Trains a supervised learning or analytical model to define a spatial transformation.
Arguments
- gcp_data
An
sfobject of homologous points fromread_gcps().- pai_method
A character string specifying the algorithm. One of: "lm","tps", "gam", "rf", "svmRadial", "svmLinear", or "helmert".
- seed
An integer for setting the random seed for reproducibility.
- ...
Additional arguments passed to the underlying model fitting functions (
mgcv::gam,stats::lm,ranger::ranger,fields::Tps,e1071::svm).
Details
This function serves as a factory for creating transformation models. It supports machine learning methods ("lm", "gam", "rf", "svmRadial", "svmLinear") that learn the relationship between source coordinates and displacement vectors, as well as the analytical "helmert" method which solves for a global similarity transformation.
Important: The more flexible machine learning models, gam and rf,
require a sufficient number of data points to produce stable and reliable
results. This function will prevent training these models with fewer than
60 homologous points to avoid overfitting. If you have a small number of
points, please use the more robust "lm" or "helmert" methods.
Examples
# Load the ground control points data
data(gcps)
# Train a General Additive Model (GAM)
gam_model <- train_pai_model(gcps, pai_method = "gam")
#> Training 'gam' model...
summary(gam_model$model)
#>
#> Family: Multivariate normal
#> Link function:
#>
#> Formula:
#> dx ~ s(source_x, source_y)
#> <environment: 0x5566ca005740>
#> dy ~ s(source_x, source_y)
#> <environment: 0x5566ca005740>
#>
#> Parametric coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 0.05257 0.01722 3.053 0.00227 **
#> (Intercept).1 -0.31945 0.02119 -15.074 < 2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df Chi.sq p-value
#> s(source_x,source_y) 23.845 27.45 234.5 <2e-16 ***
#> s.1(source_x,source_y) 7.624 10.63 156.8 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Deviance explained = 39.9%
#> -REML = -305.73 Scale est. = 1 n = 300
# Train a linear model
lm_model <- train_pai_model(gcps, pai_method = "lm")
#> Training 'lm' model...
summary(lm_model$model$model_dx)
#>
#> Call:
#> stats::lm(formula = formula, data = data)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.27422 -0.18591 0.00183 0.15729 1.18893
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -6.644e+03 7.461e+02 -8.904 <2e-16 ***
#> source_x 5.886e-05 1.373e-04 0.429 0.668
#> source_y 1.477e-03 1.663e-04 8.880 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.3619 on 297 degrees of freedom
#> Multiple R-squared: 0.2109, Adjusted R-squared: 0.2056
#> F-statistic: 39.68 on 2 and 297 DF, p-value: 5.333e-16
#>
summary(lm_model$model$model_dy)
#>
#> Call:
#> stats::lm(formula = formula, data = data)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.22190 -0.22767 -0.03835 0.20294 1.60099
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -6.104e+03 7.848e+02 -7.778 1.22e-13 ***
#> source_x -1.228e-03 1.444e-04 -8.505 9.02e-16 ***
#> source_y 1.434e-03 1.749e-04 8.196 7.53e-15 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.3806 on 297 degrees of freedom
#> Multiple R-squared: 0.3129, Adjusted R-squared: 0.3083
#> F-statistic: 67.64 on 2 and 297 DF, p-value: < 2.2e-16
#>