Estimating 3-D location parameters using dual number quaternions

Walker, Michael; Shao, Lei; Volz, Richard A.

doi:10.1016/1049-9660(91)90036-o

Cited by 327 publications

(218 citation statements)

References 5 publications

(4 reference statements)

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“…Eggert et al [10] reviewed the main methods that give an analytical solution to this rigid 3D registration problem: singular value decomposition (SVD) [9,19], unit quaternions [20], orthonormal matrix [21], and dual quaternions [22]. In [11], Gower and Dijksterhuis reviewed multiple different Procrustes problems and many generalizations.…”

Section: Rigid 3d Registration or Orthogonal Procrustes Problemmentioning

confidence: 99%

Decomposition and dictionary learning for 3D trajectories

2014

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A new model for describing a three-dimensional (3D) trajectory is proposed in this article. The studied trajectory is viewed as a linear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This article is divided into two parts based on this model. On the one hand, the 3DRI decomposition estimates the active patterns, their coefficients, their rotations and their shift parameters. Based on sparse approximation, this is carried out by two non-convex optimizations: 3DRI matching pursuit (3DRI-MP) and 3DRI orthogonal matching pursuit (3DRI-OMP). On the other hand, a 3DRI learning method learns the characteristic patterns of a database through a 3DRI dictionary learning algorithm (3DRI-DLA). The proposed algorithms are first applied to simulation data to evaluate their performances and to compare them to other algorithms. Then, they are applied to real motion data of cued speech, to learn the 3D trajectory patterns characteristic of this gestural language.

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Section: Rigid 3d Registration or Orthogonal Procrustes Problemmentioning

confidence: 99%

Decomposition and dictionary learning for 3D trajectories

2014

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“…Also, the algorithm provides merging shape data without surface normals, relieving the need for calculating meshes of the cloud (with expense of reduced accuracy). For calculation of transformation from the error function (mean distance between closest points identified), Zhang's algorithm uses dual-quaternion method, which was introduced in Walker et al (1991). Figure 3 shows results from merging Test Map1 and 2, where the local model was tilted to 45 degrees against the center of the reference model.…”

Section: Implementing Icp-based Merging Algorithm and Testmentioning

confidence: 99%

Merging Point Clouds from Heterogeneous 3D Scanners for Fast Update of an Earthwork Site Model

Jung¹,

Kwon²,

Kim³

et al. 2010

Proceedings -- The 27th International Symposium on Automation and Robotics in Construction

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In earthwork sites, its terrain shapes are changing continuously as the work proceeds. If someone wants to grab three-dimensional geometry data of such sites, currently available technologies such as 3D laser scanners are unable to collect reasonably precise data in pseudo-real time (i.e., 1-10 scans per second). To tackle the problem, the authors took 'dual scanners' approach, where low-speed (yet highly-precise) laser scanners are used for initial scan of the work site, then augment the initial data using the 3D geometry data collected from excavator-mounted stereovision. For this approach, the authors used ICP (Iterative ClosestPoint)-based algorithms for merging the stereovision data with the laser scan data, where similarities of both data are limited due to changed site shape.

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“…Table 1 lists the RMS distances after manual alignment, point-based rigid registration according to [10], and rigid & semi-affine registration using our methods. The automatic registration converges correctly for all patients with an execution time of ∼ 20 seconds.…”

Section: Optimization Strategymentioning

confidence: 99%

Simulation and Fully Automatic Multimodal Registration of Medical Ultrasound

Wein

Khamene

Clevert

et al. 2007

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007

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Abstract. The fusion of 3D freehand ultrasound with CT and CTA has benefits for a variety of clinical applications, however a lot of manual work is usually required for correct registration. We developed new methods that allow one to simulate medical ultrasound from CT in real-time, reproducing the majority of ultrasonic imaging effects. The second novelty is a robust similarity measure that assesses the correlation of a combination of multiple signals extracted from CT with ultrasound, without knowing the influence of each signal. This serves as the foundation of a fully automatic registration, which aligns a freehand ultrasound sweep with the corresponding 3D modality using a rigid or an affine transformation model, without any manual interaction. We also present the used initialization, global and local parameter optimization schemes, and validation on abdominal CTA and ultrasound imaging of 10 patients.

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Estimating 3-D location parameters using dual number quaternions

Cited by 327 publications

References 5 publications

Decomposition and dictionary learning for 3D trajectories

Decomposition and dictionary learning for 3D trajectories

Merging Point Clouds from Heterogeneous 3D Scanners for Fast Update of an Earthwork Site Model

Simulation and Fully Automatic Multimodal Registration of Medical Ultrasound

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