Transition Graphs for SAR Image Texture Characterization - Visualization and Results of Experiments

Pacotes e códigos auxiliares

if(!require(plotly)){
  install.packages("plotly")
  require(plotly)
}
if(!require(ggplot2)){
  install.packages("ggplot2")
  require(ggplot2)
} 
if(!require(ggrepel)){
  install.packages("ggrepel")
  require(ggrepel)
} 
if(!require(ggthemes)){
  install.packages("ggthemes")
  require(ggthemes)
} 
if(!require(rgl)){
  install.packages("rgl")
  require(rgl)
} 
source('plot_PCA.R')
source('White_Noise_Mixture.R')
source('theory_information.R')

theme_set(theme_clean(base_size = 20, base_family = "sans"))

rainbow_colors = palette(c("#fca311",#amarelo
                           "#000000", #preto
                           "#ff006e", #rosa
                           "#40916c", #verde
                           "#6a040f", #vermelho
                           "#eb5e28", #laranja
                           "#6a4c93", #roxo
                           "#50514f", #cinza
                           "#5e3023", #marrom
                           "#3f88c5", #azul
                           "#60d394"))

Estrutura espacial dos pontos

O objetivo deste experimento consiste em obter uma visão global da variação das bandas de intensidade no momento da caracterização de texturas no plano HC. Uma vez que sabemos que o uso de \(\tau = 1\) nos fornece uma maior separabilidade entre as classes, abaixo fornecemos tais análises apenas variando a dimensão \(D\) dos embeddings.

Para representar as bandas de intensidade (que são variáveis categóricas) no plot tridimensional realizamos o encoding de tal forma que:

• Band = 1, equivale aos dados obtidos pela banda HH de intensidade,

• Band = 2, equivale aos dados obtidos pela banda HV de intensidade,

• Band = 3, equivale aos dados obtidos pela banda VV de intensidade.

# Bandt-Pompe parameters -------------------------------------------------------
D = 3
Tau = 1

# WATG results -----------------------------------------------------------------
hc_hh = read.csv(file = paste0("../Data/WATG_HHHH_D", D, "T", Tau, ".csv"), header = TRUE, sep = ",")
hc_hv = read.csv(file = paste0("../Data/WATG_HVHV_D", D, "T", Tau, ".csv"), header = TRUE, sep = ",")
hc_vv = read.csv(file = paste0("../Data/WATG_VVVV_D", D, "T", Tau, ".csv"), header = TRUE, sep = ",")

hc_df = data.frame(H = c(rbind(hc_hh$V1, hc_hv$V1, hc_vv$V1)),
                   C = c(rbind(hc_hh$V2, hc_hv$V2, hc_vv$V2)),
                   Classes = c(rep('Forest', 120), rep('Ocean', 240), rep('Urban', 120), rep('Pasture', 120)),
                   Band = rep(c(1, 2, 3), 200))

# Cotas and Trozos -------------------------------------------------------------
c1x = readingMPR(factorial(D)^2, 1)
c1y = readingMPR(factorial(D)^2, 2)
c2x = readingMPR(factorial(D)^2, 3)
c2y = readingMPR(factorial(D)^2, 4)

cx = c(c1x, c2x)
cy = c(c1y, c2y)

cotas = data.frame("cx" = c(cx[1:124364], cx[1:124364], cx[1:124364]), 
                   "cy" = c(cy[1:124364], cy[1:124364], cy[1:124364]),
                   Band = c(rep(1, length(cx)*3 - 1), rep(2, length(cx)*3 - 1), rep(3, length(cx)*3 - 1)))

# Plot without add limits in axes ----------------------------------------------
fig <- plot_ly() %>%  
  add_trace(data = cotas, x = ~cx, y = ~cy, z = ~Band, type = 'scatter3d', mode = 'lines', line = list(color= 'rgba(169, 169, 169, 0.8)', width = 4)) %>% 
  add_trace(data = hc_df, x = ~H, y = ~C, z = ~Band, type = 'scatter3d', mode = 'lines+markers', 
            line = list(width = 1),
            marker = list(size = 3),
            color = ~Classes, colors = c('#3F84E5', '#B20D30', '#3F784C', '#EFCD4A')) %>% 
  layout(scene = list(xaxis = list(title = 'H'), 
                      yaxis = list(title = 'C'), 
                      zaxis = list(title = '',
                      ticktext = list("HH", "HV", "VV"), 
                      tickvals = list(1, 2, 3),
                      tickmode = "array")))
fig

# Plot with limits in axes -----------------------------------------------------
fig <- plot_ly() %>%  
  add_trace(data = cotas, x = ~cx, y = ~cy, z = ~Band, type = 'scatter3d', mode = 'lines', line = list(color= 'rgba(169, 169, 169, 0.85)', width = 4)) %>% 
  add_trace(data = hc_df, x = ~H, y = ~C, z = ~Band, type = 'scatter3d', mode = 'lines+markers', 
            line = list(width = 1),
            marker = list(size = 3),
            color = ~Classes, colors = c('#3F84E5', '#B20D30', '#3F784C', '#EFCD4A')) %>% 
  layout(scene = list(xaxis = list(title = 'H', range = c(min(hc_df$H), max(hc_df$H))),
                      yaxis = list(title = 'C', range = c(min(hc_df$C), max(hc_df$C))),
                      zaxis = list(title = '',
                      ticktext = list("HH", "HV", "VV"), 
                      tickvals = list(1, 2, 3),
                      tickmode = "array")))
fig

Misturas de patches homogêneos com ruídos

Neste experimento estudamos o comportamento do ponto emblemático característico da classe de regiões urbanas quando temos \(D = 6\) e \(\tau = 1\).

hh_horizontal_vertical = read.csv('../Data/hh_horizontal_vertical.csv')

ggplot(data = hh_horizontal_vertical, aes(x = H, y = C)) +
      geom_point(size = 1.5, alpha = .4) + 
      geom_point(data = hh_horizontal_vertical[1,], aes(x = H, y = C), size = 1.5, alpha = .4, color = "red") + 
      geom_label_repel(aes(label = paste("Delta ==", Steps)), parse = TRUE, segment.size = 0.5, min.segment.length = 0, force = 18) +
      scale_color_manual(values = rainbow_colors) +
      ggtitle('HHHH, Horizontal and vertical') + 
      xlab(expression(italic(H))) + ylab(expression(italic(C))) +
      theme(plot.title = element_text(hjust = 0.5), legend.position = "none")

hv_horizontal_vertical = read.csv('../Data/hv_horizontal_vertical.csv')

ggplot(data = hv_horizontal_vertical, aes(x = H, y = C)) +
      geom_point(size = 1.5, alpha = .4) + 
      geom_point(data = hv_horizontal_vertical[1,], aes(x = H, y = C), size = 1.5, alpha = .4, color = "red") + 
      geom_label_repel(aes(label = paste("Delta ==", Steps)), parse = TRUE, segment.size = 0.5, min.segment.length = 0, force = 18) +
      scale_color_manual(values = rainbow_colors) +
      xlab(expression(italic(H))) + ylab(expression(italic(C))) +
      ggtitle('HVHV, Horizontal and vertical') + 
      theme(plot.title = element_text(hjust = 0.5), legend.position = "none")

vv_horizontal_vertical = read.csv('../Data/vv_horizontal_vertical.csv')

ggplot(data = vv_horizontal_vertical, aes(x = H, y = C)) +
      geom_point(size = 1.5, alpha = .4) + 
      geom_point(data = vv_horizontal_vertical[1,], aes(x = H, y = C), size = 1.5, alpha = .4, color = "red") + 
      geom_label_repel(aes(label = paste("Delta ==", Steps)), parse = TRUE, segment.size = 0.5, min.segment.length = 0, force = 18) +
      scale_color_manual(values = rainbow_colors) +
      xlab(expression(italic(H))) + ylab(expression(italic(C))) +
      ggtitle('VVVV, Horizontal and vertical') + 
      theme(plot.title = element_text(hjust = 0.5), legend.position = "none")

Analisando as sequências produzidas pelas misturas

p = plot.ts.mixtures('HHHH')

HHHH - i: 1 of 9
HHHH - i: 2 of 9
HHHH - i: 3 of 9
HHHH - i: 4 of 9
HHHH - i: 5 of 9
HHHH - i: 6 of 9
HHHH - i: 7 of 9
HHHH - i: 8 of 9
HHHH - i: 9 of 9

print(p)

p = plot.ts.mixtures('HVHV')
print(p)

p = plot.ts.mixtures('VVVV')
print(p)

Analisando os histogramas produzidos pelas misturas

p = plot.hist.mixtures('HHHH')
print(p)

p = plot.hist.mixtures('HVHV')
print(p)

p = plot.hist.mixtures('VVVV')
print(p)