Total Least Squares Algorithms for Fitting 3d Straight Lines

Guo, Cuiping; Peng, Junhuan; Li, Chuantao

doi:10.18642/ijamml_7100121818

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…Object Counter 3D (OC3D) is an open-source algorithm implemented in Fiji [94] based on voxel connectivity to perform teh segmentation. In other words, OC3D identifies a single 3D-Object as all voxels with an intensity value higher than a certain cutoff value (foreground) that are connected without interruption by voxels with intensity values below the cutoff (background).…”

Section: Supplementary Informationmentioning

confidence: 99%

High-throughput three-dimensional characterization of morphogenetic signals during the formation of the vertebrate retina

Ledesma-Terrón,

Pérez-Dones,

Mazó-Durán

et al. 2024

Preprint

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The precise differentiation of neural progenitors during development ensures the correct cognitive, sensory and motor functions of higher organisms. This balance between self-renewal and terminal differentiation is regulated by a complex interplay of signaling pathways, that set the spatial and temporal cues that ultimately shape and organize neurogenic tissues. The developing vertebrate retina is a widely used model to study how these key signaling cascades modulate the mode and rate of division of neural progenitors, despite its complex three-dimensional architecture and the asymmetric differentiation dynamics. Here, we present a comprehensive multi-step framework that integrates in toto experiments with three dimensional image analysis and theoretical tools to provide a quantitative characterization of the dynamics of growth and differentiation of the developing vertebrate retina. Additionally, we use small molecule inhibitors to show that Hh and FGF activation promote differentiation and cell cycle pro- gression, while Wnt and Notch activation respectively increase and decrease the average division rate. These results represent a detailed and accurate quantitative characterization of the development and regulation of the vertebrate retina. We propose that the same framework can be directly used to characterize other in vitro or in vivo tissues.

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Section: Supplementary Informationmentioning

confidence: 99%

High-throughput three-dimensional characterization of morphogenetic signals during the formation of the vertebrate retina

Ledesma-Terrón,

Pérez-Dones,

Mazó-Durán

et al. 2024

Preprint

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“…e three-dimensional information of the discrete points of the laser spot is obtained from the premeasured PSD translation information, the two-dimensional spot information is obtained by the actual measurement, and then the three spatial straight lines of the emitted laser beam are fitted by the principle of least squares [20].…”

Section: Line Fitting Of the Laser Beammentioning

confidence: 99%

A High-Precision Dynamic Six Degree-of-Freedom Pose Measurement of the Subreflectors of Large Antennas Based on a Position Sensitive Detector and Laser Array

Lin,

Wang,

Wang

et al. 2022

Advances in Astronomy

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Subreflector misalignment of a large steerable radio telescope induces a pointing error and reduces the gain of the antenna system. To improve the antenna’s operational efficiency, it is necessary to measure and adjust the position and attitude of the subreflector in real time. In this paper, a method based on a position sensitive detector (PSD) and laser array without an optical system is proposed to measure the six degree-of-freedom (DOF) poses of the subreflector. The laser emitted by the laser module array ensures that the PSD can be covered as it moves with the subreflector, and the PSD can obtain more than three laser beams. These ensure the measurement of all attitude changes of a large-aperture antenna subreflector. The two-dimensional coordinates of the centroids of three laser spots are extracted using the PSD, and then the bursa model is established to complete the coordinate transformation. Finally, the 6-DOF attitude information of the antenna subreflector is obtained. The results of a 6.05 m measurement simulation show that it can obtain high 6-DOF PSD attitude information. The experimental results show that the 6-DOF position and attitude information of the subreflector at a distance of 5.78 m can be obtained within seconds. Moreover, the error of the translation is within 0.014 mm and the error of the rotation is within 0.37°. This method can meet the pose measurement requirements of the subreflector.

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“…It should be noted that this issue is an extension of the problem of fitting a straight line in two-dimensional space, presented in Schaffrin et al (2006) and Schaffrin (2007). Another way of fitting a straight line in a three-dimensional space, by using the principles of the total least-squares method, has been presented in Guo et al (2017). In a classical approach, defining a straight line in three-dimensional space, with a parametric form (for À∞<t<∞):…”

Section: General Overview Of Line Fitting In 3d Euclidean Spacementioning

confidence: 99%

“…It should be noted that this issue is an extension of the problem of fitting a straight line in two‐dimensional space, presented in Schaffrin et al (2006) and Schaffrin (2007). Another way of fitting a straight line in a three‐dimensional space, by using the principles of the total least‐squares method, has been presented in Guo et al (2017). In a classical approach, defining a straight line in three‐dimensional space, with a parametric form (for

‐ \infty < t < \infty

B = \{p |p = a + t b, p = [p_{x}, p_{y}, p_{z}], ‐ \infty < t < \infty\}

is performed by using three parameters that determine the position of the point on the line as a = [ a x , a y , a z ] T , and by three parameters defining the orientation of the line in this space as b = [ b x , b y , b z ] T .…”

Section: General Overview Of Line Fitting In 3d Euclidean Spacementioning

confidence: 99%

3D point‐cloud spatial expansion by total least‐squares line fitting

Dąbrowski

Zienkiewicz

2020

The Photogrammetric Record

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Point‐cloud spatial expansion (PCSE) allows the creation of a new point‐cloud form that presents an alternative geometry of an entire object in a single spatial view. Spatial expansion facilitates the analysis process and introduces an additional spatial parameter describing the point cloud. An important element of the PCSE method is determining the position of the axis of symmetry of a symmetrical object: the procedure for determining the parameters of this axis (set of cross‐sectional centres) of the object’s point cloud by the total least‐squares method is presented. The estimation results were used to create a spatial expansion of the point cloud of a cylindrical object, demonstrating the usefulness of total least‐squares fitting to the PCSE method.

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Total Least Squares Algorithms for Fitting 3d Straight Lines

Cited by 5 publications

References 13 publications

High-throughput three-dimensional characterization of morphogenetic signals during the formation of the vertebrate retina

High-throughput three-dimensional characterization of morphogenetic signals during the formation of the vertebrate retina

A High-Precision Dynamic Six Degree-of-Freedom Pose Measurement of the Subreflectors of Large Antennas Based on a Position Sensitive Detector and Laser Array

3D point‐cloud spatial expansion by total least‐squares line fitting

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