Least squares fitting of two planar point sets for use in photolithography overlay alignment

1998 ◽  
Author(s):  
Divyendu Sinha ◽  
Edward T. Polkowski
Keyword(s):  
Least Squares ◽  
Point Sets ◽  
Planar Point ◽  
Least Squares Fitting

Least-squares fitting of multiple M-dimensional point sets

2006 ◽  
Vol 22 (6) ◽  
pp. 387-398 ◽  
Author(s):  
Gaojin Wen ◽  
Zhaoqi Wang ◽  
Shihong Xia ◽  
Dengming Zhu
Keyword(s):  
Least Squares ◽  
Point Sets ◽  
Least Squares Fitting

scholarly journals Least-Squares Fitting of Two 3-D Point Sets

1987 ◽  
Vol PAMI-9 (5) ◽  
pp. 698-700 ◽  
Author(s):  
K. S. Arun ◽  
T. S. Huang ◽  
S. D. Blostein
Keyword(s):  
Least Squares ◽  
Point Sets ◽  
Least Squares Fitting

Total least squares fitting of point sets in m-D

2005 ◽  
Author(s):  
Gaojin Wen ◽  
Dengming Zhu ◽  
Shihong Xia ◽  
Zhaoqi Wang
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Point Sets ◽  
Least Squares Fitting

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

scholarly journals Planar point sets determine many pairwise crossing segments

2021 ◽  
Vol 386 ◽  
pp. 107779
Author(s):  
János Pach ◽  
Natan Rubin ◽  
Gábor Tardos
Keyword(s):  
Point Sets ◽  
Planar Point

scholarly journals An Error-Reduction Method for Temporal Phase Unwrapping Based on Double Three-Step Phase-Shifting and Least-Squares Fitting

2012 ◽  
Vol 6-7 ◽  
pp. 76-81
Author(s):  
Yong Liu ◽  
Ding Fa Huang ◽  
Yong Jiang
Keyword(s):  
Least Squares ◽  
Reduction Method ◽  
Intermediate Phase ◽  
Error Reduction ◽  
Phase Unwrapping ◽  
Phase Shifting ◽  
Surface Measurement ◽  
Acquisition Time ◽  
Least Squares Fitting ◽  
Temporal Phase

Phase-shifting interferometry on structured light projection is widely used in 3-D surface measurement. An investigation shows that least-squares fitting can significantly decrease random error by incorporating data from the intermediate phase values, but it cannot completely eliminate nonlinear error. This paper proposes an error-reduction method based on double three-step phase-shifting algorithm and least-squares fitting, and applies it on the temporal phase unwrapping algorithm using three-frequency heterodyne principle. Theoretical analyses and experiment results show that this method can greatly save data acquisition time and improve the precision.

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