From 9452e42623f709833e538d90977e2aa7ec7b7567 Mon Sep 17 00:00:00 2001 From: Arthur DANJOU Date: Wed, 14 Jan 2026 23:32:34 +0100 Subject: [PATCH] Add TP2 --- M2/Clustering In Practice/compression_image.R | 76 ++++++++++++++++++ .../data/PampasGrass.jpg | Bin 0 -> 261031 bytes .../data/image_compressed.jpg | Bin 0 -> 49813 bytes 3 files changed, 76 insertions(+) create mode 100644 M2/Clustering In Practice/compression_image.R create mode 100644 M2/Clustering In Practice/data/PampasGrass.jpg create mode 100644 M2/Clustering In Practice/data/image_compressed.jpg diff --git a/M2/Clustering In Practice/compression_image.R b/M2/Clustering In Practice/compression_image.R new file mode 100644 index 0000000..f89dd10 --- /dev/null +++ b/M2/Clustering In Practice/compression_image.R @@ -0,0 +1,76 @@ +# 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/PampasGrass.jpg") + +# 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 <- 12 + +# 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/PampasGrass.jpg") +(taille_octets_reelle <- info$size/1024) + +info <- file.info("./data/image_compressed.jpg") +(taille_octets_compresse <- info$size/1024) diff --git a/M2/Clustering In Practice/data/PampasGrass.jpg b/M2/Clustering In Practice/data/PampasGrass.jpg new file mode 100644 index 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