Three-dimensional image modeling based on least squares fitting by using adaptive subdivision of a tetrahedron

1997 ◽  
Author(s):  
Kun Lee ◽  
Oubong Gwun
Keyword(s):  
Least Squares ◽  
Three Dimensional ◽  
Image Modeling ◽  
Dimensional Image ◽  
Least Squares Fitting ◽  
Adaptive Subdivision

Optimality Conditions for Constrained Least-Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums

2018 ◽  
Vol 18 (3) ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Optimality Conditions ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Constrained Least Squares ◽  
Least Squares Fitting ◽  
Candidate Solution ◽  
Cylinders And Spheres ◽  
New Algorithms

This paper addresses the combinatorial characterizations of the optimality conditions for constrained least-squares fitting of circles, cylinders, and spheres to a set of input points. It is shown that the necessary condition for optimization requires contacting at least two input points. It is also shown that there exist cases where the optimal condition is achieved while contacting only two input points. These problems arise in digital manufacturing, where one is confronted with the task of processing a (potentially large) number of points with three-dimensional coordinates to establish datums on manufactured parts. The optimality conditions reported in this paper provide the necessary conditions to verify if a candidate solution is feasible, and to design new algorithms to compute globally optimal solutions.

Optimality Conditions for Constrained Least-Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums

2017 ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Optimality Conditions ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Constrained Least Squares ◽  
Least Squares Fitting ◽  
Candidate Solution ◽  
Cylinders And Spheres ◽  
New Algorithms

This paper addresses the combinatorial characterizations of the optimality conditions for constrained least-squares fitting of circles, cylinders, and spheres to a set of input points. It is shown that the necessary condition for optimization requires contacting at least two input points. It is also shown that there exist cases where the optimal condition is achieved while contacting only two input points. These problems arise in digital manufacturing, where one is confronted with the task of processing a (potentially large) number of points with three-dimensional coordinates to establish datums on manufactured parts. The optimality conditions reported in this paper provide the necessary conditions to verify if a candidate solution is feasible, and to design new algorithms to compute globally optimal solutions.

scholarly journals Three dimensional least-squares fitting of ellipsoids and hyperboloids

2017 ◽  
Vol 890 ◽  
pp. 012121
Author(s):  
Elvira Rahmadiantri ◽  
Made Putri Lawiyuniarti ◽  
Intan Muchtadi-Alamsyah ◽  
Gantina Rachmaputri
Keyword(s):  
Least Squares ◽  
Three Dimensional ◽  
Least Squares Fitting

scholarly journals Easy-DHPSF 2.0: open-source software for three-dimensional localization and two-color registration of single molecules with nanoscale accuracy

2019 ◽  
Author(s):  
Camille Bayas ◽  
Alex von Diezmann ◽  
Anna-Karin Gustavsson ◽  
W. E. Moerner
Keyword(s):  
Least Squares ◽  
Single Molecule ◽  
Template Matching ◽  
Double Helix ◽  
Single Molecules ◽  
Three Dimensional ◽  
Wide Field ◽  
3D Registration ◽  
Position Measurement ◽  
Least Squares Fitting

Abstract Automated processing of double-helix (DH) microscope images of fluorescent single molecules (SMs) streamlines the protocol required to obtain super-resolved three-dimensional (3D) reconstructions of ultrastructures in biological samples by single-molecule active control microscopy (SMACM). Here, we present a suite of MATLAB subroutines, bundled with an easy-to-use graphical user interface (GUI), that facilitates 3D localization of single emitters (e.g. SMs, fluorescent beads, or quantum dots) with typical precisions of tens of nanometers in multi-frame movies acquired using a wide-field DH epifluorescence microscope. The algorithmic approach is based upon template matching for SM recognition and least‑squares fitting for 3D position measurement, both of which are computationally expedient and precise. Overlapping images of SMs are ignored, and the precision of least-squares fitting is not as high as maximum likelihood-based methods. Version 2.0 of Easy-DHPSF augments the approach of Version 1.0 by incorporating code that facilitates combining localization data from two spectral channels using a locally-weighted quadratic 3D registration function.

scholarly journals Easy-DHPSF 2.0: open-source software for three-dimensional localization and two-color registration of single molecules with nanoscale accuracy

2019 ◽  
Author(s):  
Camille Bayas ◽  
Alex von Diezmann ◽  
Anna-Karin Gustavsson ◽  
W. E. Moerner
Keyword(s):  
Least Squares ◽  
Single Molecule ◽  
Template Matching ◽  
Double Helix ◽  
Single Molecules ◽  
Three Dimensional ◽  
Wide Field ◽  
3D Registration ◽  
Position Measurement ◽  
Least Squares Fitting

Abstract Automated processing of double-helix (DH) microscope images of fluorescent single molecules (SMs) streamlines the protocol required to obtain super-resolved three-dimensional (3D) reconstructions of ultrastructures in biological samples by single-molecule active control microscopy (SMACM). Here, we present a suite of MATLAB subroutines, bundled with an easy-to-use graphical user interface (GUI), that facilitates 3D localization of single emitters (e.g. SMs, fluorescent beads, or quantum dots) with typical precisions of tens of nanometers in multi-frame movies acquired using a wide-field DH epifluorescence microscope. The algorithmic approach is based upon template matching for SM recognition and least‑squares fitting for 3D position measurement, both of which are computationally expedient and precise. Overlapping images of SMs are ignored, and the precision of least-squares fitting is not as high as maximum likelihood-based methods. Version 2.0 of Easy-DHPSF augments the approach of Version 1.0 by incorporating code that facilitates combining localization data from two spectral channels using a locally-weighted quadratic 3D registration function.

Least-squares fitting of a three-dimensional ellipsoid to noisy data

2014 ◽  
Vol 8 ◽  
pp. 7409-7421 ◽  
Author(s):  
Alexandra Malyugina ◽  
Konstantin Igudesman ◽  
Dmitry Chickrin
Keyword(s):  
Least Squares ◽  
Three Dimensional ◽  
Noisy Data ◽  
Least Squares Fitting

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

A Three-dimensional Camera: Development and Applications of a Three-dimensional Image Measurement System

2011 ◽  
Vol 131 (2) ◽  
pp. 320-328 ◽  
Author(s):  
Cunwei Lu ◽  
Hiroya Kamitomo ◽  
Ke Sun ◽  
Kazuhiro Tsujino ◽  
Genki Cho
Keyword(s):  
Measurement System ◽  
Three Dimensional ◽  
Image Measurement ◽  
Dimensional Image
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