Entropy-based segmentation by (stochastic) EM (R6)

Unsupervised segmentation of SAR/PolSAR images from maps of estimated Shannon entropies (Ferreira and Nascimento, 2020; Nascimento, Ferreira and Frery, 2023). By the asymptotic normality of the entropy estimators, the entropy vector of a pixel of the $g$-th region is approximately Gaussian, so the image is modelled as a finite mixture of Gaussian laws (with diagonal covariance matrices) fitted by the expectation-maximisation algorithm (method = "em") or by its stochastic version (method = "sem"), in which the E-step is followed by a random allocation of every pixel to a class drawn from its posterior probabilities. Pixels are then labelled by the maximum a posteriori rule.

References

Ferreira, J. A. and Nascimento, A. D. C. (2020). Shannon entropy for the G0I model: a new segmentation approach. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 13, 2547–2553. doi:10.1109/JSTARS.2020.2997666

Nascimento, A. D. C., Ferreira, J. A. and Frery, A. C. (2023). Unsupervised segmentation of PolSAR data with complex Wishart and G0m distributions and Shannon entropy. Statistics and Computing, 33, 129. doi:10.1007/s11222-023-10298-0

Public fields

k: Number of classes.
method: "em" or "sem".
weights: Mixture weights.
means: Matrix (k x features) of class means.
variances: Matrix (k x features) of class variances.
posterior: Matrix of posterior probabilities.
labels: Integer vector of labels (classes ordered by the mean of the first feature).
loglik: Trace of the log-likelihood.
iterations: Number of iterations.
converged: Logical convergence flag.
dim: Spatial dimensions when fitted to a map (NULL otherwise).

Methods

`EntropySegmenter$new()`

Create a segmenter.

Usage

EntropySegmenter$new(
  k = 2,
  method = c("em", "sem"),
  max_iter = 200L,
  tol = 1e-08
)

Arguments

k: Number of classes.
method: "em" or "sem".
max_iter: Maximum number of iterations.
tol: Tolerance for the relative change of the log-likelihood.

`EntropySegmenter$fit()`

Fit the mixture.

Usage

EntropySegmenter$fit(x, init = NULL, is_map = TRUE)

Arguments

x: Entropy features: a matrix (one map, or pixels in rows and features in columns when is_map = FALSE), an array nrow x ncol x features (several maps), or a numeric vector.
init: Initial labels (integer vector) or NULL for k-means.
is_map: Treat a matrix x as a single map? Default TRUE.

`EntropySegmenter$predict()`

Labels of new observations (maximum a posteriori).

Usage

EntropySegmenter$predict(x, is_map = TRUE)

Arguments

x: Entropy features in the same format used in $fit().
is_map: Treat a matrix x as a single map?

`EntropySegmenter$label_map()`

Labels as a matrix with the spatial dimensions of the fitted map.

Usage

EntropySegmenter$label_map()

`EntropySegmenter$print()`

Print a summary.

Usage

EntropySegmenter$print(...)

Arguments

...: Ignored.

`EntropySegmenter$clone()`

The objects of this class are cloneable with this method.

Usage

EntropySegmenter$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

H <- entropy_map(SanFrancisco150, model = "wishart", window = 7, L = 4)
set.seed(1)
seg <- EntropySegmenter$new(k = 3)$fit(H)
seg
#> <EntropySegmenter> k = 3 | method: EM 
#>   iterations: 20 | converged: TRUE 
#>   weights: 0.265 0.268 0.467 
#>   class sizes: 5933 5773 10794 
plot_map(seg$label_map(), main = "Entropy-based segmentation")

kappa_statistics(SanFrancisco150_gt, seg$label_map())
#> # A tibble: 1 × 5
#>   kappa   variance std_error overall_accuracy     n
#>   <dbl>      <dbl>     <dbl>            <dbl> <dbl>
#> 1 0.914 0.00000566   0.00238            0.945 22500