mnist.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import Levenshtein"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_idx3(filename):\n",
    "    with open(filename, 'rb') as fo:\n",
    "        buf = fo.read()\n",
    "        \n",
    "        index = 0\n",
    "        header = np.frombuffer(buf, '>i', 4, index)\n",
    "        \n",
    "        index += header.size * header.itemsize\n",
    "        data = np.frombuffer(buf, '>B', header[1] * header[2] * header[3], index).reshape(header[1], -1)\n",
    "        \n",
    "        return data\n",
    "    \n",
    "def read_idx1(filename):\n",
    "    with open(filename, 'rb') as fo:\n",
    "        buf = fo.read()\n",
    "        \n",
    "        index = 0\n",
    "        header = np.frombuffer(buf, '>i', 2, index)\n",
    "        \n",
    "        index += header.size * header.itemsize\n",
    "        data = np.frombuffer(buf, '>B', header[1], index)\n",
    "        \n",
    "        return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000,) (60000, 784)\n"
     ]
    }
   ],
   "source": [
    "train_labels = read_idx1(\"mnist/train-labels.idx1-ubyte\")\n",
    "\n",
    "train_images = read_idx3(\"mnist/train-images.idx3-ubyte\")\n",
    "\n",
    "print(train_labels.shape, train_images.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "   0   0   0   0   0   0   0   0   3  18  18  18 126 136 175  26 166 255\n",
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      " 170 253 253 253 253 253 225 172 253 242 195  64   0   0   0   0   0   0\n",
      "   0   0   0   0   0  49 238 253 253 253 253 253 253 253 253 251  93  82\n",
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      " 253 253 253 253 198 182 247 241   0   0   0   0   0   0   0   0   0   0\n",
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      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  35 241\n",
      " 225 160 108   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0  81 240 253 253 119  25   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0  45 186 253 253 150  27   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0  16  93 252 253 187\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0 249 253 249  64   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0  46 130 183 253\n",
      " 253 207   2   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0  39 148 229 253 253 253 250 182   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0  24 114 221 253 253 253\n",
      " 253 201  78   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0  23  66 213 253 253 253 253 198  81   2   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0  18 171 219 253 253 253 253 195\n",
      "  80   9   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "  55 172 226 253 253 253 253 244 133  11   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0 136 253 253 253 212 135 132  16\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
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      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0]\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "print(train_images[0])\n",
    "\n",
    "print(train_labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)\n",
    "plt.imshow(train_images[0, :].reshape(28, -1), cmap='gray')\n",
    "plt.title('train 0')\n",
    "\n",
    "print(train_labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 获取测试集合\n",
    "\n",
    "test_labels = read_idx1(\"mnist/t10k-labels.idx1-ubyte\")\n",
    "\n",
    "test_images = read_idx3(\"mnist/t10k-images.idx3-ubyte\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'test 0')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(test_labels[0])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.imshow(test_images[0, :].reshape(28, -1), cmap='gray')\n",
    "plt.title('test 0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 784)\n"
     ]
    }
   ],
   "source": [
    "print(test_images.shape)\n",
    "\n",
    "# 使用测试集 作为预处理\n",
    "\n",
    "from collections import defaultdict\n",
    "\n",
    "data = defaultdict(lambda : [])\n",
    "\n",
    "def sHash(img):\n",
    "    \"\"\"感知哈希\n",
    "\n",
    "    Args:\n",
    "        img ([type]): 一维 784 的数组\n",
    "\n",
    "    Returns:\n",
    "        [str]: 感知哈希\n",
    "    \"\"\"\n",
    "    # 感知 哈希\n",
    "    hash_val = ''\n",
    "    avg = img.mean()\n",
    "    \n",
    "    for x in range(len(img)):\n",
    "        if img[x] > avg:\n",
    "            hash_val += '1'\n",
    "        else:\n",
    "            hash_val += '0'\n",
    "    return hash_val\n",
    "\n",
    "for i in range(len(test_images)):\n",
    "    img = test_images[i, :]\n",
    "    # 感知 哈希\n",
    "    \n",
    "    data[test_labels[i]].append(sHash(img))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 使用训练集的第一张用来测试\n",
    "\n",
    "to_test_image = train_images[0, :]\n",
    "\n",
    "test_hash = sHash(to_test_image)\n",
    "\n",
    "def recognize_number(to_test_image_sHash:str):\n",
    "    \n",
    "    result = [ 0 for i in range(10)]\n",
    "    \n",
    "    \n",
    "    for k,v in data.items():\n",
    "    # k - 数字  v - 每个数字的所有感知哈希值\n",
    "    # 遍历所有的哈希并计算值\n",
    "        for hash_val in v:\n",
    "            leven_val = Levenshtein.ratio(to_test_image_sHash, hash_val)\n",
    "            if leven_val > result[k]:\n",
    "                result[k] = leven_val\n",
    "\n",
    "    return result\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9553571428571429\n",
      "5\n",
      "[0.9183673469387755, 0.9260204081632653, 0.9451530612244898, 0.9438775510204082, 0.8864795918367347, 0.9553571428571429, 0.9260204081632653, 0.9387755102040817, 0.9438775510204082, 0.9158163265306123]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "result = recognize_number(test_hash)\n",
    "print(max(result))\n",
    "\n",
    "print(result.index(max(result)))\n",
    "\n",
    "print(result)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9438775510204082\n",
      "6\n",
      "[0.9285714285714286, 0.9119897959183674, 0.9323979591836735, 0.9349489795918368, 0.8877551020408163, 0.9298469387755102, 0.9438775510204082, 0.8915816326530612, 0.9260204081632653, 0.9081632653061225]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用我们自己写的图片\n",
    "\n",
    "from PIL import Image\n",
    "\n",
    "diy_image = Image.open('MNIST-4.jpg')\n",
    "\n",
    "\n",
    "diy_arr = np.array(diy_image).flatten()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.imshow(diy_arr.reshape(28, -1), cmap='gray')\n",
    "plt.title('diy 0')\n",
    "\n",
    "diy_arr = diy_arr.flatten()\n",
    "# print(sHash(diy_arr))\n",
    "r = recognize_number(sHash(diy_arr))\n",
    "print(max(r))\n",
    "\n",
    "print(r.index(max(r)))\n",
    "\n",
    "print(r)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 测试结果准确率\n",
    "\n",
    "statis = {}\n",
    "\n",
    "for i in range(0, 10):\n",
    "    statis[i] = {}\n",
    "    \n",
    "    statis[i][\"correct\"] = 0\n",
    "    statis[i][\"all\"] = 0\n",
    "\n",
    "for i in range(100):\n",
    "    shash_val = sHash(train_images[i, :])\n",
    "    \n",
    "    r = recognize_number(shash_val)\n",
    "    \n",
    "    real_val = train_labels[i]\n",
    "    if r.index(max(r)) == real_val:\n",
    "        statis[real_val][\"correct\"] += 1\n",
    "    \n",
    "    statis[real_val][\"all\"] += 1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.0\n",
      "1 0.9285714285714286\n",
      "2 0.8333333333333334\n",
      "3 0.9090909090909091\n",
      "4 0.9090909090909091\n",
      "5 1.0\n",
      "6 1.0\n",
      "7 0.9\n",
      "8 1.0\n",
      "9 0.8181818181818182\n"
     ]
    }
   ],
   "source": [
    "from icecream import ic\n",
    "\n",
    "\n",
    "\n",
    "for i in range(10):\n",
    "    print(i, statis[i][\"correct\"] / statis[i][\"all\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 展示图片\n",
    "def img_show_array(a):\n",
    "    plt.imshow(a, cmap='gray')\n",
    "    \n",
    "# 展示投影图， 输入参数arr是图片的二维数组，direction是x,y轴\n",
    "def show_shadow(arr, direction = 'x'):\n",
    "\n",
    "    a_max = max(arr)\n",
    "    if direction == 'x': # x轴方向的投影\n",
    "        a_shadow = np.zeros((a_max, len(arr)), dtype=int)\n",
    "        for i in range(0,len(arr)):\n",
    "            if arr[i] == 0:\n",
    "                continue\n",
    "            for j in range(0, arr[i]):\n",
    "                a_shadow[j][i] = 255\n",
    "    elif direction == 'y': # y轴方向的投影\n",
    "        a_shadow = np.zeros((len(arr),a_max), dtype=int)\n",
    "        for i in range(0,len(arr)):\n",
    "            if arr[i] == 0:\n",
    "                continue\n",
    "            for j in range(0, arr[i]):\n",
    "                a_shadow[i][j] = 255\n",
    "\n",
    "    plt.imshow(a_shadow)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MtOuo1Wp88803kukWSuv5esvlcklewbZ4vo2srKywefNm9O3bV28bMcYKqOwv6ij4ZR05OTl069YtCg8Pp7t37xIR0cSJE8nJyUk7Ob2lpSW5u7vTwYMHKTw8XJseP35MKSkp1KZNG6pevbpkQntnZ2e6ceMGhYeH0/3797VfFJGWlqZd/7vvvpOsY2lpSfHx8RQfH68tk5SURA8ePCAPDw+ysrKSlDc3Nyc3Nzfav3+/tnx2djZt2bKFGjVqpPPlHp999pm2XHJysrZOUVFR2nwvLy9teRcXF/rss89Io9HQnTt3JMc+c+ZMcnV11ZnIv27duuTv7y8pe/PmTfL19aXatWtLyspkMmrUqBGtWrWKVCqV9u/w999/k4eHB1WrVq1YXx4wbdo0g1/WUb9+fbp+/brk71DweMPDw+m///2vtvzw4cO1+fHx8do2evTokTa/T58+lf1lCZw4VWYy+GUdVWb6gXPnzmH9+vU6+adPn8aDBw+0r9PS0hAeHo5Tp07p3ADMyMjA9evXdeb+zsjIwPHjxwu90rt586bktUqlwoYNG3S6f548eYJbt27pXPlmZGTg1q1bOH36NGJiYgAAx48fx5EjRxAREaGzvzt37uidUiEfESE5+X+Dj+7du4ejR49i7dq1OmUvX76s9yvwHj58CDMzM8l+iAjXr19HXFycpKxGo0FERAT++usvyZOvsbGxCA8PL/Yw07CwMKxbt07nK/aA3O6i48ePF/pk7Y0bNyT7LqyNgNy/B2NMl3iRY8MNVkKIyq8EY4y9fC4SURt9C7jTkjHGjBAHd8YYM0Ic3BljzAhxcGeMMSPEwZ0xxowQB3fGGDNCHNwZY8wIcXBnjDEjxMGdMcaMEAd3xhgzQhzcGWPMCHFwZ4wxI8TBnTHGjBAHd8YYM0Ic3BljzAhxcGeMMSPEwZ0xxowQB3fGGDNCZQ7uQgi5EOKyEGJv3usGQoizQogIIcRWIYRJ2avJGGOsJMrjyn06gBsFXn8L4HsiagQgEcC4ctgHY4yxEihTcBdC1APQB8Avea8FgO4AtucVWQ9gQFn2wRhjrOTKeuX+XwAzAGjyXtsDSCIiVd7raAB19a0ohBgvhLgghLhQxjowxhh7TqmDuxCiL4DHRHSxNOsTUQARtSGiNqWtA2OMMf0UZVi3I4D+QojeAMwAWAP4AYCtEEKRd/VeD8DDsleTMcZYSZT6yp2IZhNRPSJyATAMwN9ENAJACIDBecVGAdhV5loyxhgrkYoY5z4TwEdCiAjk9sGvqYB9MMYYK4QgosquA4QQlV8Jxhh7+Vw0dN+Sn1BljDEjxMGdMcaMEAd3xhgzQmUZClnulEolmjRpAplMhszMTNy8ebPQ8nZ2dnB2dgYAPH78GDExMeVep9q1a6N27doAgKioKDx9+rTctq1UKtG0aVMIIZCRkYHw8HC4urpCJpMhIiJCUtbDwwNpaWmIiorS5snlcjRp0gQKhQLZ2dm4ceMGCt5DcXFxgUKhQEREBBo1agSVSoV79+7Bw8MD6enpePDgQbkdC2OsiiGiSk8ACADVrVuXMjMziYjo+vXrlHej1WAaOXIk5fvuu+8KLVva9OWXX2r3MWnSpHLdtrOzM2VnZxMR0T///EMAKCgoiI4ePSopJ5PJ6ObNm7R69WpJvq2tLT179oyIiKKiosjExESyfM+ePXTy5EkCQCdPnqQ9e/aQEILCwsJo3bp1FdJenDhxeqHpgsG4WtmBPT+4v/vuu3T06FHSaDRERJSSkkIHDhwgHx8fnQMSQlBAQABdvXpVG3jv3btHwcHBFBwcTMOGDSuyURYvXkzBwcH0119/kYuLi85yMzMz+v333+nOnTuUlJRE/fr1o2+//Va7jy5duhS6fZlMRoGBgRQcHEy7d+8mW1tbyfJJkybRsWPHJMcbHBxM8fHxeoN7eHg4RUVFafcfHBxMf//9N6lUKp3g7uTkRH/99Rc9efKEEhMTKTg4mBITE+nJkycUHBxMKSkp9PDhQ9qzZw/VqFGjsk9OTpw4lT4ZDO5VolumWrVqeO211+Dj44MTJ05Ao8mdqsbExAReXl7IzMxEaGioZB2lUomnT5/i6NGj2jwLCwv4+PjgyJEjRe6zbdu2ePXVVwEA1tbWkmV169ZF8+bN0bNnTyQkJODIkSM4cOAAGjZsiFdffRXt27fHmjWGh+/XrFkTnp6e6NmzJxwdHZGRkQETE+nMxx4eHmjXrh2OHz+u7UoxNTXFtWvX8M8//0jKEhHOnTuH+vXrw9TUVLLsxIkTaNiwoSRPCAFTU1OEhYVpt5u/TVNTU8hkMsjlcpiZmSF3rjfGmNGp7Kt2IkLr1q0Ndi3s3r2bTp8+Xax3MSsrK0pISKDZs2cXWfbIkSPaq34vLy/JsqlTp2qXzZ07V7LM1dWVVCoVDRkyxOC2Bw8eTAWlp6dTrVq1JGV++OEHunfvHimVyjK/ey9ZskRv2+lL3C3DiZNRJYNX7lVmtMyPP/6Ivn37Iicnp0L307RpU5w7dw6rVq3C1KlTDZbLyMhAjx498Msvv1RofRhjrCJUiW4ZAIiOjtbpjihv7du3R5cuXdC2bVvExMQUOvJFJpOhbt26iI6OLtEonG7duqFevXrYsWMHAKBBgwZwd3cvc931USqV8PPzQ0ZGBoKCgrTdWYbUrl0bHTt21OmGYowZnypz5V5WQgjI5fJCy8ycOROLFi2CRqORDBl8HhFBqVRi3bp1GDJkiGQfMlnhTbZkyRJ07NgRgwYNwuDBgxEQEFCyAykBS0tLbNy4EUlJSRg/fjxUKlWh5du0aYPt27fD0dGxyDcCxtjLzWiC+6hRo3D+/HnY2NgUWu7q1ato0qQJzp8/b7DMxo0b0bp1ayQlJUny586diwMHDhT5JgLkXvkHBwdj3rx5xan+C0NE6Nu3Lz799NPKrgpjrAJVmW6Z0mjUqJF2xEvPnj3h7OyMTZs26Yyssba2xhtvvIGIiAhcvHgRt27dKnS7SUlJuHHjBtatWwchBMaNy/0a2K5du6JGjRpYu3YtIiMjJevUqVMHffr0wfHjx3Hz5k0IIdCgQQPUqlULGRkZevdjZWWFsWPHSq64g4ODER0dXeSxe3l5oWvXrjqjcIrj/v37iIuLK/F6jLGXR5UI7gWHAmZlZQHI7QIxMTEpdKjeK6+8IrnhmZKSgunTpyMxMVFSrlatWvjll18wePBgbV94UbKysjBr1izMnTtXso/IyEiMHz8earVam6dUKtGiRQusXr0arVu3xqVLlyCXy5GVlWWwqyQnJwcWFhb473//CyD3St/ExAT9+/fH48ePkZ2dXWj9evfujYULFxa6j4JMTEygVCqLceSMMWNQJbplrl69Cnt7e5w+fVp7JdqwYUNERkaiR48elVInCwsLXLhwAdOmTSuy7MaNG7Fp0yZJnlqtRteuXTFnzhy968yfPx+urq7a5OfnBwBYt24dfvvtt2LVMTk5GV5eXsUa0bN9+/ZCx+YzxoxLlbhyz8nJwdGjR6HRaPDRRx8ByL1y//XXXzF48GCD6129ehXffPONJG/ixIkICQnBmTNnAAB+fn5o1aoVFi1aVGR3TL7WrVujT58+cHV1xaVLl3DixAkAQK9eveDs7IwZM2Zgx44d2rlv7O3tkZKSgoCAAEl3x5MnT3DkyBFYWloiLS1Nso/k5GQkJydrXxMRvvnmGwwdOhStWrXCrFmzsH79esTGxhqsp0ajQVxcnM629bG3t0dCQgJWrlyJ+Pj4YrUDY+wlVtkPMFGBuWXq1KlDcXFxlJiYSGfPniUhRKkeYpo/fz7Z2NgQAAoICKCIiAiyt7cnW1tbSRo4cCAREXXq1IksLCy028l/iCkpKYlmzJihzV+yZIl2LpeCDzEdOnSIjh07prP955OZmVmRx7B9+3ZKSUkhIqJ27doZLDdr1ixKTEwka2vrYrVN/twyxSnLiROnlyZV7ekH8sXFxcHNzQ1CCKjV6kKHKxZmxowZGDZsGLy8vADkjjWPjIzU2V5+H3RQUBC2bt2Kd999V7ssPT0dLVu2lFw5z5kzBxs2bMDFixd19tmhQwfcu3ev0HotXrwYX3/9daFl3nnnHbz66qvYv39/oeUYY6wwVSq4E5Gkq6K0QkJCsHv3buTk5GD79u24ffu23nJubm549913Ua1aNVhYWEiWaTQapKSkaG/wAkBmZiZSUlJ0thMQEIDg4GBJnhACM2bMgL29PXJycrBw4cJizXmTnp5eaDeLQqHA7NmzIZfLMXfuXGRmZha5TcbYv0+VCu4FKRQK1KpVC2ZmZiVe99ixY1ixYgUA4MCBAzhw4IDecj179sS7776Lx48f64ywKYlt27bp5Mnlcvj7+6Np06YwNTXF8uXL8fjx4yK3ZW9vD3t7e4PLFQoFJk2ahPXr12PZsmVFbs/ExAQ1a9ZEcnJyuc5Fzxir2soU3IUQtgB+AeCJ3P6fsQDCAWwF4ALgHoAhRFTiyNmwYUOEhobCxMQE586dK0s1i9SnTx+dsfFlpVar0a1bN4wfPx6LFi0q9nrr1q1Dr169yq0e3t7eOHr0KHr06IFTp06V23YZY1VbWYdC/gDgLyLyANACwA0AswAcJqLGAA7nvS6x/Glrf/rpJ3z11VfafC8vL6xduxaOjo6S8j179sTPP/8MS0vLEu8rOztbZ6y4mZkZli1bhv79+5em+pDJZFiwYAHeeustvcuHDx+OxYsXa592rVevHtauXYuWLVvi7t27GDNmjM6DUqWth4mJCVQqVbHGwzPGjEOpr9yFEDYAugAYDQBElA0gWwjhD6BrXrH1AI4AmFnYtszMzODi4iLJq1evHm7cuIGdO3ciJCREm29rawsfHx94enpKJsDq3r073nrrLURERJS5+yEhIQF37tzBkCFD8PTpU8kQytq1a+PGjRvFujfQsmVLNGjQQO8yHx8fDB48GOvXr4dKpYK7uzvGjBmDqKgonD17FuvWrdNZx8bGBs7Ozrh7926xungYY/9iZRi+2BLAOQDrAFxGbveMJYCkAmVEwdeFzeeuVqslKSwsjBQKhd7hP3K5nK5evSopr9FoKDk5mezt7Yv8er781LNnT73zuQO5wyrj4+NJo9FI9hMREVHsOdiFEDRp0iSD87kTkaT+RESvv/66wfqPGzeO0tLSyNHRsdjH2KFDByIi6tChQ2UP2eLEiVP5pwoZCqkA4A1gKhGdFUL8gOe6YIgoPwjpEEKMBzAeAMzNzTFo0CDJ8uTkZIPdCGq1GtOmTdOZujY7OxvJycnFHkJ5+fJl+Pv76x3CmJ6ejrffflvnm4/S0tKK3b1BRAgKCkJUVJTOJGSrV6/G33//rbPOxYsXDdb/4MGDGDp0KJ4+fVrsY7xx4wYGDBiAGzduFKs8Y8w4iNKOJRdC1AZwhohc8l53Rm5wbwSgKxHFCiHqADhCRIVOaG7oDYAxxlihLhJRG30LSn1DlYjiAEQJIfIDty+A6wB2AxiVlzcKwK7S7oMxxljplHWc+1QAm4QQJgAiAYxB7hvGNiHEOAD3AQwpZH3GGGMVoNTdMuVaCe6WYYyx0ij/bhnGGGNVFwd3xhgzQhzcGWPMCHFwZ4wxI8TBnTHGjBAHd8YYM0Ic3BljzAhxcGeMMSPEwZ0xxowQB3fGGDNCHNwZY8wIcXBnjDEjxMGdMcaMEAd3xhgzQhzcGWPMCHFwZ4wxI8TBnTHGjBAHd8YYM0Ic3BljzAhxcGeMMSNUpuAuhPhQCBEmhLgmhNgihDATQjQQQpwVQkQIIbYKIUzKq7KMMcaKp9TBXQhRF8A0AG2IyBOAHMAwAN8C+J6IGgFIBDCuPCrKGGOs+MraLaMAYC6EUACwABALoDuA7XnL1wMYUMZ9MMYYK6FSB3cieghgCYAHyA3qzwBcBJBERKq8YtEA6pa1kowxxkqmLN0ydgD8ATQA4AjAEoBfCdYfL4S4IIS4UNo6MMYY009RhnVfA3CXiJ4AgBDiTwAdAdgKIRR5V+/1ADzUtzIRBQAIyFuXylAPxhhjzylLn/sDAD5CCAshhADgC+A6gBAAg/PKjAKwq2xVZIwxVlKCqPQXzUKILwEMBaACcBnAu8jtY/8NQPW8vLeJKKuI7RisxBtvvIHGjRsbXFetVmPlypVISUnRu9zPzw8tW7bUu+zu3bvYunVrYVUDAFhYWGDSpElQKpXavJ07d+LmzZtFrtuyZUv4+envrXr27BlWrVoFjUZT5HYqw+uvv44WLVroXRYZGYlt27YVun6nTp3QqVMnvcvi4uKwbt26slaxwrz55pto2LChweUqlQorV65EamqqJL9atWqYOHEiFIrCPxQTEdasWYP4+PhyqS/717pIRG30LiGiSk8A6Pkkk8nI1taWgoKCSKVSUWJiok5KS0uj7OxsatasGZmbm0vWF0KQra0trV+/ntRqtd71d+/eTba2tiSXy3X2n5/MzMyoUaNGlJ6eTgUNGTLE4Dr5ydramiZPnqx335mZmfTgwQOqWbMmKZXKIrf1IlN+2/36668G227nzp1ka2tLMplM7zZsbGxo8eLFpNFoKCkpSbJudnY2hYaGkq2tLSkUiko/Xn1p3759hZ53WVlZ5OHhoXPeOTo6UmZmJhGRwbZLTEykhIQE8vDwqPTj5PTSpwsG42plB3ZDwd3NzY0SExMpJyeHzp07RzY2NjppwoQJRESUnJxMX3/9tWT9WrVqUVxcHGVnZ1NERATZ2dnprN+vXz9KSkoiT09Pg403e/ZsSk5OpucVFdzlcjldvnyZli1bprfuK1asII1GQ8+ePaM333yzsk8QSXJwcKBHjx5RdnY23b59W2/b9e/fnxITE6lp06Y661taWlJkZCRlZmbS48ePqXbt2pJ1d+7cSWq1mpKSkqhLly6Vfrz60r59++jMmTN6/3aTJk3Snnfz58+XrFcwuN+6dUtv2+UnQ2+MnDiVIBkM7mW5oVqhZDIZbGxsIISAWq3Gs2fPdMqkp6cDAKysrGBubq53/d27dyMoKAhJSUn5byRaWVlZsLGxwccff4zg4GBs2bJFZx/Hjh2DSpU7snPgwIF45ZVXin0MVlZWUCgUeuu+bds2JCQkYNasWUV+hH/RZDIZrK2toVQqodFo8OzZM52uo6ysLNja2uKTTz7BgQMHJG0nhIC1tTWOHDmCXbt2IT4+XtuGALB27Vrcu3cP06dPh1wuf2HHVRwODg74z3/+Aw8PD8TExOj92x0/fhyzZ8/G7NmzYWZmZnBbhtqOsRehys4to1Kp8PDhQ0RHR+PJkyel3k5wcDDWrFmjE9gLGjVqFPr166d32cmTJ7F48WIsXrwYly9fLtY+zczMULdu3UKDdkhICAICAqBWq4u1zcqQlJSER48eFVpm9OjR6Nu3r95lJ06cwIoVKySBHQB2796NX3/9tdzqWZ5q1KiBjz/+GDY2Ngb7w69du4alS5ciOTnZ4Hby264s97QYK4uqdclYwJ07d7Q3tF62f5DXX38dv/32G0xMXu5pdWbPno01a9b8K688x40bh/3795d6/ZkzZyIwMPClO3eZ8aiyV+5EhOzsbGRnZyMnJ8dgObVajY8++gibN28u8T6uXbuGsWPHIioqqixV1SGXy1/6wA4AOTk5Bts+v+2io6PLtI+ZM2fik08+KdM2KkJR511RCrbd1KlTERgYiMDAQDRq1Ki8qshYoapscC+Ki4sLHB0dodFosH37dly4UPIHXWNiYhAYGIjExMRyrVtKSgpu3rxZpuBQHDKZDG5ubqhevXqF7kefhw8flkvb9erVC7169SqnWlUdjo6OcHV1BQC4ubnBx8cHPj4+aN68OTw8PODh4QFTU9NKriUzZi9lcBdCYM+ePVi4cGFlV0Wv4OBgeHl5lfsngudZW1vj7NmzGDVqVIXuh5XcggULsHfvXshkMkybNg3NmjVDs2bN8OGHHyIsLAzXrl0r9PkNxsqqyva5G9K6dWvMnTsXzs7OOHr0KJYuXVqmG64VRaPRgIjg5+eHnTt3AgC2bt2KvXv3YvXq1TAzM4OFhUWZR8rIZDLIZFXrPTojIwMjR46Ej4+P9thXrlyJ0NBQ/Pzzz5DJZLC1ta3UOlaUhIQEDB48GHK5HMnJydr7Ffl9759++il69OiBuXPn4scff8SePXvw/fffV2aVmZF6qYJ706ZN4eXlBQcHB1y/fh0hISHYs2dPZVdLLyJCaGgo6tWrB0dHR7Rq1QoJCQmIi4tDnTp1YGpqWuaP5Wq1GhcuXEBMTEw51bp8qNVqBAUFoX79+toulyZNmkAul6N27dqQyWSwtLSs5FpWjMzMTOzdu9fg8hMnTsDKygoA0K1bNzx8qHfqJcbK7KUK7qtWrUJycjJ8fHwquypF0mg0GDw4d4odc3Nz3Lt3D2PGjEH//v3h4uKC1NRUODs74/bt26XeR0pKCnx9fcuryuUuICAAAQEBAIAVK1Zg8uTJcHd3h1qthre3Ny5evFjJNWTMeFWtz/MGNGvWDMePH8eqVaswY8aMcttumzZtcPz4ce2Nr4qSlZWF/v37o3Pnzujbt6/24auXWbt27XD8+PFC518p6LvvvsOwYcN0xvV/8MEH+OCDDyqghlXXmTNn0LlzZ9y9e7eyq8KMWJW/cm/dujW8vLyQkpKCS5cu4fr16yVa39PTE126dMGxY8d0llWvXh2dOnXCiRMnEBoaWk411qXRaHD27FlJnoeHB9q3b1+h/eWtW7eGUqnEmTNnSrV+8+bNDbadnZ1didouIiJCb/6VK1dw7dq1UtWvIrVt2xaJiYl6265u3bpo3bq1zlPRAGBqaoquXbsiLCzM4DBRuVwOKyurKnevhBmZyp5XxtDcMvlp9+7ddPr06RLPuVC7dm3tZF+3bt3SO49Hr169iIjIy8urWNtcvnx5iSYOKyz98MMP2m0NHz68Quad2LNnD508ebLE69WpU4cyMjKIiCg8PFxv2/n5+RERFTovT2GpdevWpNFoqFu3bhVy7KVNzZo1I7VaTUREx48f11tmzJgx2r/dokWLJMvy55YZN26cwX28/vrr2vU3bNhQ6cfM6aVOL9/EYS4uLhQaGkrJycmlCu4KhYI8PT1p+/bteoP72rVrKTIyssKCu0wmo3379tGVK1fo3LlzVL16dcnyH374gWJiYqhly5Zka2tbIX94FxcXatiwYanb7o8//tAb3AMDA+nu3bsGg7uFhQUdO3aMrly5QiEhIWRmZiZZvmTJEtq1axd5enqSpaVlZf9zSJKpqSl5enrSsWPHKC0tja5cuaI9P4QQtHPnToqKiqLs7Gzy9fWl2rVrS9bPD+5RUVG0a9cuypvOWpLyg/vAgQOpfv36lX7MnF7q9PJNHGZmZgYvLy8IIVCjRg0MHz680PLh4eG4dOmS9rVKpcK1a9cQFBSEhIQEDB8+XPIY/SuvvAJzc3Ns3LgRSUlJOttTKBTw9/eXPGnq5uam/b1Tp06SSa8eP36Mw4cP69SpZs2aaNGiBYYOHSrZT2pqKn7//XdcvXq1wuaXuXfvXqnWK9h28fHxOm3n4+MDU1NTbNy4Ue/EWmq1GtevX0fHjh3h7e2N4cOHIzMzU7u8c+fOUCgUVbI7JisrC9euXcPu3buRmZmJHj16YODAgWjWrBnkcjnatm2LzMxMbN68GZcuXdJ5iCs9PR2//fYbOnfujLZt22LEiBE6f18HBwds3LgR58+fL/MTvowZVNlX7Yau3D08PCgrK4uys7OLlRYvXmzw3a1Ro0aUmZmps86+ffsMrmNpaUmxsbHF3n9wcLDe7YwfP15v+SlTplT2O36xkqG227NnT5Hrzps3z2B7nT17ttKPrajUoUMHvXVfvXp1kesGBAQYPPbitB0nTsVMBq/cy/RNTOVF3zcxKRQKODo6Ivcb/IqWnJxs8FF4Q9vKyMjA48ePDdUJdevWLfaUtJmZmXpnUKxWrRrs7e118hMSEgx+e1RVUpq2y2djY2PwYaWsrCzExcWVVzUrhKmpKWrXrq2Tn5qaiqdPnxa6rr29PapVq6Z3WXHajrFiMvhNTFU2uDPGGCuSweDOY7EYY8wIcXBnjDEjVGRwF0KsFUI8FkJcK5BXXQhxUAhxO++nXV6+EEL8KISIEEJcEUJ4V2TlGWOM6VecK/d1APyey5sF4DARNQZwOO81ALwOoHFeGg9gRflUkzHGWEkUGdyJ6BiAhOey/QGsz/t9PYABBfJ/zXvO5wwAWyFEnXKqK2OMsWIqbZ+7AxHF5v0eB8Ah7/e6AAp+Q0V0Xh5jjLEXqMxPqBIRlWYooxBiPHK7bhhjjJWz0l65P8rvbsn7mf9ExkMA9QuUq5eXp4OIAoiojaExmowxxkqvtMF9N4BReb+PArCrQP47eaNmfAA8K9B9wxhj7AUpsltGCLEFQFcANYQQ0QC+APANgG1CiHEA7gMYkld8P4DeACIApAMYUwF1ZowxVgSefoAxxl5ePP0AY4z9m3BwZ4wxI8TBnTHGjBAHd8YYM0Ic3BljzAhxcGeMMSPEwZ0xxowQB3fGGDNCHNwZY8wIcXBnjDEjxMGdMcaMEAd3xhgzQhzcGWPMCHFwZ4wxI8TBnTHGjBAHd8YYM0Ic3BljzAhxcGeMMSPEwZ0xxoxQkV+QXdUpFAqsXLkSNWrU0OZt3LgR27dvL3S9r7/+Gs2aNQMAfPDBB7h3757ecsOHD8fQoUMBAKtWrUJQUFCh2126dClcXV21r//66y+sXLmyOIdS7ubMmYM2bf739YoXLlzAV199Ve776dKlCz766CPt68zMTLz33ntISUmRlKtduzZ+/vlnyGT/u6aYM2cOrl27Vi71mDdvHlq2bAkA+PjjjxEREVEu2wWANm3aYM6cOQCAw4cPY9myZUWuU7duXfz0008QQmjzPv30U1y/ft3gOmZmZli9ejWsrKyQlJSE8ePHIzs7u8z1t7a2xurVq2FqaorHjx9j4sSJ0Gg0ha4jk8mwfPly1KlTB9nZ2Rg/fjySkpLKXJd8AwcOxKhRowAA69atw86dO4u97rJly3Dnzh389NNPWLlyJU6ePInAwMByq5sxqJLB3dXVFTVr1gQAhIeHGzyhatSoAQ8PD/Tr1w+1atWCRqPB5cuXYWlpqbd8o0aNYG9vDwB4/fXX0apVKwDA3LlzdcrKZDK0atUKr732Gvz9/QEAt27dQmxsLEJDQ3XKW1tbo0mTJujduzfc3d21+RqNBhcuXEBoaChUKlWx2+B5LVq0gJmZmfZ1TEwMoqKi9JY1NzeHl5cXevXqhU6dOmnz7e3tcfDgQVy5cgUZGRna/Dp16sDJyUlnO5GRkXjy5Emh9fL09ETXrl21bQQAqampMDExkZRzcXFB69at4e/vjzt37iArKwuenp44ePAgVCoVbt68WXgDFMLCwgLNmzeHn58f2rdvDwDYtWsXABQrwJuYmKBly5YQQiAjIwNXrlyRLG/WrJnkGOVyOc6dOwcAiI2NxYMHD7RllUolWrRoAblcDmdnZ/j7+0uCe1BQENRqNcLDw7V5Qgi0aNECpqamsLCwQP/+/WFtbY2EhAT4+Pjg5s2bePz4cSlbJ/dNxtPTE/3794eZmRliY2Ph4+OD8PBwPH36VKe8p6cnLC0tIYRAvXr10KxZMzg6OiIwMBBXr15FdHR0oftzd3eHra0tACAsLAypqamS5fnH2717d22bRkVFITY2FoD0vHNzc4OdnZ3O+n369MHNmzdx4cIF9OvXD8nJyaVqG6NGRIUmAGsBPAZwrUDeYgA3AVwBsAOAbYFlswFEAAgH0Kuo7eetQwVTYGAg5evXrx89vzw/jRw5kgpKTk4mOzs7g+X//PNP0sfLy0unrKWlJcXHx+uUvXPnDsnlcp3y3bp107ttIqL09HSqVauWwXoVlWQyGYWHh0u2uXDhQoPlmzZtShqNRm9dNBoNNW3aVFL+P//5j96y48aNK7JuV65c0VkvJSWF7O3tJeVWrFihXT548GDy9vbWvj506FCp2wYAeXl56a3/n3/+Waz169evT1lZWUREdPXqVRJCSJafPn3a4N920aJFkrKOjo6UmZlpsDwR0f79+yXrKJVKun//vsHyEyZMKFP7fPHFF3q3O3ToUL3lL1y4QEREKpWKGjVqRBMmTNCus2DBgiL3t3//fm359u3b6yw3NTWlhw8fGjze0aNHa8vu3r270LbMt3Tp0jK10UucLpCBuFqcK/d1AH4C8GuBvIMAZhORSgjxLXID+kwhRFMAwwA0A+AI4JAQwo2I1MXYT7EJIbB+/Xq0b98eKpUKw4YNw6NHj6BSqXS6Ap538+ZNvPfee5K8O3fuSF6/8cYb+Oijj2BjY4O1a9dKPu5Vr14df//9N+bNm4eQkBCd7b/77ruSq7IBAwbg/fffL81hAgA6deqEhQsXon79+ti7dy+WLl2K33//vVjrzpw5E6dOndK+7tChA7755ptS16Wgdu3aYcmSJZg/fz7i4uIky1QqFZ49e6azTkxMDN566y2EhYUhMzMTnTt3xg8//FDmuty5cwedO3eW5K1evRpdunTB0aNHMWLECINXm1OmTME777wDpVJpcPsTJ06ElZWVJE+pVGLbtm06ZePj4+Hr6yu5Wi9o+fLlOnkqlQpvvPGG5JMZkHuuFfdvrY+ZmRl+//13eHl54dmzZ3jzzTcln9iGDx+OXr16YezYsTrrHj16FHPmzEF0dDR27dqFiIiIMtVFn82bN2PFihU6+bdv39b+PmvWLCxatEjv+r169cKsWbMwbNgwXLx4sVzrZgyKDO5EdEwI4fJc3oECL88AGJz3uz+A34goC8BdIUQEgHYAThenMqampujatSsSEhJw/PhxnX/Yglq1aoVq1aohKCgIR48eRXx8vMGyFhYW6NKlCx4+fIgHDx7gxIkThdbD0dER7du3x5EjR3Do0CFJeVdXV3Ts2FHbbQTk9sfmdwdcvnwZly5d0i7z9PSEXC6Hr68vzp8/X+J+4Pw3rPy6nD59uth9sNevX5fUPf+j8vMiIyMl9xLy/w6FsbOzQ+fOnfH+++8X2mduYmKCrl27wsnJCRkZGThx4gTU6tz3+hMnTpRLH25aWprO3zQ4OBhdunRBp06ddIJmQa6urmjevDkOHDiA5s2b6y3zzz//6OSZmJggMzNTJz87OxsnT540uD993QdEhAsXLujkOzg4QK1Wo1mzZujSpQuOHTtmcLv6yGQy+Pj4ICkpCUFBQTh27BiysrK0y6dMmSLpQiwoPj5e26ZxcXF49uwZsrOz0bhxY7z22msICQnR/h3zVatWDZ06dcL9+/dx9uxZ7f+EIdHR0UX+LxZ2f6JBgwYgIpw7d85gF+W/WXn0uY8FsDXv97rIDfb5ovPydAghxgMYXzCvRo0a2L17NyZMmIDVq1cX+ocFcm9svfPOO0VW0NHREfv27cPgwYOxY8eOIssDQEZGBoYNG1bom0a+b775Br6+vvldTDpMTEywefNmfPXVV/j888+Ltf98Z86cQe/evbWvCwtURaH/dYNJ7NixQ9IuderUQWRkZKHbEkIYPN6CbG1tsWPHDlhYWOh8QqpIH3zwAQYOHFjkjXUAePLkCfr164c1a9Zo78NUJVOnToWfnx+aNGmiE1CLY9OmTZg3b1651GXo0KF47bXX4OLiotOX7uLigv3796NPnz7YtGkTjh8/Xi77ZKVTpqGQQojPAKgAbCrpukQUQERtiKhN0aVfPAsLCxw9ehQTJkwoVvlz587By8tL5w1p27ZtaNu2LRISEiqimjoWLFiAHTt26O0WOHbsGFq1aoXvvvsOCxYsKPU+AgMDMWLECHh5eRX5SSQhIQHt2rUr94/0ZWVtbY3Tp08jLi4OPXv2LNPN7oq2YMEC9OvXr1SBvbzld3elp6dXdlVYEUod3IUQowH0BTCC/ncJ9xBA/QLF6uXlFally5bo2bMntm3bVuhVo6OjI9566y2DXQzlITw8HNu3b0fDhg3h4OCgzW/Tpg369++vN3Cmpqbi2rVrOh/VExISEBYW9sKCR/369VG7dm1s3rxZp585JSUFV69ehZOTE+rXr29gC0XLH82k73ifp1KpEBYWpndURkXy8/ODi4sLNm/erHOFCeSOeGnWrBlycnJw8+bNYn0KqSwPHz6U3Md5EZycnDB8+HBUq1ZNkv/o0SNcv35dZxhlhw4d0LFjR2zatAkxMTEVXr8+ffqgTp062LJlC9LS0ip8fy+jUnXLCCH8AMwA8CoRFXwL3w1gsxBiKXJvqDYGcK4423zrrbcwfPhwNGzYENnZ2fDw8NBbrkWLFti4cSNUKhU0Go3eG2FqtVrvGF6FQqG3fE5OjuT1gQMHcPLkSdy/fx8ymUy7zrhx4zBx4kTtvquq6OhovP322y8kYCkUCp03OyLSeTNTqVRQq9VQKpWSce4ajaZcrkif/7vOmzcPDx48wJAhQ3TKymQyKBQK5OTkFPvvKISAQvG/fxelUmnwPHuZCCGgVCqhUqm054tKpUKbNm2wYcMGeHp64s6dO9r20ndOKRQKTJ48GV5eXvDy8gIRSYbgGlLwfwvQf94YqvM333yDy5cvF6tb9t+qyOAuhNgCoCuAGkKIaABfIHd0jCmAg3n/2GeIaCIRhQkhtgG4jtzumsnlPVIGyD0JevfujQYNGkjurOf79ttv9d6FX758ORYvXqyT7+fnZ3Cc9QcffIDRo0cDyB0n/uDBA3Tr1k1nhMi/1d69e3XeiNPT09GhQwfJzdIvvvgCmzZtwvXr1yXB/cMPPyz0BmRxeHh44K+//pLkTZgwQXJj+/ll77//Pjp27IiHD4v1wRK+vr745ZdftK9zcnLwxhtvvND7CBWhadOmiIiIwIgRI7Q3NwcMGIABAwZgxYoVOHz4MHJycpCVlYV+/frpPOzn6OiIY8eOwcHBweCDgIaMHz8eb775pvb1o0eP0Llz53J5aIsVb7TMcD3Zawop/zWAr0tSiVq1aiEjIwNr164t1lWcEALdu3dHamqq9mEVIPfG5ZgxY9C7d2/k5OQgMDBQsr2aNWvi8ePH+O233yTb69evH1xcXHQCBADY2NjAxsZG+/rx48e4f/9+lej/rEzOzs6YNm0arl69KukyaNmyJby9vSGXyyXlExIS8OTJEzg5OUmWJSUllekBHSB3BMrOnTsxcOBA7cNYPXr0gEKhwL59+3TK29raom7dunj48GGRQ2fzmZubw9nZWftarVajT58++Pvvv4sc8QHkPp07ZMgQnDp1qsib1QDg4+ODV155BQEBAbh69Wqx6mhI+/bt8d577yEwMBAqlQrW1tZ455134ObmBqVSCScnJ5ibm2vLx8XFaR8icnR0BJA7wCA2NlZndJNCoYCTkxNCQkIQEhJSrE+LarUaa9askfxfderUCe7u7pg8eTKCgoLK9FAby1UlnlCtX78+UlNT9V5VGzJr1ixs2LBB8rHMysoKffv2Ra9evdCmTRts3LhREoSzsrJw8+ZNTJ8+XbKtf/75B2FhYdrgrlAotE/o5V+1ALkjVWQyGapVq4bU1NR/dYBv3Lgxvv76a/j4+CAsLEybP23aNHh7e8PCwgLJycnaLi8TExOYmZkhLS1NcuWen19U331hYmJi8MEHH6BBgwaoXr06gNxPBI0bN8aRI0eQnp6uDToWFhYAUOJ+WpVKpdN3P2/ePFSrVq3I4G5mZgY3Nzd8/fXX6NWrl+TZA30sLCwwaNAgvPPOO2jQoIFkbHpJpaWloVOnTmjatCl27tyJ9PR0ODo64quvvoJcLtceU8HuEHNzcygUCsnxZmVlwdzcHCYmJpIra41Gg7S0NAQGBupcNBmiUql0ngpfsGABPvroIyxduhSJiYkGg7tcLoe5uTmys7PLdM78G1SJ4F5eUlNT0aJFC3z++ecYNmyYzvIJEyYUa/6K0aNH49tvv4WdnR0WLVqkfdNZvHgxRo0ahTt37mDcuHGSTw3/NkePHsWQIUP0jlOvVq0aQkND8X//93/47rvvAOTO5ePr64vGjRtL3hTXrVuH8ePH44033ihznUaOHAmlUgkhBA4ePAg/Pz9ERkbilVdeQWRkJExNTXH+/Hns3LkTLVq00Huj1ZDDhw/DxcVF+9rU1LTYD86sXr0ajo6OcHFx0ftwV0GWlpYIDQ1F3bp1y/xIfXp6Ory9vSGEgJ2dHS5evAgLCwtER0fD3d1dEtAL7mvPnj149OiR5HjNzMxw+PBhrF+/HgsXLtTmx8TEoFGjRiVqS30WLlyIrVu3Ftmm3bp1w+bNm9G/f/9ym5PIWFWZ4N6zZ0/JnfkaNWpACIG33noLDg4Okv5OQ4gICQkJBq90kpOTi/znAnKvXKysrLBo0SLs379fO9Lj999/x7NnzzB9+nSYmpoW88iMU05OTqEjYKpXrw5zc3NYWlriww8/RLdu3WBtbY2nT59Kgvu2bdvg6uqKL7/8EitWrCjTvYyCAWr58uXw9fXFkCFDtJ8UhBCoXr06unTpovfGXYsWLeDg4IAvv/wSv/76q2SYZ3Z2tuR45XI5Fi1aBGtra8yePRvff/+9zpVkjRo1MGXKFLRt2xZJSUnFGjGUX8dTp05h3759Ojf7Syp/CG5GRgZWrFgBpVKJpKQkPHnyBG+88QZq1KihvT/l4uKCMWPGoGnTpjr1VSgUWLVqFaytrTFr1iwsXboU3bt3xyuvvKJ3v/ndY+PHj4erqyu2bNlSaD3T09ORmJhY5PEolUrUqFEDKSkpZX5DMXZVIrirVCq0aNECLVq00Obl98sOGzYMLi4u2uCek5ODJ0+eaD9+V5SsrCwsXrxYcoIHBQUhPDwcU6dOLfZ2zMzMULNmTUlXREVTKBSoVasWEhMTJR+hTUxMYGdnJxn1Ud4yMjIQHx+vnaDN0tISn376KdRqNW7cuKFTfsOGDfD19cWhQ4ewY8eOcrtR/csvv+Dp06eS0TJEhPj4eLi7u0uezJTJZNr6qtVqTJw4EceOHSt0DL9arcb333+PTz75BJ999hl+/vlnneBub2+Pzz//HKmpqbh7926RdTY3N0eNGjWQkJCAvXv34r///W8Jj9qw9PR0yRU3kDvNhru7uyS4z507F4mJiTqfGlQqFb7//nt89tln+OSTT/DTTz+hY8eOBp8DyR8FM2jQICiVyiKDOyt/VSK4X716VfIREMidDe7SpUs6w+xCQkLQoEEDnD9//gXWsPTefvtt/Pjjj5IbVhWtcePGiIyMxODBgyXTCvj6+mL79u0wNzfH6dPFmhGixAIDA7Fr1y6dQP7ZZ58hICCgUu9TZGVloV27djrnVL169XDt2jUolUrcunULbdu2Ldf+3Pfeew+7d+8ustzYsWMxd+5ceHt749GjR+W2/5Lq37+/dtbLwsyfP1/nDSNfhw4dcPDgQQwYMABnzpzRW4ZVrCoR3DUajc4Tb/n/XKtWrcLBgwe1+Wq1Gunp6XqDhKmpKRYsWIDu3btXbIX1cHNzw7Jly7Bo0SLJPBcKhQIKhQKzZ8/WO9FYeduwYQOioqIwZ84cnRErcrkcFhYW+Oqrr3DkyJEy7adJkyZYtmwZFi5cKHlopVOnThg0aBC+/PJLyY1DQzfApk6dCl9f3zLVpST0ddnFxMRg+vTpGD16NCwsLCQ3YA1RKBT44osvDJ5rI0aMQOvWrTF9+nScO3eu0DcLuVyOL774AgDw+eefIz4+vlKfmJ02bRoOHDhQZFdoTk6OwW6j/OPNzMyUzGdTFh9++CEcHBwwdepU7fTAzLAq/01M+/btwx9//KF3WbVq1eDi4qINYiYmJnj33Xfh6uqKBw8e6PyDOjg4aId2Abkfg11cXHTmHgdyP6o7OzsX60nY2NhYKBQKTJkyRTKhWD6VSoW1a9fi7NmzRW6rrA4fPowtW7aAiODg4IA6depIlhMRtmzZgsOHD+td387ODk5OToV2I8XGxsLU1BRTpkzR6R7z8vLCmDFjsGnTJly4cAFqtRr37t2DiYkJ6tWrp7OtAQMGoFevXrh7926pxjfXrFkTdevqTl/k6Ogoebq4MKmpqVixYoXBp0Dr1Kmjsy2ZTIbRo0ejWbNmuH//vvZhJrlcDhcXF/j7+6N37974+eefCx3/bWlpiQYNGmDcuHGwsrJCQEBAuQVDQxQKBVxcXJCWliZ5Y87MzMTdu3fh7+8PPz8/yTpCCDg5OUEIgfv375f7A3LVq1cv8qnpQYMGoXnz5li+fPkLm87jZVblg3thBgwYgLCwMJ0A9t1336FDhw46/yTLly+XvFF06tQJt2/f1vs0rIWFBc6dO4cpU6YUWY/Ro0dXySflAgICsHXr1qILFvDxxx/j5MmTet/w8o0YMQJjxowp1vaePn0KLy8veHh44PDhwzqfJgDg1KlTcHNzK3KiOH2WLl2qt8vjjz/+0Du9bmls27bN4Ldp/fLLL/D29taOl69VqxauXr2KwYMH6y3/vP79++PGjRuSi46KVq9ePdy4cQOHDh1C//79tflnz56Fm5ub3lEoZmZmOHnyJExNTdG2bdtyf+R/xowZOHHiRKHnHSuZKtEtU1JEhBkzZqBv376YOHEifv75Z6SnpyMnJwfTp0/H+fPnJd02cXFxGD58OD7++GO4ublpx+PWrl0bCoUCM2fOlEynGhQUhNGjR2PZsmUYOnQoPD09tcvS0tIwcuRISZ+1Wq3GP//8g2HDhmH8+PGSq/27d+/inXfeKdYoHX3atGmDjz/+WPtaJpPBzs4O/v7+aNCgAYDcrpiCD+tER0dj+PDhmDlzJpo2bao93vx2eH7OmT59+mDkyJEAcq+88wPwhAkT0KNHDwDAkiVLtNPSqtVqXL58GcOHD8fUqVMlD6PcuXMHo0ePljwcpFKpIISAo6MjNm/eLLnq8/T0xNWrV0vdDSGXy+Hq6qozxtrNzQ0XL17EkiVLynyTVqFQoF27dpJ9qNVqfP7557h8+bLkXMt/nL/g8T4vNDRUO6++XC7X3uDu3bu3zoUKkDuU0tAnreIYPHiw5M0mLS0NY8eOxcmTJyV1z3/8n4jQvn17yfHK5XLtV1mW9b6JQqHAjz/+KPnU16JFCyQnJ2PatGnFeiiMFa3KBvfMzEyEhoYaHOsbFBQEuVyODh06aD/O5T+x+vw6qamp2LZtG9q3bw+lUikZKREaGoqdO3fi1q1b2ryIiAg8fPgQo0ePhq2traR8dHQ0tm3bpnOCP378GFu3boW/v7+k/NWrV4s17awhVlZWOnNu5z/gkZ//fNdIcnIytm7dio4dO6Jz587acvl1fF716tW1ZbKysrRfI1iwrZ7/soq4uDj89ttvGDRoEBo3bqzNv3jxot5utOjoaERERMDNzU2SHxMTU6ZH+O/fv4979+7ptNGDBw9w/PhxvV+oUdi28h9yKujWrVswMzOT7CMnJwcffvihztO1OTk5+Oeff7RXoPrmSy/41YWJiYmSr23UV76sk+TZ29tLthsTE6P3HM4XHh4OuVyu97wr7htlamoqQkND9V7hy2QyNGrUSNKFmZmZifPnz2Pr1q0G+/EjIiJ4+GMJiKowG17e15oxxhgrmYuGpk1/qfvcGWOM6cfBnTHGjBAHd8YYM0Ic3BljzAhxcGeMMSPEwZ0xxowQB3fGGDNCHNwZY8wIcXBnjDEjxMGdMcaMEAd3xhgzQhzcGWPMCFWVWSHjAaTl/WSG1QC3UVG4jYrGbVS0l6WNnA0tqBKzQgKAEOKCodnNWC5uo6JxGxWN26hoxtBG3C3DGGNGiIM7Y4wZoaoU3AMquwIvAW6jonEbFY3bqGgvfRtVmT53xhhj5acqXbkzxhgrJ5Ue3IUQfkKIcCFEhBBiVmXXpyoRQtwTQlwVQoQKIS7k5VUXQhwUQtzO+2lX2fV8kYQQa4UQj4UQ1wrk6W0TkevHvHPrihDCu/Jq/uIYaKN5QoiHeedSqBCid4Fls/PaKFwI0atyav1iCSHqCyFChBDXhRBhQojpeflGcy5VanAXQsgBLAfwOoCmAIYLIZpWZp2qoG5E1LLAsKxZAA4TUWMAh/Ne/5usA+D3XJ6hNnkdQOO8NB7AihdUx8q2DrptBADf551LLYloPwDk/b8NA9Asb52f8/4vjZ0KwH+IqCkAHwCT89rCaM6lyr5ybwcggogiiSgbwG8A/Cu5TlWdP4D1eb+vBzCg8qry4hHRMQAJz2UbahN/AL9SrjMAbIUQdV5IRSuRgTYyxB/Ab0SURUR3AUQg9//SqBFRLBFdyvs9BcANAHVhROdSZQf3ugCiCryOzstjuQjAASHERSHE+Lw8ByKKzfs9DoBD5VStSjHUJnx+SU3J61JYW6A771/fRkIIFwCtAJyFEZ1LlR3cWeE6EZE3cj8SThZCdCm4kHKHOvFwpwK4TQxaAaAhgJYAYgF8V6m1qSKEENUA/AHgAyJKLrjsZT+XKju4PwRQv8Drenl5DAARPcz7+RjADuR+XH6U/3Ew7+fjyqthlWGoTfj8ykNEj4hITUQaAKvxv66Xf20bCSGUyA3sm4joz7xsozmXKju4nwfQWAjRQAhhgtwbO7sruU5VghDCUghhlf87gJ4AriG3fUblFRsFYFfl1LBKMdQmuwG8kzfSwQfAswIfuf9VnusfHojccwnIbaNhQghTIUQD5N4wPPei6/eiCSEEgDUAbhDR0gKLjOdcIqJKTQB6A7gF4A6Azyq7PlUlAXAF8E9eCstvGwD2yL2LfxvAIQDVK7uuL7hdtiC3WyEHuf2e4wy1CQCB3NFYdwBcBdCmsutfiW20Ia8NriA3UNUpUP6zvDYKB/B6Zdf/BbVRJ+R2uVwBEJqXehvTucRPqDLGmBGq7G4ZxhhjFYCDO2OMGSEO7owxZoQ4uDPGmBHi4M4YY0aIgztjjBkhDu6MMWaEOLgzxpgR+n99QgyE2NLSQwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./out/gray-no-title.jpg', cv2.IMREAD_GRAYSCALE)\n",
    "\n",
    "ret,img_threshed=cv2.threshold(img, 95, 255, 1)\n",
    "\n",
    "img_show_array(img_threshed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140, 229)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img_threshed.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def img_y_shadow(img_b):\n",
    "    ### 计算投影 ###\n",
    "    (h,w)=img_b.shape\n",
    "    # 初始化一个跟图像高一样长度的数组，用于记录每一行的黑点个数\n",
    "    a=[0 for _ in range(0,h)]\n",
    "    # 遍历每一列，记录下这一列包含多少有效像素点\n",
    "    for i in range(0,h):          \n",
    "        for j in range(0,w):      \n",
    "            if img_b[i,j]==255:     \n",
    "                a[i]+=1  \n",
    "    return a\n",
    " \n",
    "shadow_on_y = img_y_shadow(img_threshed)\n",
    "\n",
    "\n",
    "show_shadow(shadow_on_y, 'y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def img2rows(a,w,h):\n",
    "    \n",
    "    ### 根据投影切分图块 ### \n",
    "    inLine = False # 是否已经开始切分\n",
    "    start = 0 # 某次切分的起始索引\n",
    "    mark_boxs = []\n",
    "    for i in range(0,len(a)):        \n",
    "        if inLine == False and a[i] > 10:\n",
    "            inLine = True\n",
    "            start = i\n",
    "        # 记录这次选中的区域[左，上，右，下]，上下就是图片，左右是start到当前\n",
    "        elif i-start >5 and a[i] < 10 and inLine:\n",
    "            inLine = False\n",
    "            if i-start > 10:\n",
    "                top = max(start-1, 0)\n",
    "                bottom = min(h, i+1)\n",
    "                box = [0, top, w, bottom]\n",
    "                mark_boxs.append(box) \n",
    "                \n",
    "    return mark_boxs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 10, 229, 26], [0, 46, 229, 62], [0, 82, 229, 96], [0, 116, 229, 132]]\n"
     ]
    }
   ],
   "source": [
    "(img_h,img_w)=img.shape\n",
    "row_mark_boxs = img2rows(shadow_on_y,img_w,img_h)\n",
    "print(row_mark_boxs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['./cut-rows/part_0.jpg', './cut-rows/part_1.jpg', './cut-rows/part_2.jpg', './cut-rows/part_3.jpg']\n"
     ]
    }
   ],
   "source": [
    "# 裁剪图片,img 图片数组， mark_boxs 区域标记\n",
    "def cut_img(img, mark_boxs):\n",
    "\n",
    "    img_items = [] # 存放裁剪好的图片\n",
    "    for i in range(0,len(mark_boxs)):\n",
    "        img_org = img.copy()\n",
    "        box = mark_boxs[i]\n",
    "        # 裁剪图片\n",
    "        img_item = img_org[box[1]:box[3], box[0]:box[2]]\n",
    "        img_items.append(img_item)\n",
    "    return img_items\n",
    "\n",
    "# 保存图片\n",
    "def save_imgs(dir_name, imgs):\n",
    "\n",
    "    img_paths = []\n",
    "    for i in range(0,len(imgs)):\n",
    "        file_path = dir_name+'part_'+str(i)+'.jpg'\n",
    "        cv2.imwrite(file_path,imgs[i])\n",
    "        img_paths.append(file_path)\n",
    "    \n",
    "    return img_paths\n",
    "\n",
    "# 切图并保存\n",
    "row_imgs = cut_img(img_threshed, row_mark_boxs)\n",
    "imgs = save_imgs('./cut-rows/', row_imgs) # 如果要保存切图\n",
    "print(imgs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAA3CAYAAAAVMxFfAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAJB0lEQVR4nO3de2yV9R3H8fe3p4UydYhzKhY2oVS8bILGCSJxMqcrLAHUZCnOaDIzskyNRqaBmWXL/pj84Vzm4pw4nZcgjEWnmJHpvCT7oyIXlSJUsOANgi3FQWnp5Vy+++M8wGk5p4e2p8/p035eyck5z++5ffPt73xzzu95zq/m7oiISPSUFDsAERHpHxVwEZGIUgEXEYkoFXARkYhSARcRiSgVcBGRiBpQATezajPbYWYNZra0UEGJiEh+1t/7wM0sBuwErgP2ABuBRe6+vXDhiYhILgP5BH4F0ODuu929C1gNLChMWCIikk/pAPatAD7PWN4DzOhthzPPiPl5E8sGcEoRkZFnc11ns7t/vWf7QAr4STGzxcBigG9UlLLh1YlZt7t0Yw2HG07PeRyPwWs3PERl2alZ11+7fT6fbjk367oxk1vYOuP5vLHuS7Ry1UtLKInbsbY7q//NPeM+ybvvLxsvYc2bs7KuS45NsHPu45RZLO9ximGgubv54zlsWD81+8pzOmmY87eBhjhopm1YRNuusTnXewxev+EhJvXodx/HW7n2pV9Qkuj9+G6wcuGjzCwfmn97iYbY+IZPs7UPpIDvBTKr8YSgrRt3XwGsALh8WvkJA+5xT1Ifj1O++nTOWrU+58ls9Ghe/P40bvnqFsaXHn8zJT3Fh/FOml+ZQOUfa7Pue+TGGdRd2sHUshijLfs3gKZkG+vapjD1ge2kDh8+1v78Bd/JW8B3xttYtXEG5y/JHn/s/Eo2fw8uHNXO2JIxvR4rTEdzd+DlCVT+KXvu2m7qPXf1XUfY/OYFVP7q7az7p2ZPp+6qDqaUlvCVklEFjb8QxvxjLOeszN3vSsrLefm6b3HzV7dxVuyUY+27E2OZuqyO1JEjvZ/AjNrrq5hZvrtQIYscM5Ax8I1AlZlNMrNRQA2wtq8HebalgmVXLmTsi+/1up13dvLWNedx9er7ugfR6dw/p4ZzH383576nvPIey2Yu4LGDVTm3mbn2Xl64+tvdivfJ6PQ4P7/tLi5Y8mHObZINn/DbK+dSvfWWPh17sK3vhPvn1DD+idy5O3VtOncrDk45Yd2eRCv3zv8Jk5fX5dw/tv4Dls6Yz9175xQk5rClOjp47buVzFqzpNihiJyg3wXc3RPAncCrQD2wxt239fU4cY+R+KIR7+zMu22y+QCxduvW1kWMVFMzqY6O3LHGu0h80chfn5vHlVtuyrpNSYeR3L+/b8EHyv7X3nvhTyVJNjbR0TW0xv/jXnrSuXv8uR9yVd2N3dalgJIDLaTa2nLvn0iQbGyiLTG0Pn1v6IxTufpnjNvWknfbZPMBYh2WdzuRsA1oDNzd1wHrChTLoKtYXktTyyyYVpjjHUq1syNeiiVShTngEFaxvJamw7PgkmJHUhi1R6qYsuQdUppOWSJs0C9iDmcL62sYc0s7yf0NxQ5FREYg/ZR+ADoSpSQbmyCVLHYoQ972v1/IxW//uNhhiAwrKuARkPQU27raaU7mHmse6s5+pJZxq7LfAioi/aMCHgG7Eu3cN/dWrnjrrmKHIiJDiAp4BCTdYP+XeId+DBI57jy5sprZPe7gESkEFXCRQTbhwVpa/3VOscOQYShvATezp8ysycw+yGg7w8z+Y2YfBc/jBjdMERHp6WQ+gT8NVPdoWwq84e5VwBvBsoiIhChvAXf3/wJf9mheADwTvH4GWFjYsKQvPku0siveWuwwRCRk/f0hz9nuvi94/QVwdoHikX5Y+Lv7KD/o1D78l2KHIiIhGvBFTE//S5+cv0c2s8VmtsnMNu0/oB+8DIayNhjVotyKjDT9/QTeaGbj3X2fmY0HmnJtmG862aGgvutIzsmKWtrKqes6PtnTaZY4YW5oEZFi6G8BXwvcBiwPnl8uWEQh25do5d4FP2VyQx3ZpqSavPgzlo6ef2y5ubqSDQ8+Fl6AIiI55C3gZrYKuAY408z2AL8mXbjXmNntwKfAjwYzyMGUBEqaD5HIMSVq8uChbsujWieFEJWISH55C7i7L8qx6toCxyIiIn1gHuJ8yGa2H2gDmkM7aTSdiXKUj3KUn3KUX1Ry9M1s/9Q41AIOYGab3P3yUE8aMcpRfspRfspRflHPkeZCERGJKBVwEZGIKkYBX1GEc0aNcpSfcpSfcpRfpHMU+hi4iIgUhoZQREQiKrQCbmbVZrbDzBrMTNPPBszsEzPbambvm9mmoG1Ez7felznoLe2RoF/VmdllxYs8PDly9Bsz2xv0pffNbF7GumVBjnaY2Q+KE3W4zGyimb1lZtvNbJuZ3R20D5u+FEoBN7MY8CgwF7gIWGRmF4Vx7oiY4+7TM25nGunzrT/Nyc9BPxeoCh6LgZEyz8HTnJgjgD8EfWm6u68DCN5rNcDFwT5/Dt6Tw10CWOLuFwEzgTuCXAybvhTWJ/ArgAZ33+3uXcBq0nOKS3Yjer71Ps5BvwB41tPWA6cHE6wNazlylMsCYLW7d7r7x0AD6ffksObu+9z93eD1YaAeqGAY9aWwCngF8HnG8p6gTdJT8b5mZpvNbHHQpvnWT5QrJ+pb3d0ZfP1/KmPobcTnyMzOAy4F3mEY9SVdxCy+2e5+Gemvb3eY2dWZK/PNtz4SKSc5PQZUAtOBfcDvixrNEGFmpwIvAPe4e0vmuqj3pbAK+F5gYsbyhKBtxHP3vcFzE/BP0l9tG49+dcs33/oIkisn6lsBd29096S7p4AnOD5MMmJzZGZlpIv3Snd/MWgeNn0prAK+Eagys0lmNor0BZW1IZ17yDKzU8zstKOvgeuBDzg+3zpEfL71AsqVk7XArcEdBDOBQxlfj0eUHuO1N5DuS5DOUY2ZjTazSaQv0m0IO76wmZkBTwL17v5wxqrh05fcPZQHMA/YCewCHgjrvEP5AUwGtgSPbUfzAnyN9NXxj4DXgTOKHWvIeVlFegggTnoc8vZcOQGM9B1Ou4CtwOXFjr+IOXouyEEd6WI0PmP7B4Ic7QDmFjv+kHI0m/TwSB3wfvCYN5z6kn6JKSISUbqIKSISUSrgIiIRpQIuIhJRKuAiIhGlAi4iElEq4CIiEaUCLiISUSrgIiIR9X+PffNxi9HrwwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 切每行\n",
    "\n",
    "for index, row_img in enumerate(row_imgs):\n",
    "    # 纵向映射\n",
    "    if index != 2:\n",
    "        continue\n",
    "    #! 膨胀图片\n",
    "    row_img = cv2.dilate(row_img, np.ones((2,1),np.uint8), iterations=10)\n",
    "    ### 计算投影 ###\n",
    "    # plt.imshow(row_img, cmap='gray')\n",
    "    (h,w)=row_img.shape\n",
    "\n",
    "    dots_num = [0 for _ in range(0,w)]\n",
    "    # 遍历每一列，记录下这一列包含多少有效像素点\n",
    "    # 每列\n",
    "    for i in range(0,w):\n",
    "        # 第 i 列的每一行          \n",
    "        for j in range(0,h):   \n",
    "            # 判断白点   \n",
    "            if row_img[j,i] == 0:     \n",
    "                dots_num[i] += 1\n",
    "     ### 根据投影切分图块 ### \n",
    "    show_shadow(dots_num, 'x')\n",
    "    is_start = False # 是否已经开始切分\n",
    "    start_index = 0 # 每次切分的起始索引\n",
    "    mark_boxs = []\n",
    "    for i in range(0,len(dots_num)):        \n",
    "        if is_start == False and dots_num[i] < 15:\n",
    "            is_start = True\n",
    "            start_index = i\n",
    "            # print(f\"start_index: {start_index}\")\n",
    "        # 记录这次选中的区域[左，上，右，下]，上下就是图片，左右是start到当前\n",
    "        elif is_start and dots_num[i] >= 15:\n",
    "            is_start = False\n",
    "            if i-start_index > 4:\n",
    "                left = max(start_index-1, 0)\n",
    "                right = min(w, i+1)\n",
    "                box = [left, 0, right, 0]\n",
    "                mark_boxs.append(box)\n",
    "                # print(left) \n",
    "    print(len(mark_boxs))\n",
    "    # 裁剪图片\n",
    "    \n",
    "    img_items = [] # 存放裁剪好的图片\n",
    "    for i in range(0,len(mark_boxs)):\n",
    "        img_org = img.copy()\n",
    "        box = mark_boxs[i]\n",
    "        # 裁剪图片\n",
    "        img_item = img_org[box[1]:box[3], box[0]:box[2]]\n",
    "        img_items.append(img_item)\n",
    "    # 保存图片\n",
    "    # img_paths = []\n",
    "    # for i in range(0,len(img_items)):\n",
    "    #     file_path = './cut-rows/'+'row-'+str(index)+ '/' + str(i) +  '.jpg'\n",
    "    #     cv2.imwrite(file_path,img_items[i])\n",
    "    #     img_paths.append(file_path)\n",
    "    \n",
    "    "
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "幻灯片",
  "interpreter": {
   "hash": "b486024881bd5bec090869095d006737bfa080e96b026fae63476258b2d8db6e"
  },
  "kernelspec": {
   "display_name": "cv",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}