file..ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import keras\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras.layers import Input\n",
    "from keras.utils import to_categorical\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from keras.datasets import mnist\n",
    "\n",
    "\n",
    "(X_train, y_train), (X_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x14fa88be750>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(X_train[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# flatten images into one-dimensional vector\n",
    "\n",
    "num_pixels = X_train.shape[1] * X_train.shape[2] \n",
    "\n",
    "X_train = X_train.reshape(X_train.shape[0], num_pixels).astype('float32') \n",
    "X_test = X_test.reshape(X_test.shape[0], num_pixels).astype('float32') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalize inputs from 0-255 to 0-1\n",
    "X_train = X_train / 255\n",
    "X_test = X_test / 255"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "# one hot encode outputs\n",
    "y_train = to_categorical(y_train)\n",
    "y_test = to_categorical(y_test)\n",
    "\n",
    "num_classes = y_test.shape[1]\n",
    "print(num_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define classification model\n",
    "def classification_model():\n",
    "    # create model\n",
    "    \n",
    "    model = Sequential()\n",
    "    model.add(Input(shape=(num_pixels,)))\n",
    "    model.add(Dense(num_pixels, activation='relu'))\n",
    "    model.add(Dense(100, activation='relu'))\n",
    "    model.add(Dense(num_classes, activation='softmax'))\n",
    "    \n",
    "    \n",
    "    # compile model\n",
    "    model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      "1875/1875 - 11s - 6ms/step - accuracy: 0.9439 - loss: 0.1869 - val_accuracy: 0.9685 - val_loss: 0.1047\n",
      "Epoch 2/10\n",
      "1875/1875 - 12s - 7ms/step - accuracy: 0.9755 - loss: 0.0789 - val_accuracy: 0.9717 - val_loss: 0.0909\n",
      "Epoch 3/10\n",
      "1875/1875 - 13s - 7ms/step - accuracy: 0.9832 - loss: 0.0532 - val_accuracy: 0.9799 - val_loss: 0.0668\n",
      "Epoch 4/10\n",
      "1875/1875 - 10s - 5ms/step - accuracy: 0.9873 - loss: 0.0401 - val_accuracy: 0.9804 - val_loss: 0.0639\n",
      "Epoch 5/10\n",
      "1875/1875 - 14s - 8ms/step - accuracy: 0.9904 - loss: 0.0302 - val_accuracy: 0.9796 - val_loss: 0.0732\n",
      "Epoch 6/10\n",
      "1875/1875 - 9s - 5ms/step - accuracy: 0.9919 - loss: 0.0262 - val_accuracy: 0.9807 - val_loss: 0.0814\n",
      "Epoch 7/10\n",
      "1875/1875 - 9s - 5ms/step - accuracy: 0.9930 - loss: 0.0217 - val_accuracy: 0.9800 - val_loss: 0.0872\n",
      "Epoch 8/10\n",
      "1875/1875 - 10s - 5ms/step - accuracy: 0.9934 - loss: 0.0204 - val_accuracy: 0.9787 - val_loss: 0.0950\n",
      "Epoch 9/10\n",
      "1875/1875 - 14s - 8ms/step - accuracy: 0.9938 - loss: 0.0180 - val_accuracy: 0.9820 - val_loss: 0.0873\n",
      "Epoch 10/10\n",
      "1875/1875 - 17s - 9ms/step - accuracy: 0.9955 - loss: 0.0146 - val_accuracy: 0.9737 - val_loss: 0.1241\n"
     ]
    }
   ],
   "source": [
    "#it takes time\n",
    "model = classification_model()\n",
    "\n",
    "\n",
    "model.fit(X_train, y_train, validation_data=(X_test, y_test), epochs=10, verbose=2)\n",
    "\n",
    "\n",
    "scores = model.evaluate(X_test, y_test, verbose=0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9736999869346619% \n",
      " Error: 0.026300013065338135\n"
     ]
    }
   ],
   "source": [
    "print('Accuracy: {}% \\n Error: {}'.format(scores[1], 1 - scores[1]))      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.save('classification_model.keras')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pretrained_model = keras.saving.load_model('classification_model.keras')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def preprocess_custom_image(image_path):\n",
    "    # Load and convert to grayscale\n",
    "    img = Image.open(image_path).convert('L') \n",
    "    \n",
    "    img = img.resize((28, 28))\n",
    "   \n",
    "    img_array = np.array(img)\n",
    "   \n",
    "    img_array = 255 - img_array\n",
    "    \n",
    "    # Normalize pixel values to [0, 1]\n",
    "    img_array = img_array / 255.0\n",
    "    \n",
    "    # Flatten to match model input shape\n",
    "    img_array = img_array.reshape(1, -1)  # Shape: (1, 784)\n",
    "    \n",
    "    return img_array\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m1/1\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 41ms/step\n",
      "The model predicts the digit is: 5\n"
     ]
    }
   ],
   "source": [
    "\n",
    "image_path = \"555.png\"\n",
    "custom_image = preprocess_custom_image(image_path)\n",
    "\n",
    "prediction = model.predict(custom_image)\n",
    "predicted_class = np.argmax(prediction)\n",
    "\n",
    "print(f\"The model predicts the digit is: {predicted_class}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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t21er4y4AoOnZs2fPWb8cMeIC6MzvGkFkO9t/NvWx6YaM5svmUw7Om2o6zvV+3mjHgObPn6/OnTsrLi5OOTk5ev/9989ruabwsVtUVFTYt0hej61Irw+RrzluQzbPqTmOg3Tu9/NGCaA//OEPmjVrlh566CF9+OGH6tevn/Ly8vjiKABAUKNcB5STk6PLL7882LG3pqZGGRkZuvPOO3X//fefddlAIBDy9cKRyKuPDSL944n6vpzsbE6ePNkIlaCpao4f43q1d9IUPoosLy8PfoNvXRp8D6iqqkqbNm0K+SKtFi1aKDc3V+vWras1f2VlpQKBQMgNAND8NXgAffXVVzp58qRSUlJCpqekpKi0tLTW/IWFhfL7/cEbZ8ABwHeD8wtR58yZo/Ly8uBtz549rksCAHigwU/DbteunaKjo1VWVhYyvaysrM6vUfb5fPL5fA1dBgAgwjX4HlBsbKwGDBigVatWBafV1NRo1apVGjRoUEOvDgDQRDXKhaizZs1Sfn6+LrvsMg0cOFBPPPGEKioqNGXKlMZYHQCgCWqUAJo4caK+/PJLPfjggyotLVX//v21fPnyWicmAAC+uyLu+4CawnVANry63sHLK6RtNp2WLcP/n8fm2qEI26zRgLy8Pi6Sr1OK9L91ycF1QAAAnA8CCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAONEo3bCbO5smgDYNCqOjo8NexqZxp03DRcmuQSGNRXGmSN/GvWr46WWD1UjCHhAAwAkCCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAOEEAAQCcoBu2BZsutF51/bXpqmuzHi/ZjLdXXYxxYSL9tbVZV6Rve5HUeZs9IACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwgmakHrFp+NmyZfgvT3V1ddjL2DYjtWmwaiPSmzsCsMMeEADACQIIAOAEAQQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QTNSCzExMWEvY9Mk9MSJE2EvY1Pb8ePHw17Glk1jUZtljDFhLwPv2TS0tWme26KF3f/aXtXnZcPdSPrbYA8IAOAEAQQAcKLBA+jhhx9WVFRUyC0rK6uhVwMAaOIa5RhQ7969tXLlyv9bicUXqwEAmrdGSYaWLVsqNTW1MR4aANBMNMoxoB07dig9PV1dunTRTTfdpN27d9c7b2VlpQKBQMgNAND8NXgA5eTkaNGiRVq+fLkWLFigkpISXXHFFTpy5Eid8xcWFsrv9wdvGRkZDV0SACACRZlGPin88OHD6tSpkx5//HFNnTq11v2VlZWqrKwM/h4IBCI+hLy6DsiGzfE22+uAbK6R4DognCnSrwOy2fa8ug6oKWzj5eXlSkxMrPf+Rj87oE2bNurRo4d27txZ5/0+n08+n6+xywAARJhGvw7o6NGj2rVrl9LS0hp7VQCAJqTBA+iee+5RUVGRPvvsM/3v//6vrrnmGkVHR+vGG29s6FUBAJqwBv8Ibu/evbrxxht18OBBtW/fXkOGDNH69evVvn37hl4VAKAJa/STEMIVCATk9/tdl9HgIvkgo+16bJazOYHD5qAumi8v/5ZsTl6oqamxWle4mkID03OdhEAvOACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwotG/kK458rIJYCTz6tsibb7l9cSJE2EvA+9FcrNP23V59f4QYX2krbAHBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACfohm3BpgutVx1yo6Ojw17GpkO17bps2NbnlUjufmz7Gnk15l51m7Z9jWzqi+T3B8nb94hzYQ8IAOAEAQQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QQABAJygGakFr5oh2jQ19LJhpY0WLcL/n8emIaTNemzXZTPmNvXZrMfLRq5evbY2f0s267HlVbPPSG80ez7YAwIAOEEAAQCcIIAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJ2hGasGrJqE2bJou2jYntGmGGMnjIEmxsbFhL1NVVRX2MtXV1WEv41WzT1u2DWDD5WVT1pYtvXmLtGmwavucImk7Yg8IAOAEAQQAcCLsAFq7dq3Gjh2r9PR0RUVF6bXXXgu53xijBx98UGlpaWrVqpVyc3O1Y8eOhqoXANBMhB1AFRUV6tevn+bPn1/n/Y899piefPJJPfPMM9qwYYPi4+OVl5en48ePX3CxAIDmI8pcwFHhqKgoLV26VOPHj5d0au8nPT1ds2fP1j333CNJKi8vV0pKihYtWqQbbrjhnI8ZCATk9/ttS4KFEydOWC1ncxKCV98EasurkxBsDiBH0sHjunASgj2bkxBsebkdlZeXKzExsf5arB61HiUlJSotLVVubm5wmt/vV05OjtatW1fnMpWVlQoEAiE3AEDz16ABVFpaKklKSUkJmZ6SkhK879sKCwvl9/uDt4yMjIYsCQAQoZyfBTdnzhyVl5cHb3v27HFdEgDAAw0aQKmpqZKksrKykOllZWXB+77N5/MpMTEx5AYAaP4aNIAyMzOVmpqqVatWBacFAgFt2LBBgwYNashVAQCauLBP8Th69Kh27twZ/L2kpERbtmxRUlKSOnbsqJkzZ+oXv/iFunfvrszMTD3wwANKT08PnikHAIBkEUAbN27Uj370o+Dvs2bNkiTl5+dr0aJFuvfee1VRUaFbb71Vhw8f1pAhQ7R8+XLFxcU1XNUAgCbvgq4DagxN4Togm3P2bZaxOffeq/VIdtcPxcTEhL2MzXOyvbbJq/GzuRbDy2tFbNhcbG7zj6lX423L5pojm+vPvLzGy5an1wEBAHC+CCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACQIIAOAEAQQAcCLsr2OAZNNA3Kum417W1rKlN5tPpHf9XbJkSdjLTJw4sREqqc22C7TNmNt0trbpoB0dHR32MjYdqiW7cbCpz+Zv0LY7uk19tt3lz4U9IACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwgmakFmJjY8NepqqqqhEqqc2m0aBts0+bZoheNWW1bdTo1XPyaj22421Tn01j0Uhn08zVpvGpV38XUuM1FrXBHhAAwAkCCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAOEEzUgteNRb1qhGiTQNTL9k0xmzZ0m7TtmnUaPM62TSA9Wo9tuvyqqGmzTbuJZuxs1nG9u+2urraarnGwB4QAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwggACADhBM1KP2DTUtGkkadOE07a5o00zRK8an9o0FZW8bfgZLptmn7bjbbNN2IydDZvx9nIcbOrzaplIwx4QAMAJAggA4ETYAbR27VqNHTtW6enpioqK0muvvRZy/+TJkxUVFRVyGzlyZEPVCwBoJsIOoIqKCvXr10/z58+vd56RI0dq//79wdtLL710QUUCAJqfsI9Yjxo1SqNGjTrrPD6fT6mpqdZFAQCav0Y5BrRmzRolJyerZ8+emj59ug4ePFjvvJWVlQoEAiE3AEDz1+ABNHLkSD3//PNatWqVHn30URUVFWnUqFH1ns5YWFgov98fvGVkZDR0SQCACBRlbC4uOL1wVJSWLl2q8ePH1zvP3//+d3Xt2lUrV67U8OHDa91fWVmpysrK4O+BQKBZhpDNdUA2L43NdUDHjx8PexnJu+uAvLzeIZKvA7LZhmyvzeE6oFNsxsFmGa+uj/NaeXm5EhMT672/0beYLl26qF27dtq5c2ed9/t8PiUmJobcAADNX6MH0N69e3Xw4EGlpaU19qoAAE1I2J/XHD16NGRvpqSkRFu2bFFSUpKSkpI0d+5cTZgwQampqdq1a5fuvfdedevWTXl5eQ1aOACgaQs7gDZu3Kgf/ehHwd9nzZolScrPz9eCBQv08ccf67nnntPhw4eVnp6uESNG6Oc//7l8Pl/DVQ0AaPIu6CSExhAIBOT3+12X0eC8OgnBhs2JC5J9w89weTl2Xq3L5oC9zXoifRxsRHJttuuyeU42y0jejoXzkxAAAKgLAQQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QQABAJwggAAATti1QUbYvPqqZ5tOtzZfIWwr0jsZx8TEhL1MVVVV2Mt4+TXjNppbh2/brwv36m8wkr8KvjGxBwQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QQABAJwggAAATtCM1CNeNfyM9KaGkd6M1KaxqFfPKTo62pP1SHbbhM0ytk1CwxXp27iXYxdJTUzZAwIAOEEAAQCcIIAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJ2hG2szYNEJsDk0Nv83L5+RVA1ivGtpKdtuRDZtmqV42p7VZl1evk+3fn01T28Z6TuwBAQCcIIAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJwggAIATNCO1YNOo0WaZSG9YacPmObVsGf5meuLEibCXkewai3o15l42kfSq4afNeqqqqsJeJjY2NuxlbNlsQzbL2GwPklRdXW21XGNgDwgA4AQBBABwIqwAKiws1OWXX66EhAQlJydr/PjxKi4uDpnn+PHjKigoUNu2bdW6dWtNmDBBZWVlDVo0AKDpCyuAioqKVFBQoPXr12vFihWqrq7WiBEjVFFREZzn7rvv1p/+9CctXrxYRUVF2rdvn6699toGLxwA0LRFmQs42vjll18qOTlZRUVFGjp0qMrLy9W+fXu9+OKLuu666yRJ27dv1/e+9z2tW7dOP/jBD875mIFAQH6/37YkT0TySQjNUaSfhODV6xRJ32TZUJrjSQg2z8lmG28KJyGUl5crMTGx3vsv6BhQeXm5JCkpKUmStGnTJlVXVys3Nzc4T1ZWljp27Kh169bV+RiVlZUKBAIhNwBA82cdQDU1NZo5c6YGDx6s7OxsSVJpaaliY2PVpk2bkHlTUlJUWlpa5+MUFhbK7/cHbxkZGbYlAQCaEOsAKigo0NatW/Xyyy9fUAFz5sxReXl58LZnz54LejwAQNNgdSHqjBkz9MYbb2jt2rXq0KFDcHpqaqqqqqp0+PDhkL2gsrIypaam1vlYPp9PPp/PpgwAQBMW1h6QMUYzZszQ0qVLtXr1amVmZobcP2DAAMXExGjVqlXBacXFxdq9e7cGDRrUMBUDAJqFsPaACgoK9OKLL2rZsmVKSEgIHtfx+/1q1aqV/H6/pk6dqlmzZikpKUmJiYm68847NWjQoPM6Aw4A8N0R1mnY9Z1KvHDhQk2ePFnSqQtRZ8+erZdeekmVlZXKy8vT008/Xe9HcN/Gadj/h9OwT+E07FM4DfsUTsM+pTmchn1B1wE1hqYQQF6x2cBs3nhtwlGK7DdrWzbPyeYN0fbNI1y2f96220SksnldJe+asnr5t+TlP3SNeh0QAAC2CCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACQIIAOAEAQQAcMLqG1G/62JiYsJexqYFuk0rfZsuxrYdf2065Np04rWpz8tuzjb1ebWMbRfoysrKsJex+Wbj5tZ1W/Lu/cH2tbXtbN0Y2AMCADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACdoRmrBpnGgbcNPL9g0PZXsGova8LJhZU1NTdjL2DaFjNT1SN411GyObMahOTZlPR/sAQEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEzQjbWZsmmlGR0c3QiV1i+Rmn5J3Y+Hlc7Jh8zrBnk2z4khucHy+IvuvAADQbBFAAAAnCCAAgBMEEADACQIIAOAEAQQAcIIAAgA4QQABAJwggAAAThBAAAAnCCAAgBMEEADACZqRWrBpWBkVFdUIldRm0+TSy8aTkV6fV6+TV01jT548GfYyF7IcEA72gAAAThBAAAAnwgqgwsJCXX755UpISFBycrLGjx+v4uLikHmGDRumqKiokNvtt9/eoEUDAJq+sAKoqKhIBQUFWr9+vVasWKHq6mqNGDFCFRUVIfNNmzZN+/fvD94ee+yxBi0aAND0hXUSwvLly0N+X7RokZKTk7Vp0yYNHTo0OP2iiy5Sampqw1QIAGiWLugYUHl5uSQpKSkpZPoLL7ygdu3aKTs7W3PmzNGxY8fqfYzKykoFAoGQGwCg+bM+DbumpkYzZ87U4MGDlZ2dHZz+k5/8RJ06dVJ6ero+/vhj3XfffSouLtarr75a5+MUFhZq7ty5tmUAAJqoKGOMsVlw+vTp+vOf/6z33ntPHTp0qHe+1atXa/jw4dq5c6e6du1a6/7KykpVVlYGfw8EAsrIyLApyTNeXo8Rrki/zibS6/PqOiCbP7tI3u6AupSXlysxMbHe+632gGbMmKE33nhDa9euPWv4SFJOTo4k1RtAPp9PPp/PpgwAQBMWVgAZY3TnnXdq6dKlWrNmjTIzM8+5zJYtWyRJaWlpVgUCAJqnsAKooKBAL774opYtW6aEhASVlpZKkvx+v1q1aqVdu3bpxRdf1NVXX622bdvq448/1t13362hQ4eqb9++jfIEAABNU1jHgOr7fHzhwoWaPHmy9uzZo5tvvllbt25VRUWFMjIydM011+j//b//d9bPAc8UCATk9/vPtyQnIvmz+Eg/xhLp9XEMCGg45zoGZH0SQmMhgC5MpL/BR3p9BBDQcBrlJITvOps/aps3XhtedVmW7MbBqzDx8jl5xaY2rwLVdl1e/nOByEMzUgCAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwgmakHvGq6aJNQ0jbBpw2DT9txsGmc3RzbHIZ6d2wI6yxPpoA9oAAAE4QQAAAJwggAIATBBAAwAkCCADgBAEEAHCCAAIAOEEAAQCcIIAAAE4QQAAAJwggAIATEdcLjn5SF8bL8bNZl1f1NcftqDk+JzRv59pmIy6Ajhw54roEnKfm2PAzkjHeaGqOHDkiv99f7/1RJsL+raqpqdG+ffuUkJBQq7NzIBBQRkaG9uzZo8TEREcVusc4nMI4nMI4nMI4nBIJ42CM0ZEjR5Senq4WLeo/0hNxe0AtWrRQhw4dzjpPYmLid3oDO41xOIVxOIVxOIVxOMX1OJxtz+c0TkIAADhBAAEAnGhSAeTz+fTQQw/J5/O5LsUpxuEUxuEUxuEUxuGUpjQOEXcSAgDgu6FJ7QEBAJoPAggA4AQBBABwggACADhBAAEAnGgyATR//nx17txZcXFxysnJ0fvvv++6JM89/PDDioqKCrllZWW5LqvRrV27VmPHjlV6erqioqL02muvhdxvjNGDDz6otLQ0tWrVSrm5udqxY4ebYhvRucZh8uTJtbaPkSNHuim2kRQWFuryyy9XQkKCkpOTNX78eBUXF4fMc/z4cRUUFKht27Zq3bq1JkyYoLKyMkcVN47zGYdhw4bV2h5uv/12RxXXrUkE0B/+8AfNmjVLDz30kD788EP169dPeXl5OnDggOvSPNe7d2/t378/eHvvvfdcl9ToKioq1K9fP82fP7/O+x977DE9+eSTeuaZZ7RhwwbFx8crLy9Px48f97jSxnWucZCkkSNHhmwfL730kocVNr6ioiIVFBRo/fr1WrFihaqrqzVixAhVVFQE57n77rv1pz/9SYsXL1ZRUZH27duna6+91mHVDe98xkGSpk2bFrI9PPbYY44qrodpAgYOHGgKCgqCv588edKkp6ebwsJCh1V576GHHjL9+vVzXYZTkszSpUuDv9fU1JjU1FTz61//Ojjt8OHDxufzmZdeeslBhd749jgYY0x+fr4ZN26ck3pcOXDggJFkioqKjDGnXvuYmBizePHi4Dx//etfjSSzbt06V2U2um+PgzHGXHnlleauu+5yV9R5iPg9oKqqKm3atEm5ubnBaS1atFBubq7WrVvnsDI3duzYofT0dHXp0kU33XSTdu/e7bokp0pKSlRaWhqyffj9fuXk5Hwnt481a9YoOTlZPXv21PTp03Xw4EHXJTWq8vJySVJSUpIkadOmTaqurg7ZHrKystSxY8dmvT18exxOe+GFF9SuXTtlZ2drzpw5OnbsmIvy6hVx3bC/7auvvtLJkyeVkpISMj0lJUXbt293VJUbOTk5WrRokXr27Kn9+/dr7ty5uuKKK7R161YlJCS4Ls+J0tJSSapz+zh933fFyJEjde211yozM1O7du3Sv/zLv2jUqFFat26doqOjXZfX4GpqajRz5kwNHjxY2dnZkk5tD7GxsWrTpk3IvM15e6hrHCTpJz/5iTp16qT09HR9/PHHuu+++1RcXKxXX33VYbWhIj6A8H9GjRoV/Llv377KyclRp06d9Morr2jq1KkOK0MkuOGGG4I/9+nTR3379lXXrl21Zs0aDR8+3GFljaOgoEBbt279ThwHPZv6xuHWW28N/tynTx+lpaVp+PDh2rVrl7p27ep1mXWK+I/g2rVrp+jo6FpnsZSVlSk1NdVRVZGhTZs26tGjh3bu3Om6FGdObwNsH7V16dJF7dq1a5bbx4wZM/TGG2/onXfeCfn+sNTUVFVVVenw4cMh8zfX7aG+cahLTk6OJEXU9hDxARQbG6sBAwZo1apVwWk1NTVatWqVBg0a5LAy944ePapdu3YpLS3NdSnOZGZmKjU1NWT7CAQC2rBhw3d++9i7d68OHjzYrLYPY4xmzJihpUuXavXq1crMzAy5f8CAAYqJiQnZHoqLi7V79+5mtT2caxzqsmXLFkmKrO3B9VkQ5+Pll182Pp/PLFq0yHz66afm1ltvNW3atDGlpaWuS/PU7NmzzZo1a0xJSYn5y1/+YnJzc027du3MgQMHXJfWqI4cOWI2b95sNm/ebCSZxx9/3GzevNl8/vnnxhhjfvWrX5k2bdqYZcuWmY8//tiMGzfOZGZmmm+++cZx5Q3rbONw5MgRc88995h169aZkpISs3LlSnPppZea7t27m+PHj7suvcFMnz7d+P1+s2bNGrN///7g7dixY8F5br/9dtOxY0ezevVqs3HjRjNo0CAzaNAgh1U3vHONw86dO80jjzxiNm7caEpKSsyyZctMly5dzNChQx1XHqpJBJAxxjz11FOmY8eOJjY21gwcONCsX7/edUmemzhxoklLSzOxsbHmkksuMRMnTjQ7d+50XVaje+edd4ykWrf8/HxjzKlTsR944AGTkpJifD6fGT58uCkuLnZbdCM42zgcO3bMjBgxwrRv397ExMSYTp06mWnTpjW7f9Lqev6SzMKFC4PzfPPNN+aOO+4wF198sbnooovMNddcY/bv3++u6EZwrnHYvXu3GTp0qElKSjI+n89069bN/PM//7MpLy93W/i38H1AAAAnIv4YEACgeSKAAABOEEAAACcIIACAEwQQAMAJAggA4AQBBABwggACADhBAAEAnCCAAABOEEAAACf+P5ge+Kk2OPbPAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(custom_image.reshape(28, 28), cmap='gray')\n",
    "plt.title(\"Preprocessed Image\")\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}