From 80b38f059227125bf8bdf7aa54f00d63d08e418c Mon Sep 17 00:00:00 2001 From: Arthur DANJOU Date: Thu, 15 Jan 2026 10:45:54 +0100 Subject: [PATCH] Edit TP2 --- M2/Clustering In Practice/compression_image.R | 111 +++++++++++++++++- .../compression_image_poissons.R | 105 +++++++++++++++++ M2/Clustering In Practice/data/Guppy 2.jpeg | Bin 0 -> 862136 bytes 3 files changed, 215 insertions(+), 1 deletion(-) create mode 100644 M2/Clustering In Practice/compression_image_poissons.R create mode 100644 M2/Clustering In Practice/data/Guppy 2.jpeg diff --git a/M2/Clustering In Practice/compression_image.R b/M2/Clustering In Practice/compression_image.R index f89dd10..2bfa38f 100644 --- a/M2/Clustering In Practice/compression_image.R +++ b/M2/Clustering In Practice/compression_image.R @@ -22,7 +22,7 @@ head(img_matrix) # 2. Application de l'algorithme K-means # Choix du nombre de couleurs (k) -k <- 12 +k <- 8 # Application de K-means # On augmente iter.max car la convergence sur des milliers de pixels peut être lente @@ -55,12 +55,121 @@ title(paste("Compressée (k =", k, ")")) # l'image compressée : # Plus $k$ est petit, plus le résumé est ..., plus le MSE ..... +library(imager) + + +mse_imager <- function(img1, img2) { + # Harmoniser dimensions (recadrage ou redimensionnement si besoin) + if (!all(dim(img1) == dim(img2))) { + # Ici, on redimensionne img2 sur la taille d'img1 + img2 <- imresize(img2, size_x = width(img1), size_y = height(img1)) + if (spectrum(img2) != spectrum(img1)) { + img2 <- grayscale(img2) # fallback simple si nb de canaux diffère + img1 <- grayscale(img1) + } + } + # Convertir en vecteurs numériques [0,1] + x <- as.numeric(img1) + y <- as.numeric(img2) + mean((x - y)^2) +} + + +mse_val <- mse_imager(img, img_compressed) +cat("MSE =", mse_val, "\n") + +mse_matrix <- mean((img_matrix - img_compressed_matrix)^2) +cat("MSE =", mse_matrix, "\n") + +######################################################################## + + + + + # Règle du coude (Elbow Method) # tracez l'évolution de la Within-Cluster Sum of Squares (WCSS) en fonction de $k$ # Prnde k = 2 à 32 # A partir de quel $k$ le gain visuel devient-il négligeable pour l'œil humain ? + +# X : matrice/df n x d +# ks : valeurs de k à tester (par défaut 1:10) +elbow_wss <- function(X, ks = 2:32, nstart = 10, scale_data = FALSE) { + X <- as.matrix(X) + if (scale_data) { + X <- scale(X) + } + wss <- numeric(length(ks)) + + # Cas k = 1 : WSS = TSS (variance totale) + total_ss <- sum(scale(X, scale = FALSE)^2) # TSS + for (i in seq_along(ks)) { + k <- ks[i] + cat(" k =", k, "\n") + if (k == 1) { + wss[i] <- total_ss + } else { + set.seed(123) # reproductible + km <- kmeans(X, centers = k, nstart = nstart, iter.max = 100) + wss[i] <- km$tot.withinss + } + } + + plot(ks, wss, type = "b", pch = 19, xlab = "Nombre de clusters (k)", + ylab = "Inertie intra-classe (WSS)", + main = "Méthode du coude (k-means)") + grid() +# invisible(data.frame(k = ks, WSS = wss)) +} + +# Exemple d'utilisation : + res <- elbow_wss(img_compressed, ks = 2:32, nstart = 20, scale_data = FALSE) + +############################################################################### + + elbow_wss_safe <- function(X, ks = 2:32, nstart = 20, scale_data = FALSE, seed = 123) { + X <- as.matrix(X) + if (scale_data) X <- scale(X) + set.seed(seed) + + # Nombre de lignes distinctes + n_unique <- nrow(unique(X)) + if (n_unique < 2) stop("Moins de 2 points distincts : k-means n'a pas de sens.") + + # Tronquer ks si nécessaire + ks <- ks[ks <= n_unique] + if (length(ks) == 0) stop("Tous les k demandés dépassent le nombre de points distincts.") + + wss <- numeric(length(ks)) + # TSS (k = 1) + total_ss <- sum(scale(X, scale = FALSE)^2) + + for (i in seq_along(ks)) { + k <- ks[i] + cat(" k =", k, "\n") + if (k == 1) { + wss[i] <- total_ss + } else { + km <- kmeans(X, centers = k, nstart = nstart, iter.max = 100) + wss[i] <- km$tot.withinss + } + } + + plot(ks, wss, type = "b", pch = 19, xlab = "Nombre de clusters (k)", + ylab = "Inertie intra-classe (WSS)", main = "Méthode du coude (k-means)") + axis(1, at = ks) + grid() +# invisible(data.frame(k = ks, WSS = wss)) + } + + # Exemple : + res <- elbow_wss_safe(img_compressed, ks = 2:32, nstart = 20) + + + + # Taille de stockage # Ouvrir un fichier JPG jpeg("./data/image_compressed.jpg") diff --git a/M2/Clustering In Practice/compression_image_poissons.R b/M2/Clustering In Practice/compression_image_poissons.R new file mode 100644 index 0000000..6276b9a --- /dev/null +++ b/M2/Clustering In Practice/compression_image_poissons.R @@ -0,0 +1,105 @@ +# Objectifs pédagogiques +# Comprendre la représentation matricielle d'une image. +# Interpréter les centroïdes comme une palette de couleurs optimale (résumé). +# Analyser le compromis entre distorsion (perte de qualité) et taux de compression. + +library(jpeg) + +# 1. Chargement de l'image + + +img <- readJPEG("./data/Guppy 2.jpeg") + +# Dimensions +dims <- dim(img) +dims + +# Reshaping : Transformation en matrice (Pixels x 3 canaux) +# Chaque ligne est une observation dans R^3 +img_matrix <- matrix(img, ncol = 3) +colnames(img_matrix) <- c("R", "G", "B") + +head(img_matrix) + +# 2. Application de l'algorithme K-means +# Choix du nombre de couleurs (k) +k <- 10 + +# Application de K-means +# On augmente iter.max car la convergence sur des milliers de pixels peut être lente +set.seed(123) +km_model <- kmeans(img_matrix, centers = k, iter.max = 20, nstart = 3) + +# Les "résumés" de l'information (les centres des clusters) +palette_optimale <- km_model$centers +print(palette_optimale) + +# 3. Reconstruction de l'image compressée +# Associer chaque pixel à son centroïde +img_compressed_matrix <- palette_optimale[km_model$cluster, ] + +# Re-transformer la matrice en Array 3D +img_compressed <- array(img_compressed_matrix, dim = dims) + +# Affichage comparatif +par(mfrow = c(1, 2), mar = c(1, 1, 1, 1)) +plot(0, 0, type='n', axes=FALSE, ann=FALSE) +rasterImage(img, -1, -1, 1, 1) +title("Originale (Millions de couleurs)") + +plot(0, 0, type='n', axes=FALSE, ann=FALSE) +rasterImage(img_compressed, -1, -1, 1, 1) +title(paste("Compressée (k =", k, ")")) + +# 4. Questions : coût de l'information (Distorsion) +# Calculez l'erreur quadratique moyenne (MSE) entre l'image originale et +# l'image compressée : +# Plus $k$ est petit, plus le résumé est ..., plus le MSE ..... + +# Règle du coude (Elbow Method) +# tracez l'évolution de la Within-Cluster Sum of Squares (WCSS) en fonction de $k$ +# Prnde k = 2 à 32 +# A partir de quel $k$ le gain visuel devient-il négligeable pour l'œil humain ? + +# Taille de stockage +# Ouvrir un fichier JPG +jpeg("./data/image_compressed.jpg") + +# Afficher l'image compressée dans le fichier +plot(0, 0, type='n', axes=FALSE, ann=FALSE) +rasterImage(img_compressed, -1, -1, 1, 1) + +info <- file.info("./data/Guppy 2.jpeg") +(taille_octets_reelle <- info$size/1024) + +info <- file.info("./data/image_compressed.jpg") +(taille_octets_compresse <- info$size/1024) + + +library(colordistance) + +repertoire <- "poissons" + +clusters <- colordistance::getHistList(repertoire, lower = NULL, upper = NULL) +names(clusters) + +kmeans_fits <- getKMeansList(repertoire, bins = 3, plotting = TRUE) + +centroids_list <- extractClusters(kmeans_fits, ordering = TRUE) + +emd_distance_matrix <- getColorDistanceMatrix(centroids_list, method = "color.dist", ordering = TRUE) + +colordistance::imageClusterPipeline(repertoire, cluster.method = "hist") + +clusters + + + + + + + + + + + diff --git a/M2/Clustering In Practice/data/Guppy 2.jpeg b/M2/Clustering In Practice/data/Guppy 2.jpeg new file mode 100644 index 0000000000000000000000000000000000000000..812b1396c2de88de8371d22542efab1a4aa40063 GIT binary patch literal 862136 zcmW(+2|UyP|KHq4EICS;q(YIRoZDQLl#GNBxfkZjH8YyfN^(RZ*&LyAUy~yyU-z+z zTnls0m0`K7|L6Dj*d89+!{g(#_vih2zMj`!n41|337ixFfj~kgH?Q3VfjHqH5SYrx z1H2PfQf&tO0tenTHUyRSOD_R0xKIXn3_zfYM8QL6Zs0Y)|4rLK5a?LY|DNDU4_OQd z^e^A!n!!DcWAC4NlC(|QuLy-}9#${9h9-ErTs(lEG-Zz)J+Iv}+&xx9W=$b%mh_j6 zy^i6nhT%zFHMOE!mErZ&x`z))G2QX;@kj1Yjq8S_4wtFY+l6j*X{4w~-6jWHj*(Mj zGB1z=Z?}c`oUOOguz~CT)~s~3j2*E?OO4fkS{`exF#JsRG}Bqf%S>Bv38lO^y(_#%+Q*#g$Xz01bMZD zJ{;jg_Ic9aqep8c%P{ZkCpF0(9E@8d^&Cg^JU~=PrOyHJdDv^%b>hW2Nk`*tL@O!= zJ-JowGyW&l=jZPasMdZ3^q&L+vhRVueS;6aWMX`3_`l-G?^J7_U)~oqw#oBS*s<@y zaP(!{YZAq4(kpbyL%s2t zi@$3+cEeO*@YaWKf8y!ygc2n+uF6|U>Ez$Nsa+tZR@3X{bRM1v!+_x~C{ze;~t zG41vr$FG#+Zd^gf+DC4jgrtnR2V(15d%tQ}d*90Y4VWHr#PojlJ@m}C&v)#^)G`j_ z#3K{WPlp6_4qbPrRvQ*5U!>2Sb@P6xO>8opL-?Pb${fXm%U3wrk=(gLd#sUMg^KOz)2EC83snQSO zrkP9BamN|;+Zw@vUFWKrrJ9MqomIA)pSd^1&DU4DweDSPwW(~nye^-|CX6X769GlLwz9R|`EZ|EmhU=kv>KA;7OsVyy?wztym+|HE4P^Z2a=SMjZ? zg`1uAdG2)o_kVtEyhaW3Z#OF#k>8&#>>K`-rplltxu}^4M}
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