocity limits of the manipulator as well as the rotational velocity limits of the wheels). The scheme is then reformulated as a quadratic program (QP) subject to equality and bound constraints, and is solved by a discrete QP solver, i.e., a numerical algorithm based on piecewise-linear projection equations (PLPE). Simulation results substantiate the efficacy and accuracy of such a PLC-MVN-C scheme and the corresponding discrete PLPE-based QP solver.


2013 ◽  
Vol 373-375 ◽  
pp. 238-241
Author(s):  
Yao Chang Chen ◽  
Ta Ming Shih ◽  
Chung Ho Wang

This work addresses a new probabilistic observation model for a stereo simultaneous localization and mapping (SLAM) system within the standard Extended-Kalman filter (EKF) framework. The observation modal was derived by using the inverse depth parameterization as the landmark modal, and contributes to both bearing and range information into the EKF estimation. In this way the inherently non-linear problem cause by the projection equations is resolved and real depth uncertainty distribution of landmarks features can be accurately estimated. The system was demonstrated with real-world outdoor data. Analysis results show landmark feature depth estimation is more stable and the uncertainty noise converges faster than the traditional approach.


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