scholarly journals A ROBUST METHOD FOR FUNDAMENTAL MATRIX ESTIMATION WITH RADIAL DISTORTION

2018 ◽  
Vol XLII-3 ◽  
pp. 2029-2033
Author(s):  
J.-S. Xue ◽  
X.-N. Chen ◽  
H. Yi
Keyword(s):  
Fundamental Matrix ◽  
Coefficient Matrix ◽  
Estimation Result ◽  
Robust Method ◽  
Matrix Estimation ◽  
Radial Distortion ◽  
Nonlinear Minimization ◽  
Weighted Matrix ◽  
Value Decomposition ◽  
Core Part

Fundamental Matrix Estimation is of vital importance in many vision applications and is a core part of 3D reconstruction pipeline. Radial distortion makes the problem to be numerically challenging. We propose a novel robust method for radial fundamental matrix estimation. Firstly, two-sided radial fundamental matrix is deduced to describe epipolar geometry relationship between two distorted images. Secondly, we use singular value decomposition to solve the final nonlinear minimization solutions and to get the outliers removed by multiplying a weighted matrix to the coefficient matrix. In every iterative step, the criterion which is the distance between feature point and corresponding epipolar line is used to determine the inliers and the weighted matrix is update according to it. The iterative process has a fast convergence rate, and the estimation result of radial fundamental matrix remains stable even at the condition of many outliers. Experimental results prove that the proposed method is of high accuracy and robust for estimating the radial fundamental matrix. The estimation result of radial fundamental matrix could be served as the initialization for structure from motion.

A fast and robust method for fundamental matrix estimation

2018 ◽  
Vol 26 (2) ◽  
pp. 461-470
Author(s):  
颜 坤 YAN Kun ◽  
刘恩海 LIU En-hai ◽  
赵汝进 ZHAO Ru-jin ◽  
田 宏 TIAN Hong ◽  
张 壮 ZHANG Zhuang
Keyword(s):  
Fundamental Matrix ◽  
Robust Method ◽  
Matrix Estimation

scholarly journals Internet Photogrammetry for Inspection of Seaports

2017 ◽  
Vol 24 (s1) ◽  
pp. 174-181 ◽  
Author(s):  
Zygmunt Paszotta ◽  
Malgorzata Szumilo ◽  
Jakub Szulwic
Keyword(s):  
Fundamental Matrix ◽  
Laser Scanning ◽  
3D Models ◽  
Digital Cameras ◽  
Correct Orientation ◽  
The Matrix ◽  
Transport Safety ◽  
Left And Right ◽  
Value Decomposition ◽  
The Relationship

Abstract This paper intends to point out the possibility of using Internet photogrammetry to construct 3D models from the images obtained by means of UAVs (Unmanned Aerial Vehicles). The solutions may be useful for the inspection of ports as to the content of cargo, transport safety or the assessment of the technical infrastructure of port and quays. The solution can be a complement to measurements made by using laser scanning and traditional surveying methods. In this paper the authors recommend a solution useful for creating 3D models from images acquired by the UAV using non-metric images from digital cameras. The developed algorithms, created and presented software allows to generate 3D models through the Internet in two modes: anaglyph and display in shutter systems. The problem of 3D image generation in photogrammetry is solved by using epipolar images. The appropriate method was presented by Kreiling in 1976. However, it applies to photogrammetric images for which the internal orientation is known. In the case of digital images obtained with non-metric cameras it is required to use another solution based on the fundamental matrix concept, introduced by Luong in 1992. In order to determine the matrix which defines the relationship between left and right digital image it is required to have at least eight homologous points. To determine the solution it is necessary to use the SVD (singular value decomposition). By using the fundamental matrix the epipolar lines are determined, which makes the correct orientation of images making stereo pairs, possible. The appropriate mathematical bases and illustrations are included in the publication.

Method for Fundamental Matrix Estimation Combined with Line Features

2013 ◽  
Vol 33 (10) ◽  
pp. 1015003
Author(s):  
周凡 Zhou Fan ◽  
邵世维 Shao Shiwei ◽  
吴建华 Wu Jianhua ◽  
付仲良 Fu Zhongliang
Keyword(s):  
Fundamental Matrix ◽  
Matrix Estimation ◽  
Line Features

Moving Force Identification for Multi-Span Bridges by Using Acceleration Measurements

2001 ◽  
Author(s):  
F. T. K. Au ◽  
R. J. Jiang ◽  
Y. K. Cheung
Keyword(s):  
Inverse Problem ◽  
Least Squares Method ◽  
Identification Problem ◽  
Singular Value ◽  
Robust Method ◽  
Force Identification ◽  
Beam Vibration ◽  
Moving Force ◽  
Value Decomposition ◽  
Pseudo Inverse

Abstract This paper reports some initial findings in the attempt to develop a robust method to identify more than one moving force on multi-span non-uniform continuous bridges. To keep the number of unknowns in the moving force identification problem to a minimum, the modified beam vibration functions are chosen as the assumed modes of a multi-span bridge. These modified beam vibration functions satisfy the zero deflection conditions at all the intermediate supports as well as the boundary conditions at the two ends of the bridge. The least squares method is used to solve the inverse problem to get the closest approximation to the moving forces. The pseudo-inverse to obtain the solution to the inverse problem is obtained by singular value decomposition. Only acceleration measurements are used for the moving force identification. The results show that this method is applicable and robust.

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