Information Theory, Geometry and Statistics for Synthetic Aperture Radar Data

Statistical models, information-theoretic measures and image analysis tools for Synthetic Aperture Radar (SAR) and polarimetric SAR (PolSAR) data. It implements intensity models (Gamma, generalized Gamma and G0I) and matrix models (scaled complex Wishart, G0 polarimetric and the compound truncated Poisson and compound geometric complex Wishart laws), maximum likelihood and expectation-maximization estimation, closed-form Shannon entropies with their asymptotic variances, entropy-based hypothesis tests and change detection, entropy-based image segmentation by (stochastic) expectation-maximization, stochastic distances and a family of divergence-based classifiers (Kullback-Leibler, Jeffreys, Bhattacharyya and Renyi) for Gaussian vector features and complex Wishart matrix features. The main tools are 'R6' classes and the classifiers are available as a 'parsnip' model, so they can be used inside 'tidymodels' workflows. Methods are described in Ferreira, Coelho and Nascimento (2021) , Ferreira and Nascimento (2020) , Ferreira, Nascimento and Frery (2022) and Nascimento, Ferreira and Frery (2023) .

SITSAR

Information Theory, Geometry and Statistics for Synthetic Aperture Radar Data

SITSAR brings together statistical models, information-theoretic measures and image-analysis tools for Synthetic Aperture Radar (SAR) and polarimetric SAR (PolSAR) data. It gathers the methods developed in the master’s dissertation (divergence-based classifiers) and in the PhD thesis (Shannon entropies, entropy-based segmentation and change detection, and compound Wishart models) of Jodavid A. Ferreira, supervised by Abraão D. C. Nascimento (UFPE, Brazil).

The main tools are R6 classes, and the classifiers are available as a parsnip model, so they work inside tidymodels workflows (recipes, resampling, tuning and yardstick metrics).

Installation

# From CRAN
install.packages("SITSAR")

# Development version from GitHub
# install.packages("remotes")
remotes::install_github("jodavid/SITSAR")

A PolSAR image

The package ships a 150 x 150 crop of the L-band AIRSAR image of San Francisco (SanFrancisco150) and its ground truth (SanFrancisco150_gt).

library(SITSAR)

img <- SARImage$new(SanFrancisco150, looks = 4)
img
#> <SARImage> 150 x 150 PolSAR (3 x 3 covariance)
#>   channels: HH, HV, VV
#>   looks: 4
#>   mean HH  = 0.1735
#>   mean HV  = 0.04224
#>   mean VV  = 0.147

op <- par(mfrow = c(1, 2))
img$plot()
plot_map(SanFrancisco150_gt, main = "Ground truth",
         palette = c("#1f78b4", "#33a02c", "#e31a1c"))

par(op)

Models, estimation and Shannon entropy

set.seed(1)
x <- rg0i(1000, alpha = -3, gamma = 2, L = 4)

fit <- G0I$new()$fit(x)        # maximum likelihood (alpha, gamma and L)
fit
#> <G0I> fitted to n = 1000 observations
#>   alpha = -3.95788
#>   gamma = 2.80374
#>   L = 3.00607
#>   logLik = -835.636
#>   Shannon entropy = 0.835636
fit$entropy_variance()         # asymptotic variance of the entropy estimator
#> [1] 0.001158187
generics::tidy(fit)
#> # A tibble: 3 × 4
#>   term  estimate std.error fixed
#>   <chr>    <dbl>     <dbl> <lgl>
#> 1 alpha    -3.96     0.531 FALSE
#> 2 gamma     2.80     0.469 FALSE
#> 3 L         3.01     0.311 FALSE

# Polarimetric models
Sigma <- polsar_example_sigma("forest")
Z <- rg0p(500, alpha = -4, Sigma = Sigma, L = 4)
G0Polarimetric$new()$fit(Z, L = 4)$params$alpha
#> [1] -4.028688

Entropy maps and unsupervised segmentation

H <- entropy_map(img, model = "wishart", window = 7, L = 4)

set.seed(2)
seg <- EntropySegmenter$new(k = 3, method = "em")$fit(H)

op <- par(mfrow = c(1, 2))
plot_map(H, main = "Wishart entropy map")
plot_map(seg$label_map(), main = "Entropy-based segmentation",
         palette = c("#1f78b4", "#33a02c", "#e31a1c"))

par(op)

kappa_statistics(SanFrancisco150_gt, seg$label_map(), match = TRUE)
#> # 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

Divergence-based classification with tidymodels

library(parsnip)
library(workflows)
library(recipes)
library(yardstick)

feats <- sar_features(img, window = 5)
feats$class <- factor(as.vector(SanFrancisco150_gt),
                      labels = c("ocean", "vegetation", "urban"))
set.seed(3)
train <- feats[sample(nrow(feats), 450), ]

spec <- divergence_classifier(divergence = "renyi", order = 0.9) |>
  set_engine("wishart")

rec <- recipe(class ~ ., data = train) |>
  update_role(row, col, new_role = "id")

wf_fit <- workflow(rec, spec) |> fit(data = train)

pred <- augment(wf_fit, feats)
accuracy(pred, truth = class, estimate = .pred_class)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 accuracy multiclass     0.952

Entropy-based change detection

set.seed(4)
before <- matrix(rgammasar(60 * 60, mu = 1, L = 4), 60)
after <- before
after[21:40, 21:45] <- rgammasar(500, mu = 3, L = 4)

cd <- change_map(before, after, model = "gamma", window = 5, L = 4)
cd
#> <Entropy-based change map> model: gamma | level: 0.01 
#>   size: 60 x 60 
#>   changed pixels: 611 (16.97%)
plot_map(cd$change, main = "Detected changes")

Learn more

• vignette("SITSAR") — getting started;
• vignette("tidymodels", package = "SITSAR") — divergence-based classifiers with tidymodels;
• the package website: https://jodavid.github.io/SITSAR/.

References

• Ferreira, J. A., Coêlho, 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
• Ferreira, J. A. and Nascimento, A. D. C. (2020). Shannon entropy for the G_I⁰ model: a new segmentation approach. IEEE JSTARS, 13, 2547–2553. doi:10.1109/JSTARS.2020.2997666
• Ferreira, J. A., Nascimento, A. D. C. and Frery, A. C. (2022). PolSAR models with multimodal intensities. Remote Sensing, 14(20), 5083. doi:10.3390/rs14205083
• 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
• Ferreira, J. A. (2017). Classificadores induzidos de divergências para modelos vetoriais e para distribuição Wishart complexa: experimentos em imagens PolSAR. Master’s dissertation, UFPE.
• Ferreira, J. A. (2021). Entropias e somas compostas para matrizes estocásticas aplicadas a sistemas PolSAR. PhD thesis, UFPE.

Citation

citation("SITSAR")

Authors

• Jodavid Ferreira (author, maintainer) — ORCID 0000-0002-2131-6464
• Abraão Nascimento (author) — ORCID 0000-0003-2673-219X