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Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 971 (4 self)
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the rootmeansquare deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums of products of corresponding coordinates of the points. 1.
Absolute Orientation of Molecules at Interfaces
, 2005
"... A method to determine the absolute orientation of molecules at liquid interfaces by sum frequency generation (SFG) is reported. It is based on measurements of the orientations of two nonparallel vibrationally active chromophores in the molecule of interest combined with a rotation matrix formulation ..."
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Cited by 2 (0 self)
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A method to determine the absolute orientation of molecules at liquid interfaces by sum frequency generation (SFG) is reported. It is based on measurements of the orientations of two nonparallel vibrationally active chromophores in the molecule of interest combined with a rotation matrix
On the Robustness of Absolute Orientation
"... Ideally, absolute orientation (AO) algorithms should be both efficient and robust. Many researchers in need of a solution to the AO problem have used various leastsquares approaches, such as those established and popularized by B. K. P. Horn, or O. Faugeras. Although leastsquares approaches can pe ..."
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Cited by 3 (0 self)
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Ideally, absolute orientation (AO) algorithms should be both efficient and robust. Many researchers in need of a solution to the AO problem have used various leastsquares approaches, such as those established and popularized by B. K. P. Horn, or O. Faugeras. Although leastsquares approaches can
Efficient Calculation of Absolute Orientation with Outlier Rejection
"... This paper addresses a high level spatiotemporal problem, namely "absolute orientation", which arises in visualodometry (using stereo), or registering two models created by different Structure from Motion (SFM) reconstructions. We compare the very popular method due to Horn 1 usin ..."
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Cited by 1 (0 self)
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This paper addresses a high level spatiotemporal problem, namely "absolute orientation", which arises in visualodometry (using stereo), or registering two models created by different Structure from Motion (SFM) reconstructions. We compare the very popular method due to Horn 1
Implement absolute orientation instruments for odometry system integrated with Gyroscope by using IKF
, 2010
"... Abstract. In this paper, absolute orientation instruments using compass are mainly proposed to estimate absolute orientation errors combined with estimated position and orientation from differential odometry integrated with gyroscope to calculate absolute orientation of mobile robot. In the method, ..."
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Abstract. In this paper, absolute orientation instruments using compass are mainly proposed to estimate absolute orientation errors combined with estimated position and orientation from differential odometry integrated with gyroscope to calculate absolute orientation of mobile robot. In the method
A New Closed Form Approach to the Absolute Orientation Problem
, 1999
"... The absolute orientation problem has applications in numerous fields; including robotics, pose estimation, photogrammetry, and computer graphics. With the exception of the contributions by B. K. P. Horn, most absolute orientation research has focused on rotation matrixes. However, in many cases, re ..."
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The absolute orientation problem has applications in numerous fields; including robotics, pose estimation, photogrammetry, and computer graphics. With the exception of the contributions by B. K. P. Horn, most absolute orientation research has focused on rotation matrixes. However, in many cases
Automating Image Registration And Absolute Orientation: Solutions And Problems
 PHOTOGRAMMETRIC RECORD
, 1998
"... The basic concepts and tools of automatic image registration are presented and the problems which exist are discussed. The paper describes work carried out at University College London on the registration of two images and on the registration of images with maps. It is shown that strategies have ..."
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Cited by 6 (0 self)
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The basic concepts and tools of automatic image registration are presented and the problems which exist are discussed. The paper describes work carried out at University College London on the registration of two images and on the registration of images with maps. It is shown that strategies have been developed which are applicable to different types of image and reference data and that with the tuning of well tried algorithms it is possible to achieve the required matching. The PAIRS technique for automatic registration of optical images from satellites has been implemented and tested and is now being developed for use with optical and microwave images. The ARCHANGEL system for registration of images with maps or vector data is also being implemented and initial results show considerable promise.
Chapter 7 Absolute Orientation of Single Images
"... mining the 9 unknowns. However, these equations are nonlinear in the nine unknowns, the direct solution of all the unknowns from the minimum number of 5 control points is not available, or probably not existent. It is nevertheless always possible to solve these nonlinear equations by using iterative ..."
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. Afterwards, the explicit parameters can be solved in direct closedform from the implicit parameters. This is usually called Direct Linear Transform (DLT) in photogrammetry. On the other hand, if the interior orientation (x c ; y c ; f) is known, the exterior orientation (XC ; YC ; ZC
Determining the Absolute Orientation in a Corridor using Projective Geometry and Active Vision
 IEEE Trans. on Industrial Electronics
, 2001
"... The capability of a mobile robot to determine its position in the environment (selflocalization) is a prerequisite for achieving autonomous navigation. An approach is proposed for determining the absolute orientation of an autonomous robot in a system of corridors, based on the projective geometry ..."
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Cited by 9 (0 self)
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The capability of a mobile robot to determine its position in the environment (selflocalization) is a prerequisite for achieving autonomous navigation. An approach is proposed for determining the absolute orientation of an autonomous robot in a system of corridors, based on the projective geom
Analytical characterization of the accuracy of slam without absolute orientation measurements
 In Proc. Robotics: Science and Systems Conf
, 2006
"... In this report we derive analytical upper bounds on the covariance of the state estimates in SLAM. The analysis is based on a novel formulation of the SLAM problem, that enables the simultaneous estimation of the landmark coordinates with respect to the a robotcentered frame (relative map), as well ..."
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Cited by 3 (2 self)
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accuracy of the robot pose estimates is derived as a function of the accuracy of the robot’s sensors, and of the properties of the map. Contrary to previous approaches, the method presented here makes no assumptions about the availability of a sensor measuring the absolute orientation of the robot
Results 1  10
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