{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/homebrew/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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KSoqSkpI0bdo0zZo1Sz169NCkSZP09NNPG0wOAAAAAAAAkxyWZVmmQwAAAAAAAAAA4IsYiQ4AAAAAAAAAQD0o0QEAAAAAAAAAqAclOgAAAAAAAAAA9aBEBwAAAAAAAACgHpToAAAAAAAAAADUgxIdAAAAAAAAAIB6UKIDAAAAAAAAAFAPSnQAAAAAAAAAAOpBiQ4AAAAAAAAAQD0o0QEAAAAAAAAAqAclOgAAAAAAAAAA9aBEBwAAAAAA+P/t2IEAAAAAgCB/6wk2KIwAYEh0AAAAAAAYEh0AAAAAAIZEBwAAAACAIdEBAAAAAGBIdAAAAAAAGBIdAAAAAACGRAcAAAAAgCHRAQAAAABgSHQAAAAAABgSHQAAAAAAhkQHAAAAAIAh0QEAAAAAYEh0AAAAAAAYEh0AAAAAAIZEBwAAAACAIdEBAAAAAGBIdAAAAAAAGBIdAAAAAACGRAcAAAAAgBGMFlriAAqhGAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1500x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([[232.81684404, 179.14242146, 151.2550065 ],\n",
       "        [ 56.39258329,  50.61123224,  50.13707249],\n",
       "        [161.76213056, 148.06510577, 138.44198216],\n",
       "        [159.66418273, 114.8403329 ,  94.65110157],\n",
       "        [213.9649401 , 224.58773784, 227.47947498],\n",
       "        [ 79.36101907,  72.43944133,  71.07109308],\n",
       "        [208.24316215, 149.80274909, 122.8746395 ],\n",
       "        [189.78405149, 181.83050071, 174.17050289],\n",
       "        [105.50647599,  95.72964853,  92.78961083],\n",
       "        [ 34.40065376,  28.55391866,  28.28026733]]),\n",
       " ['Warm',\n",
       "  'Neutral',\n",
       "  'Warm',\n",
       "  'Warm',\n",
       "  'Neutral',\n",
       "  'Neutral',\n",
       "  'Warm',\n",
       "  'Warm',\n",
       "  'Neutral',\n",
       "  'Neutral'],\n",
       " ['Undefined',\n",
       "  'Winter',\n",
       "  'Undefined',\n",
       "  'Undefined',\n",
       "  'Undefined',\n",
       "  'Winter',\n",
       "  'Undefined',\n",
       "  'Undefined',\n",
       "  'Winter',\n",
       "  'Winter'])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Color Cluster Details:\n",
      "Cluster 0:\n",
      "  RGB Color: [232.81684404 179.14242146 151.2550065 ]\n",
      "  Undertone: Warm\n",
      "  Seasonal Type: Undefined\n",
      "Cluster 1:\n",
      "  RGB Color: [56.39258329 50.61123224 50.13707249]\n",
      "  Undertone: Neutral\n",
      "  Seasonal Type: Winter\n",
      "Cluster 2:\n",
      "  RGB Color: [161.76213056 148.06510577 138.44198216]\n",
      "  Undertone: Warm\n",
      "  Seasonal Type: Undefined\n",
      "Cluster 3:\n",
      "  RGB Color: [159.66418273 114.8403329   94.65110157]\n",
      "  Undertone: Warm\n",
      "  Seasonal Type: Undefined\n",
      "Cluster 4:\n",
      "  RGB Color: [213.9649401  224.58773784 227.47947498]\n",
      "  Undertone: Neutral\n",
      "  Seasonal Type: Undefined\n",
      "Cluster 5:\n",
      "  RGB Color: [79.36101907 72.43944133 71.07109308]\n",
      "  Undertone: Neutral\n",
      "  Seasonal Type: Winter\n",
      "Cluster 6:\n",
      "  RGB Color: [208.24316215 149.80274909 122.8746395 ]\n",
      "  Undertone: Warm\n",
      "  Seasonal Type: Undefined\n",
      "Cluster 7:\n",
      "  RGB Color: [189.78405149 181.83050071 174.17050289]\n",
      "  Undertone: Warm\n",
      "  Seasonal Type: Undefined\n",
      "Cluster 8:\n",
      "  RGB Color: [105.50647599  95.72964853  92.78961083]\n",
      "  Undertone: Neutral\n",
      "  Seasonal Type: Winter\n",
      "Cluster 9:\n",
      "  RGB Color: [34.40065376 28.55391866 28.28026733]\n",
      "  Undertone: Neutral\n",
      "  Seasonal Type: Winter\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from PIL import Image\n",
    "import colorsys\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "def rgb_to_hsv(rgb):\n",
    "    \"\"\"Convert RGB to HSV color space.\"\"\"\n",
    "    return colorsys.rgb_to_hsv(rgb[0]/255.0, rgb[1]/255.0, rgb[2]/255.0)\n",
    "\n",
    "def classify_undertone(h, s, v):\n",
    "    \"\"\"\n",
    "    Classify skin undertones based on HSV color space.\n",
    "    This is a simplified approximation and should not be used for precise skin tone analysis.\n",
    "    \"\"\"\n",
    "    # Warm tones: more yellow/orange hues\n",
    "    # Cool tones: more blue/purple hues\n",
    "    # Neutral: closer to middle of hue spectrum\n",
    "    if 0.05 <= h <= 0.15:  # Warm orange-yellow range\n",
    "        return 'Warm'\n",
    "    elif 0.55 <= h <= 0.75:  # Cool blue-purple range\n",
    "        return 'Cool'\n",
    "    else:\n",
    "        return 'Neutral'\n",
    "\n",
    "def classify_seasonal_type(h, s, v):\n",
    "    \"\"\"\n",
    "    Classify seasonal color types based on HSV values.\n",
    "    This is a highly simplified approximation.\n",
    "    \"\"\"\n",
    "    if 0.05 <= h <= 0.15 and s > 0.5 and v > 0.5:\n",
    "        return 'Spring'\n",
    "    elif 0.15 <= h <= 0.35 and s < 0.5 and v > 0.5:\n",
    "        return 'Summer'\n",
    "    elif 0.35 <= h <= 0.55 and s > 0.5 and v > 0.5:\n",
    "        return 'Autumn'\n",
    "    elif (h <= 0.05 or h >= 0.75) and s < 0.3 and v < 0.5:\n",
    "        return 'Winter'\n",
    "    else:\n",
    "        return 'Undefined'\n",
    "\n",
    "def analyze_image_colors(image_path):\n",
    "    \"\"\"\n",
    "    Analyze colors in an image, create visualizations, and perform clustering.\n",
    "    \"\"\"\n",
    "    # Open and process the image\n",
    "    img = Image.open(image_path)\n",
    "    img = img.convert('RGB')\n",
    "    \n",
    "    # Convert image to numpy array\n",
    "    img_array = np.array(img)\n",
    "    \n",
    "    # Reshape the image to be a list of pixels\n",
    "    pixels = img_array.reshape(-1, 3)\n",
    "    \n",
    "    # Perform K-means clustering\n",
    "    kmeans = KMeans(n_clusters=10, random_state=42)\n",
    "    kmeans.fit(pixels)\n",
    "    \n",
    "    # Get cluster centers and labels\n",
    "    colors = kmeans.cluster_centers_\n",
    "    labels = kmeans.labels_\n",
    "    \n",
    "    # Convert RGB to HSV for further analysis\n",
    "    hsv_colors = np.array([rgb_to_hsv(color) for color in colors])\n",
    "    \n",
    "    # Classify undertones and seasonal types\n",
    "    undertones = [classify_undertone(h, s, v) for h, s, v in hsv_colors]\n",
    "    seasonal_types = [classify_seasonal_type(h, s, v) for h, s, v in hsv_colors]\n",
    "    \n",
    "    # Visualizations\n",
    "    plt.figure(figsize=(15, 10))\n",
    "    \n",
    "    # 1. Color Gradient Plot (Improved)\n",
    "    plt.subplot(2, 2, 1)\n",
    "    # Sort colors by luminance (brightness)\n",
    "    luminance = np.dot(colors, [0.299, 0.587, 0.114])\n",
    "    sorted_indices = np.argsort(luminance)\n",
    "    sorted_colors = colors[sorted_indices] / 255.0\n",
    "    \n",
    "    # Create a gradient image\n",
    "    gradient = np.linspace(0, 1, len(sorted_colors)).reshape(1, -1)\n",
    "    plt.imshow(sorted_colors[np.newaxis, :], aspect='auto', extent=[0, 1, 0, 1])\n",
    "    plt.title('Color Gradient (Sorted by Luminance)')\n",
    "    plt.xlabel('Color Progression')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    \n",
    "    # 2. Color Bar Plot\n",
    "    plt.subplot(2, 2, 2)\n",
    "    cluster_counts = np.unique(labels, return_counts=True)[1]\n",
    "    plt.bar(range(len(colors)), cluster_counts, color=colors/255)\n",
    "    plt.title('Color Distribution')\n",
    "    plt.xlabel('Cluster')\n",
    "    plt.ylabel('Pixel Count')\n",
    "    \n",
    "    # 3. Pie Chart of Undertones\n",
    "    plt.subplot(2, 2, 3)\n",
    "    undertone_counts = np.unique(undertones, return_counts=True)\n",
    "    plt.pie(undertone_counts[1], labels=undertone_counts[0], autopct='%1.1f%%')\n",
    "    plt.title('Undertone Distribution')\n",
    "    \n",
    "    # 4. Pie Chart of Seasonal Types\n",
    "    plt.subplot(2, 2, 4)\n",
    "    seasonal_counts = np.unique(seasonal_types, return_counts=True)\n",
    "    plt.pie(seasonal_counts[1], labels=seasonal_counts[0], autopct='%1.1f%%')\n",
    "    plt.title('Seasonal Type Distribution')\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    \n",
    "    # Print detailed color information\n",
    "    print(\"\\nColor Cluster Details:\")\n",
    "    for i, (color, undertone, season) in enumerate(zip(colors, undertones, seasonal_types)):\n",
    "        print(f\"Cluster {i}:\")\n",
    "        print(f\"  RGB Color: {color}\")\n",
    "        print(f\"  Undertone: {undertone}\")\n",
    "        print(f\"  Seasonal Type: {season}\")\n",
    "    \n",
    "    return colors, undertones, seasonal_types\n",
    "\n",
    "# Example usage\n",
    "# Replace 'path/to/your/image.jpg' with the actual path to your image\n",
    "analyze_image_colors('./eeman.jpg')"
   ]
  }
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