Linear Least-Squares Computations Using Givens Transformations

1983 ◽  
Vol 37 (4) ◽  
pp. 225-233 ◽  
Author(s):  
J. A. R. Blais
Keyword(s):  
Least Squares ◽  
Error Estimates ◽  
Data Storage ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Direct Method ◽  
Linear Least Squares ◽  
Normal Equations ◽  
Estimation Problems ◽  
A Direct Method

Givens transformations provide a direct method for solving linear least-squares estimation problems without forming the normal equations. This approach has been shown to be particularly advantageous in recursive situations because of characteristics related to data storage requirements, numerical stability and computational efficiency. The following discussion will concentrate on the problem of updating least-squares parameter and error estimates using Givens transformations. Special attention will be given to photogrammetric and geodetic applications.

scholarly journals Zero Spatial Frequency Limit: Method to Characterize Photopolymers as Optical Recording Material

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sergi Gallego ◽  
Andrés Márquez ◽  
Manuel Ortuño ◽  
Cristian Neipp ◽  
Inmaculada Pascual ◽  
...  
Keyword(s):  
Spatial Frequency ◽  
Data Storage ◽  
Direct Method ◽  
Optical Recording ◽  
Optical Processing ◽  
Optical Elements ◽  
Recording Material ◽  
The University ◽  
A Direct Method ◽  
Processing Group

Photopolymers are useful for different holographic applications such as holographic data storage or diffractive optical elements. However, due to the presence of two different phenomena, polymer formation and monomer diffusion, it is difficult to characterize each parameter independently. We propose a direct method based on zero spatial frequency recording, to eliminate the diffusion influence, and on interferometric techniques, both in transmission and in reflection, to obtain quantitative values of shrinkage, polymerization rate, polymer refractive index and relation between intensity and polymerization, and so forth, This method has been implemented in the Holography and Optical Processing Group from the University of Alicante to characterize different photopolymers. In this paper, we present a compilation of the results obtained with this method for different photopolymers and we compare their characteristics.

Object Association through Multiple Camera Collaboration for Large-Scale Surveillance System

2011 ◽  
pp. 176-196
Author(s):  
Shung Han Cho ◽  
Kyung Hoon Kim ◽  
Yunyoung Nam ◽  
Sangjin Hong
Keyword(s):  
Least Squares ◽  
Surveillance System ◽  
Large Scale ◽  
Video Sequences ◽  
Linear Least Squares ◽  
Normal Equations ◽  
Multiple Camera ◽  
Real Video ◽  
Association Method ◽  
Object Association

In this chapter, we present an object association method through multiple camera collaboration for a large-scale surveillance system. The object association is achieved by locally generating homographic lines on targets in collaborating cameras. In order to maintain the object association with the insufficient separation between homographic lines due to densely populated objects, homographic points are generated in 3-D with estimated heights. The heights of targets are estimated by the linear least-squares using normal equations. The object association is confirmed by finding the pairs of the correspondences minimizing the distance between them. The proposed method is verified with real video sequences. The simulation result demonstrates that the proposed method is robust against false association because it considers all the possible pairing cases of occluded targets.

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