target_tls: Target function of the total least squares criterion of Coope...
In hoehleatsu/perfectcircle: Assess the Circularity of Circles via Image Aalysis
Description
Usage
Arguments
Details
Value
References
View source: R/perfectcircle.R
Description
Target function of the total least squares criterion of Coope (1993)
Usage
1
target_tls(theta, freehandCircleThinBorder)
Arguments
theta
A vector of length 2 containing log of the center coordinates.
Details
Denoting by c the center of the circle and by r>0 the radius we
want to find the circle for which the Euclidean distance to $m$ data points $a_j$, $j=1,...,m$ using the following criterion:
\min_{c\in \mathbb{R^2}, r>0} ∑_{j=1}^m F_j(c,r)^2
, where
F_j(c,r) = ≤ft|r - ||c-a_j||_2\right|
.
This is equation (1) and (2) of Coope (1993).
Value
The total least squares
References
Coope, I.D. 1993. “Circle Fitting by Linear and Nonlinear Least Squares.” Journal of Optimization Theory and Applications 76 (2): 381–88. doi:10.1007/BF00939613.
hoehleatsu/perfectcircle documentation built on Feb. 6, 2020, 10:13 p.m.
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Description Usage Arguments Details Value References
View source: R/perfectcircle.R
Description
Target function of the total least squares criterion of Coope (1993)
Usage
1 | target_tls(theta, freehandCircleThinBorder)
|
Arguments
theta |
A vector of length 2 containing log of the center coordinates. |
Details
Denoting by c the center of the circle and by r>0 the radius we want to find the circle for which the Euclidean distance to $m$ data points $a_j$, $j=1,...,m$ using the following criterion:
\min_{c\in \mathbb{R^2}, r>0} ∑_{j=1}^m F_j(c,r)^2
, where
F_j(c,r) = ≤ft|r - ||c-a_j||_2\right|
. This is equation (1) and (2) of Coope (1993).
Value
The total least squares
References
Coope, I.D. 1993. “Circle Fitting by Linear and Nonlinear Least Squares.” Journal of Optimization Theory and Applications 76 (2): 381–88. doi:10.1007/BF00939613.
R Package Documentation
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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