Divergence-based classifier for SAR/PolSAR features (R6)

Implements the family of divergence-based classifiers of Ferreira, Coelho and Nascimento (2021). Each pixel is represented by the model fitted to the observations of a moving window (see sar_features()) and each class by the model fitted to its training pixels. A pixel is assigned to the class that minimises the chosen divergence between the two fitted models: $$\hat\imath = \arg\min_{i \in \{1, \ldots, g\}} d(\hat\theta_h, \hat\theta_i).$$

Two families of features are available:

"gaussian": multivariate normal laws for the intensity vector, using the columns mean_* and cov_* of sar_features(). The class covariance combines the average local covariance and the covariance of the local means (law of total variance).
"wishart": scaled complex Wishart laws for the full PolSAR covariance matrix, using the columns c11, c12_re, c12_im, ... of sar_features(). Since all laws share the number of looks, it only rescales the divergences and does not affect the classification.

The classifier is also available as the 'parsnip' model divergence_classifier(), for use in 'tidymodels' workflows.

References

Ferreira, J. A., Coelho, H. and Nascimento, A. D. C. (2021). A family of divergence-based classifiers for polarimetric synthetic aperture radar (PolSAR) imagery vector and matrix features. International Journal of Remote Sensing, 42(4), 1201–1229. doi:10.1080/01431161.2020.1826060

Public fields

family: "gaussian" or "wishart".
divergence: Divergence used (see divergence_gaussian()).
order: Order of the Rényi divergence.
kind: Form (1-4) of the Rényi divergence.
classes: Class labels.
prototypes: List with the fitted model of each class.
channels: Channels (Gaussian) or matrix order (Wishart) used.

Methods

`DivergenceClassifier$new()`

Create a classifier.

Usage

DivergenceClassifier$new(
  family = c("gaussian", "wishart"),
  divergence = c("renyi", "kl", "jeffreys", "bhattacharyya"),
  order = 0.5,
  kind = 1
)

Arguments

family: "gaussian" or "wishart".
divergence: "kl", "jeffreys", "bhattacharyya" or "renyi".
order: Order of the Rényi divergence, in (0, 1).
kind: Form of the Rényi divergence (1 to 4).

`DivergenceClassifier$fit()`

Fit the class prototypes.

Usage

DivergenceClassifier$fit(x, y)

Arguments

x: Data frame of features (see sar_features()); other columns are ignored.
y: Factor (or vector) of class labels.

`DivergenceClassifier$distances()`

Divergence between every row of x and every class.

Usage

DivergenceClassifier$distances(x)

Arguments

x: Data frame of features.

`DivergenceClassifier$predict()`

Predict classes, pseudo-probabilities or distances.

Usage

DivergenceClassifier$predict(x, type = c("class", "prob", "distance"))

Arguments

x: Data frame of features.
type: "class", "prob" (softmax of minus the divergences) or "distance".

`DivergenceClassifier$print()`

Print the classifier.

Usage

DivergenceClassifier$print(...)

Arguments

...: Ignored.

`DivergenceClassifier$clone()`

The objects of this class are cloneable with this method.

Usage

DivergenceClassifier$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

img <- SARImage$new(SanFrancisco150)$crop(1:80, 1:80)
feats <- sar_features(img, window = 5)
feats$class <- factor(as.vector(SanFrancisco150_gt[1:80, 1:80]),
                      labels = c("ocean", "forest", "urban"))
set.seed(1)
train <- feats[sample(nrow(feats), 300), ]

clf <- DivergenceClassifier$new(family = "wishart", divergence = "renyi",
                                order = 0.5, kind = 3)
clf$fit(train, train$class)
pred <- clf$predict(feats)
mean(pred == feats$class)
#> [1] 0.9920313
head(clf$predict(feats, type = "distance"))
#> # A tibble: 6 × 3
#>   ocean forest urban
#>   <dbl>  <dbl> <dbl>
#> 1  1.72   6.56  9.48
#> 2  1.68   6.55  9.50
#> 3  1.65   6.53  9.50
#> 4  1.69   6.59  9.58
#> 5  1.71   6.66  9.68
#> 6  1.62   6.51  9.51