Ch03.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OpenCV 기본연산"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 참고사항\n",
    "현재 cv2는 numpy.ndarray을 이용하여 표현한다. 이러한 점에서 OpcenCV의 영상 내 자료값은 Numpy로서 치환하여 astype(), reshape()로 속성을 변경하고, 영상 화소를 y,x순으로 인덱스를 지정 접근하여 밝기 또는 컬러값을 접근한다.  \n",
    "따라서 Numpy를 사전지식으로서 알고 있어야 OpenCV의 자료를 마음대로 가공하고 접근하여 연산처리가 가능하다.  \n",
    "\n",
    "<a href=\"https://wjddyd66.github.io/dataanalysis/2019/07/07/Numpy.html\">Numpy Post</a><br>\n",
    "\n",
    "#### 필요한 라이브러리 임포트"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widgets \n",
    "import IPython.display as display\n",
    "from ipywidgets import Layout, Button, Box, Layout, Image, IntSlider\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 속성과 화소 접근\n",
    "\n",
    "OPenCV는 화소 자료형으로 표기하고, Numpy는 다중 채널 영상을 모양(shape)에 의해 표현한다.  \n",
    "\n",
    "**Numpy와 OpenCV자료형**  \n",
    "\n",
    "<table class=\"table\">\n",
    "\t<tr>\n",
    "\t\t<td>구분</td>\n",
    "\t\t<td>numpy 자료형</td>\n",
    "        <td>OpenCV 자료형</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>8비트 unsigned 정수</td>\n",
    "\t\t<td>np.uint8</td>\n",
    "        <td>cv2.CV_8U</td>\n",
    "\t</tr>    \n",
    "    <tr>\n",
    "\t\t<td>8비트 signed 정수</td>\n",
    "\t\t<td>np.int8</td>\n",
    "        <td>cv2.CV_8S</td>\n",
    "\t</tr>    \n",
    "    <tr>\n",
    "\t\t<td>16비트 unsigned 정수</td>\n",
    "\t\t<td>np.uint16</td>\n",
    "        <td>cv2.CV_16U</td>\n",
    "\t</tr>    \n",
    "    <tr>\n",
    "\t\t<td>16비트 signed 정수</td>\n",
    "\t\t<td>np.int16</td>\n",
    "        <td>cv2.CV_16S</td>\n",
    "\t</tr>    \n",
    "    <tr>\n",
    "\t\t<td>32비트 signed 정수</td>\n",
    "\t\t<td>np.int32</td>\n",
    "        <td>cv2.CV_32S</td>\n",
    "\t</tr>    \n",
    "    <tr>\n",
    "\t\t<td>32비트 실수</td>\n",
    "\t\t<td>np.float32</td>\n",
    "        <td>cv2.CV_32F</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>64비트 실스</td>\n",
    "\t\t<td>np.float64</td>\n",
    "        <td>cv2.CV_64F</td>\n",
    "\t</tr>\n",
    "\n",
    "</table>\n",
    "<br>\n",
    "\n",
    "#### 모양, 자료형\n",
    "- astype: 속성\n",
    "- ndim: 차원\n",
    "- shape: 크기\n",
    "- dtype: 원소 자료형\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Color Image\n",
      "img.ndim =  3\n",
      "img.shape =  (512, 512, 3)\n",
      "img.dtype =  uint8\n",
      "img.dtype =  int32\n",
      "img dtype =  int64\n",
      "--------------------\n",
      "GrayScale Image\n",
      "img.ndim =  2\n",
      "img.shape =  (512, 512)\n",
      "img.dtype =  uint8\n",
      "img.dtype =  int32\n",
      "img dtype =  int64\n"
     ]
    }
   ],
   "source": [
    "print('Color Image')\n",
    "img = cv2.imread('./data/lena.jpg')\n",
    "\n",
    "print('img.ndim = ',img.ndim)\n",
    "print('img.shape = ',img.shape)\n",
    "print('img.dtype = ',img.dtype)\n",
    "\n",
    "img = img.astype(np.int32)\n",
    "print('img.dtype = ',img.dtype)\n",
    "\n",
    "img = np.int64(img)\n",
    "print('img dtype = ',img.dtype)\n",
    "print('-'*20)\n",
    "\n",
    "print('GrayScale Image')\n",
    "img2 = cv2.imread('./data/lena.jpg', cv2.IMREAD_GRAYSCALE)\n",
    "\n",
    "print('img.ndim = ',img2.ndim)\n",
    "print('img.shape = ',img2.shape)\n",
    "print('img.dtype = ',img2.dtype)\n",
    "\n",
    "img2 = img2.astype(np.int32)\n",
    "print('img.dtype = ',img2.dtype)\n",
    "\n",
    "img2 = np.int64(img2)\n",
    "print('img dtype = ',img2.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 모양 변경하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "img.shape =  (512, 512)\n",
      "img.shape =  (262144,)\n",
      "img shape =  (512, 512, 1)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0f23459780954559884b9ac1f58f7152",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'', layout=\"Layout(border='solid')\", width='30%')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg',cv2.IMREAD_GRAYSCALE)\n",
    "print('img.shape = ',img.shape)\n",
    "\n",
    "img = img.flatten()\n",
    "print('img.shape = ',img.shape)\n",
    "\n",
    "img = img.reshape(512,512,-1)\n",
    "print('img shape = ',img.shape)\n",
    "\n",
    "wImg = widgets.Image(layout = widgets.Layout(border=\"solid\"),width=\"30%\") \n",
    "display.display(wImg) \n",
    "tmpStream = cv2.imencode(\".jpeg\", img)[1].tostring() \n",
    "wImg.value = tmpStream"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 화소 접근: 그레이 스케일 영상\n",
    "img를 Grayscale로 읽은 후 <code>img[100:400, 200:300]=0</code>을 통하여 img의 특정 값을 변경하였다.(ROI 지정)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0 153 150 141 151 150 151 145 144 144]\n",
      " [146 144 151 155 148 149 146 148 145 145]\n",
      " [139 146 157 148 142 146 148 146 144 140]\n",
      " [145 153 146 135 139 147 149 148 140 138]\n",
      " [151 149 139 142 148 150 149 141 142 147]\n",
      " [151 144 143 151 152 150 139 138 145 144]\n",
      " [149 151 149 151 149 148 150 143 142 141]\n",
      " [159 149 145 146 150 151 152 144 132 137]\n",
      " [151 144 144 144 152 149 139 134 140 144]\n",
      " [142 142 151 151 143 142 133 143 146 136]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a90446385c74043b0b77d3d0acd6210",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'', layout=\"Layout(border='solid')\", width='30%')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg',cv2.IMREAD_GRAYSCALE)\n",
    "\n",
    "img[100,200] = 0\n",
    "print(img[100:110,200:210])\n",
    "\n",
    "img[100:400,200:300]=0\n",
    "\n",
    "\n",
    "wImg = widgets.Image(layout = widgets.Layout(border=\"solid\"),width=\"30%\") \n",
    "display.display(wImg) \n",
    "tmpStream = cv2.imencode(\".jpeg\", img)[1].tostring() \n",
    "wImg.value = tmpStream"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 화소접근2: 컬러영상\n",
    "img를 Color로 읽은 후 <code>img[100:400, 200:300]=[0,0,255]</code>을 통하여 img의 특정 값을 변경하였다.  \n",
    "GrayScale과 달리 img의 Channel이 3이므로 대입하는 값이 단일 값이 아닌 배열로서 3차원의 값을 대입하여야 한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0   0 255]\n",
      " [109 117 213]\n",
      " [113 115 208]\n",
      " [114 101 199]\n",
      " [121 116 207]\n",
      " [105 114 209]\n",
      " [112 113 212]\n",
      " [107 109 204]\n",
      " [117 108 200]\n",
      " [110 109 202]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "90f1c0d78b8e4718a7e60b59ef77d69a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'', layout=\"Layout(border='solid')\", width='30%')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg')\n",
    "\n",
    "img[100,200] = [0,0,255]\n",
    "print(img[100,200:210])\n",
    "\n",
    "img[100:400,200:300]=[0,0,255]\n",
    "\n",
    "\n",
    "wImg = widgets.Image(layout = widgets.Layout(border=\"solid\"),width=\"30%\") \n",
    "display.display(wImg) \n",
    "tmpStream = cv2.imencode(\".jpeg\", img)[1].tostring() \n",
    "wImg.value = tmpStream"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 화소접근 3: 컬러영상 접근(채널 접근)\n",
    "img를 Color로 읽은 후  \n",
    "<code>img[100:400,200:300,0]=255</code><br>\n",
    "<code>img[100:400,200:400,0]=255</code><br>\n",
    "<code>img[100:400,200:500,0]=255</code><br>\n",
    "을 통하여 img의 특정 값을 변경하였다.  \n",
    "Image에 R,G,B로 접근하여 각각의 R,G,B의 값을 변경하였다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0   0 255]\n",
      " [109 117 213]\n",
      " [113 115 208]\n",
      " [114 101 199]\n",
      " [121 116 207]\n",
      " [105 114 209]\n",
      " [112 113 212]\n",
      " [107 109 204]\n",
      " [117 108 200]\n",
      " [110 109 202]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7df2d0271af64120856f350bc23523f3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'', layout=\"Layout(border='solid')\", width='30%')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg')\n",
    "\n",
    "img[100,200] = [0,0,255]\n",
    "print(img[100,200:210])\n",
    "\n",
    "img[100:400,200:300,0]=255 # B 채널 변경\n",
    "img[100:400,300:400,1]=255 # G 채널 변경\n",
    "img[100:400,400:500,2]=255 # R 채널 변경\n",
    "\n",
    "\n",
    "wImg = widgets.Image(layout = widgets.Layout(border=\"solid\"),width=\"30%\") \n",
    "display.display(wImg) \n",
    "tmpStream = cv2.imencode(\".jpeg\", img)[1].tostring() \n",
    "wImg.value = tmpStream"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ROI에 의한 블록 평균 영상\n",
    "하나의 Image를 선언한 Block의 개수로서 평균하는 Code이다.  \n",
    "즉, Image를 원한는 pixel로 변환하는 Code이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f3ef85038db34b52b81ea8549cf37e14",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'', layout=\"Layout(border='solid')\", width='30%')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg')\n",
    "#image와 같은 크기의 자료형 선언\n",
    "dst = np.zeros(img.shape,dtype=img.dtype)\n",
    "\n",
    "#dst의 이미지의 pixel개수를 선언\n",
    "#if)N=16이면 img를 16 x 16 개의 pixel로 나누어서 dst에 대입한다.\n",
    "N=16\n",
    "height,width,_ = img.shape\n",
    "\n",
    "#image를 나누기 위한 Parameter선언\n",
    "h = height//N\n",
    "w = width//N\n",
    "\n",
    "\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        x = i*h\n",
    "        y = j*w\n",
    "        roi = img[y:y+h,x:x+w]\n",
    "        #Color 영상이므로 단일 값이 아닌 Channel 3개의값으로 평균을 내야 한다.\n",
    "        dst[y:y+h,x:x+w] = cv2.mean(roi)[0:3]\n",
    "        \n",
    "wImg = widgets.Image(layout = widgets.Layout(border=\"solid\"),width=\"30%\") \n",
    "display.display(wImg) \n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring() \n",
    "wImg.value = tmpStream"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 마우스로 ROI 영역 지정\n",
    "\n",
    "**OpenCv**의 Window를 띄울 수 없으므로 Jupyter Widget으로서 구성하였다.  \n",
    "\n",
    "**Parameter**  \n",
    "- im: 입력 Image\n",
    "- selected_points: 마우스로 선택한 Mouse\n",
    "- fig, ax: 결과 화면\n",
    "- ka: fig(결과 화면)에 mpl_connect를 통하여 matplotlib Event를 걸었다. Click시에 onclick Method가 실행된다.\n",
    "- disconnect_button: Component 클릭 시에, disconnect_mpl Method가 실행되고 연결한 Event를 해지하는 역할을 한다.\n",
    "\n",
    "**Method**  \n",
    "- __init__: 사용할 변수 선언\n",
    "- poly_img: cv2.plotlines()를 통하여 사용자가 마우스로 지정한 Point를 연결하여 다각형으로 표시\n",
    "- onclick: 사용자가 image를 클릭시에 좌표 값을 저장한다.\n",
    "\n",
    "참조:<a href=\"https://medium.com/@khandelwalprateek01/how-to-select-roi-in-jupyter-notebook-309fe5185a54\">khandelwalprateek01</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class bbox_select():\n",
    "    %matplotlib notebook\n",
    "    def __init__(self,im):\n",
    "        self.im = im\n",
    "        self.selected_points = []\n",
    "        self.fig,ax = plt.subplots()\n",
    "        self.img = ax.imshow(self.im.copy())\n",
    "        self.ka = self.fig.canvas.mpl_connect('button_press_event', self.onclick)\n",
    "        disconnect_button = widgets.Button(description=\"Disconnect mpl\")\n",
    "        display.display(disconnect_button)\n",
    "        disconnect_button.on_click(self.disconnect_mpl)\n",
    "\n",
    "\n",
    "        \n",
    "    def poly_img(self,img,pts):\n",
    "        pts = np.array(pts, np.int32)\n",
    "        pts = pts.reshape((-1,1,2))\n",
    "        cv2.polylines(img,[pts],True,(np.random.randint(0,255),np.random.randint(0,255),np.random.randint(0,255)),7)\n",
    "        return img\n",
    "\n",
    "    def onclick(self, event):\n",
    "    #display(str(event))\n",
    "        self.selected_points.append([event.xdata,event.ydata])\n",
    "        if len(self.selected_points)>1:\n",
    "            self.fig\n",
    "            self.img.set_data(self.poly_img(self.im.copy(),self.selected_points))\n",
    "    def disconnect_mpl(self,_):\n",
    "        self.fig.canvas.mpl_disconnect(self.ka)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "im = plt.imread('./data/lena.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"431.818172458775\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6a8b90a4b14c4455a3e8bb68df944a4b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Disconnect mpl', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bs = bbox_select(im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[244.0892228890728, 163.39646258423255],\n",
       " [171.09437373528323, 351.7702668520766],\n",
       " [368.8868682165194, 339.9969040853363]]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bs.selected_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f80dc0c0550>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([bs.selected_points],'int')\n",
    "mask = cv2.fillPoly(np.zeros(im.shape,np.uint8),arr,[1,1,1])\n",
    "op = np.multiply(im,mask)\n",
    "plt.imshow(op)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 복사\n",
    "<code>numpy.copy()</code>를 이용하여 **원본 데이터를 그대로 유지하고, 원본 영상의 복사본에 라인, 사각형, 원 등을 표시한다.**  \n",
    "\n",
    "#### 영상 복사"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c84b4c5470ed437eb825d9c9a68773ac",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg',cv2.IMREAD_GRAYSCALE)\n",
    "\n",
    "img2 = img.copy()\n",
    "img2[100:400,200:300]=0\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\") \n",
    "\n",
    "wImg1.value = cv2.imencode(\".jpeg\", img)[1].tostring()\n",
    "wImg2.value = cv2.imencode(\".jpeg\", img2)[1].tostring()\n",
    "\n",
    "items = [wImg1, wImg2]\n",
    "box = Box(children=items)\n",
    "\n",
    "display.display(box)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 채널 분리와 병합\n",
    "<code>cv.split(m[,mv])</code>은 원본 Image를 단일 Channel의 Image로서 분리한다.  \n",
    "<code>cv.merge(mv[,dst])</code>은 단일 Channel의 Image를 합친다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "321202a9bd224be4a7f884a82fbe5f37",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg') \n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg3 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg4 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "items = [wImg1, wImg2, wImg3,wImg4]\n",
    "box = Box(children=items)\n",
    "\n",
    "dst = cv2.split(img)\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst[0])[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst[1])[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst[2])[1].tostring()\n",
    "wImg3.value = tmpStream\n",
    "\n",
    "merge_image = cv2.merge([dst[0],dst[1],dst[2]])\n",
    "tmpStream = cv2.imencode(\".jpeg\", merge_image)[1].tostring()\n",
    "wImg4.value = tmpStream\n",
    "\n",
    "display.display(box) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 컬러 공간 변환\n",
    "<code>cv.cvtColor(src,code[,dst[,dstCn]])</code>은 GRAY,HSV,YCrCb등의 다양한 컬러 공간 포멧으로 변환한다.  \n",
    "\n",
    "**주요 컬러 변환 코드**  \n",
    "\n",
    "<table class=\"table\">\n",
    "\t<tr>\n",
    "\t\t<td>입력영상(src)</td>\n",
    "\t\t<td>변환 코드(code)</td>\n",
    "        <td>출력영상(dst)</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>BGR</td>\n",
    "\t\t<td>cv2.COLOR_BGR2GRAY</td>\n",
    "        <td>GRAY</td>\n",
    "\t</tr>    \n",
    "    <tr>\n",
    "\t\t<td>GRAY</td>\n",
    "\t\t<td>cv2.COLOR_GRAY2BGR</td>\n",
    "        <td>BGR</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>BGR</td>\n",
    "\t\t<td>cv2.COLOR_BGR2HSV</td>\n",
    "        <td>HSV</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>HSV</td>\n",
    "\t\t<td>cv2.COLOR_HSV2BGR</td>\n",
    "        <td>BGR</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>BGR</td>\n",
    "\t\t<td>cv2.COLOR_BGR2YCrCv</td>\n",
    "        <td>YCrCv</td>\n",
    "\t</tr>\n",
    "    <tr>\n",
    "\t\t<td>YCrCv</td>\n",
    "\t\t<td>cv2.COLOR_YCrCv2BGR</td>\n",
    "        <td>BGR</td>\n",
    "\t</tr>\n",
    "\n",
    "</table>\n",
    "<br>\n",
    "\n",
    "**색상 모델**  \n",
    "<img src=\"https://t1.daumcdn.net/cfile/tistory/017E584E5199F0A436\" style=\"cursor: pointer;max-width:100%;height:auto\" width=\"550\" height=\"117\" filename=\"color_model.png\" filemime=\"image/jpeg\">\n",
    "\n",
    "- Gray 모델은 색(color) 정보를 사용하지 않고 밝기 정보만으로 영상을 표현하는 것이다. 검정색 0부터 흰색 255까지 총 256단계의 밝기값(intensity)으로 영상 픽셀값을 표현한다.\n",
    "- RGB 모델은 가장 기보적인 색상모델로서 색(color)을 Red, Green, Blue의 3가지 성분의 조합으로 생각하는 것이다. RGB 모델에서 검은색은 R=G=B=0, 흰색은 R=G=B=255, 빨강색은 R=255, G=B=0, 노란색은 R=G=255, B=0로 표현된다. R=G=B인 경우는 무채색인 Gray 색상이 된다. R, G, B 각각은 0 ~ 255 사이의 값을 가질 수 있기 때문에 RGB 색상 모델을 사용하면 총 256*256*256 = 16,777,216가지의 색을 표현할 수 있다.\n",
    "- HSV 모델은 Hue(색조), Saturation(채도), Value(명도)의 3가지 성분으로 색을 표현한다. Hue는 색조(예: 붉은색 계열인지 푸른색 계열인지, ...)를, Saturation은 그 색이 얼마나 선명한(순수한) 색인지를, Value는 밝기(intensity)를 나타낸다. HSV 모델은 우리가 색을 가장 직관적으로 표현할 수 있는 모델이며 또한 머리속에서 상상하는 색을 가장 쉽게 만들어낼 수 있는 모델이다. 영상처리/영상인식에서 HSV 모델을 사용할 때, H, S, V 각각은 0 ~ 255 사이의 값으로 표현된다. H 값은 색의 종류를 나타내기 때문에 크기는 의미가 없으며 단순한 인덱스(index)를 나타낸다. S 값은 0이면 무채색(gray 색), 255면 가장 선명한(순수한) 색임을 나타낸다. V 값은 작을수록 어둡고 클수록 밝은 색임을 나타낸다.\n",
    "- YCbCr 모델은 RGB 색에서 밝기성분(Y)과 색차정보(Cb, Cr)를 분리하여 표현하는 색상모델이다. 위 5번째 그림은 위키페디아에 있는 그림으로  Y=128일 때의 CbCr 색상평면이다. 디지털 영상에서 Y, Cb, Cr은 각각 0 ~ 255 사이의 값을 가지며 Y가 커지면 위 그림이 전체적으로 밝아지고 Y가 작아지면 전체적으로 어두워진다. YCbCr 모델은 mpeg에서 사용되는 색상모델로서 인간의 눈이 밝기차에는 민감하지만 색차에는 상대적으로 둔감하다는 점을 이용해서 Y에는 많은 비트수(해상도)를 할당하고 Cb, Cr에는 낮은 비트수를 할당하는 방식으로 비디오를 압축한다. 따라서 비디오 데이터를 처리할 경우에 YCbCr 모델을 사용하면 별도의 색상변환을 하지 않아도 되는 장점을 갖는다. YCbCr 모델은 YUV 모델로도 불린다.\n",
    "\n",
    "참조: <a href=\"https://darkpgmr.tistory.com/66\">다크 프로그래머</a><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6afe57c0956840aba3644ae632907e70",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg') \n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg3 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "items = [wImg1, wImg2, wImg3]\n",
    "box = Box(children=items)\n",
    "\n",
    "#GRAY\n",
    "gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)\n",
    "tmpStream = cv2.imencode(\".jpeg\", gray)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "#yCrCv\n",
    "yCrCv = cv2.cvtColor(img,cv2.COLOR_BGR2YCrCb)\n",
    "tmpStream = cv2.imencode(\".jpeg\", yCrCv)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "#HSV\n",
    "hsv = cv2.cvtColor(img,cv2.COLOR_BGR2HSV)\n",
    "tmpStream = cv2.imencode(\".jpeg\", hsv)[1].tostring()\n",
    "wImg3.value = tmpStream\n",
    "\n",
    "display.display(box) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 크기 변환\n",
    "<code>cv.resize(src,dsize[,dst[,fx[,fy[,interpolation]]]]])</code>: 입력 영상을 크기 변환하여 반환<br>\n",
    "**parameter**  \n",
    "- src: 입력 영상\n",
    "- dsize: 출력 영상의 크기\n",
    "- dst: 출력 영상\n",
    "- fx: 가로 스케일\n",
    "- fy: 세로 스케일\n",
    "- interpolation: 보간법 ex)cv2.INTER_NEAREST, cv2.INTER_LINEAR ...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b7f5dde93b044a40a6c36cc5a7d03ffd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dc3bfa43a4b74e33b30441a69ab26a95",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg',cv2.IMREAD_GRAYSCALE) \n",
    "\n",
    "#Image 크기 320 x 240로 변환\n",
    "dst = cv2.resize(img,dsize=(320,240))\n",
    "\n",
    "#Image 크기 원본 영상의 가로 세로 각 1.5배로 변환\n",
    "dst2 = cv2.resize(img,dsize=(0,0),fx=1.5, fy=1.2)\n",
    "\n",
    "w1,h1 = dst.shape\n",
    "w2,h2 = dst2.shape\n",
    "\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=w1, heigt=h1) \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=w2, heigt=h2)\n",
    "\n",
    "\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst2)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "display.display(wImg1,wImg2) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 회전\n",
    "<code>cv.rotate(src,rotateCode[,dst])</code>: 입력 영상 src를 크기 rotateCode에 따라 90의 배수로 회전<br>\n",
    "**parameter**  \n",
    "- rotateCode: 회전방식 ex)cv2.ROTATE_90_CLOCKWISE, cv2.ROTATE_180 ...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a87bf0fc38534abc8476b1d8b6deef57",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg') \n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "items = [wImg1, wImg2]\n",
    "box = Box(children=items)\n",
    "\n",
    "#시계 방향으로 90도 회전\n",
    "img1 = cv2.rotate(img, cv2.ROTATE_90_CLOCKWISE)\n",
    "tmpStream = cv2.imencode(\".jpeg\", img1)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "#반 시계 방향으로 90도 회전\n",
    "img2 = cv2.rotate(img,cv2.ROTATE_90_COUNTERCLOCKWISE)\n",
    "tmpStream = cv2.imencode(\".jpeg\", img2)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "display.display(box) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 어파인 변환\n",
    "\n",
    "**동차좌표**  \n",
    "동촤 좌표(Homogenous Coordinate)는 2차원상의 점의 위치를 2차원 벡터가 아닌 3차원 벡터로 표현하는 방법이다.  \n",
    "<p>$$ x = \\begin{bmatrix} x \\\\ y \\\\ 1 \\end{bmatrix}$$</p>\n",
    "\n",
    "마지막 원소가 1이 아닌 경우에는 1로 스케일링 시킨 것과 동일한 위치를 가르킨다.  \n",
    "<p>$$ \\begin{bmatrix} x \\\\ y \\\\ w \\end{bmatrix} = \\begin{bmatrix} x/w \\\\ y/w \\\\ 1 \\end{bmatrix}$$</p>\n",
    "\n",
    "동치좌표를 사용하는 예시를 한번 살펴보자.  \n",
    "먼저 동치좌표를 사용하지 않고 선형 변환(Scaleing)후 평행하게 <span>$t=(t_x,t_y)$</span>만큼 이동하는 과정을 살펴보자.  \n",
    "<p>$$ \\begin{bmatrix} x\\prime \\\\ y\\prime \\end{bmatrix} = A\\begin{bmatrix} x \\\\ y \\end{bmatrix} + \\begin{bmatrix} t_x \\\\ t_y \\end{bmatrix} = A\\begin{bmatrix} x \\\\ y \\end{bmatrix} + t$$</p>\n",
    "\n",
    "위의 과정을 동치 좌표를 사용하여 나타내면 매우 간단해 진다.  \n",
    "<p>$$ \\begin{bmatrix} x\\prime \\\\ y\\prime \\\\ 1 \\end{bmatrix} = \\begin{bmatrix} A && 0 && t_x \\\\ A && 0 && t_y \\\\ 0 && 0 && 1 \\end{bmatrix}\\begin{bmatrix} x \\\\ y \\\\ 1 \\end{bmatrix}$$</p>\n",
    "\n",
    "이렇게 하나의 3 x 3행렬로 3차원 좌표의 변환을 할 때, 이 3 x 3 행렬을 사영행렬(homography matrix)라고 불린다.  \n",
    "<p>$$x\\prime = Hx$$</p>\n",
    "\n",
    "<br>\n",
    "\n",
    "**회전 변환 행렬**  \n",
    "회전 행렬같은 경우 매우 유명한 행렬이다.  \n",
    "<p>$$H = \\begin{bmatrix} cos\\theta && -sin\\theta \\\\ sin\\theta && cos\\theta \\end{bmatrix}$$</p>\n",
    "\n",
    "자세한 증명이 궁금하신 분은 아래 링크 참조  \n",
    "<a href=\"https://ko.wikipedia.org/wiki/%ED%9A%8C%EC%A0%84%EB%B3%80%ED%99%98%ED%96%89%EB%A0%AC\">회전 변환 행렬 증명</a>\n",
    "<br>\n",
    "\n",
    "**유사 변환**  \n",
    "유사변환은 확대/축소(s), 회전(<span>$theta$</span>), 이동(t), 세가지 요소를 사용하여 이미지를 변환한다.  \n",
    "위의서 증명한 **동차 좌표와 회전 변환 행렬**을 사용하게 되면 다음과 같이 나타낼 수 있다.  \n",
    "<p>$$H = \\begin{bmatrix} scos\\theta && -ssin\\theta && t_x\\\\ ssin\\theta && scos\\theta && t_y \\\\ 0 && 0 && 1\\end{bmatrix}$$</p>\n",
    "\n",
    "위의 식을 나타내는 OpenCV Code는 다음과 같다.  \n",
    "<code>cv2.getRotationMatrix2D(center,angle,scale)</code><br>\n",
    "**parameter**  \n",
    "- center: 이미지의 중심 좌표\n",
    "- angle: 회전 시키는 각도\n",
    "- scale: 변환하려는 크기 비율\n",
    "\n",
    "\n",
    "**원근변환**  \n",
    "원근 변환은 핀홀 카메라 모형을 사용하여 2차원 이미지를 변환하는 방법이다.  \n",
    "**자세한 방법은 모르겠다....**  \n",
    "<a href=\"http://m.blog.daum.net/shksjy/235\">shksjy 블로그</a>를 보고 나중에 공부하도록 하자\n",
    "\n",
    "참조: <a href=\"https://datascienceschool.net/view-notebook/70820c6bcf154b8cb8161b4f93e4880d/\">데이터 사이언스 스쿨</a><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cea852062f4e4b1a938a49b99dd8b80f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "73d5fce3553a422fa0a5a596567b2277",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = cv2.imread('./data/lena.jpg')\n",
    "\n",
    "rows,cols,channels = img.shape\n",
    "\n",
    "M1 = cv2.getRotationMatrix2D((rows/2,cols/2),45,0.5)\n",
    "M2 = cv2.getRotationMatrix2D((rows/2,cols/2),-45,1.0)\n",
    "\n",
    "dst = cv2.warpAffine(img,M1,(rows,cols))\n",
    "dst2 = cv2.warpAffine(img,M2,(rows,cols))\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=w1, heigt=h1) \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=w2, heigt=h2)\n",
    "\n",
    "\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst2)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "display.display(wImg1,wImg2) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 영상 연산\n",
    "OpenCV_Python은 영상을 numpy.ndarray로 표현하기 때문에 numpy연산을 사용할 수 있다. \n",
    "\n",
    "#### 사칙연산\n",
    "**사칙연산 주요 함수**  \n",
    "<table class=\"table\">\n",
    "\t<tr>\n",
    "\t\t<td>함수</td>\n",
    "\t\t<td>설명</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.add()</td>\n",
    "\t\t<td>dst = src1 + src2</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.addWeighted()</td>\n",
    "\t\t<td>dst = saturate(src1*alpha + src2*bete + gamma)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.substract()</td>\n",
    "\t\t<td>dst = src1 - src2</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.scaleAdd()</td>\n",
    "\t\t<td>dst = scale*src1 + src2</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.multiply()</td>\n",
    "\t\t<td>dst = saturate(scale*src1*src2)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.divide()</td>\n",
    "\t\t<td>\n",
    "        <ul>\n",
    "            <li>dst = saturate(src1*scale/src2)</li>\n",
    "            <li>dst = saturate(scale/src2)</li>\n",
    "        </ul>\n",
    "        </td>\n",
    "    </tr>\n",
    "    \n",
    "</table>\n",
    "<br>\n",
    "참조 사이트:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d152db1c86534192805e0238291ff802",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "img1 = cv2.imread('./data/lena.jpg', cv2.IMREAD_GRAYSCALE)\n",
    "img2 = np.zeros(shape=(512,512),dtype=np.int32)+100\n",
    "\n",
    "dst1 = img1+img2\n",
    "dst2 = cv2.add(img1,img2,dtype=cv2.CV_8U)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst1)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst2)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "items = [wImg1, wImg2]\n",
    "box = Box(children=items)\n",
    "\n",
    "display.display(box) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 비트 연산\n",
    "\n",
    "**비트연산 주요 함수**  \n",
    "<table class=\"table\">\n",
    "\t<tr>\n",
    "\t\t<td>함수</td>\n",
    "\t\t<td>설명</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.bitwise_not()</td>\n",
    "\t\t<td>dst = -src1</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.bitwise_and()</td>\n",
    "\t\t<td>dst = src1 $$ src2 if mask != 0</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.bitwise_or()</td>\n",
    "\t\t<td>dst = src1 || src2 if mask != 0</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.bitwise_xor()</td>\n",
    "\t\t<td>dst = !(src1 || src2) if mask != 0</td>\n",
    "    </tr>\n",
    "    \n",
    "</table>\n",
    "<br>\n",
    "\n",
    "\n",
    "참조:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[255 255 255 ... 255 255 255]\n",
      " [255 255 255 ... 255 255 255]\n",
      " [255 255 255 ... 255 255 255]\n",
      " ...\n",
      " [255 255 255 ... 255 255 255]\n",
      " [255 255 255 ... 255 255 255]\n",
      " [255 255 255 ... 255 255 255]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8233c4fdbc5648339fcc7093b0fc6c19",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "20c1991a93b64d5ea2b3c71a56ca94cf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8ab66f7313834219a54cf3bc06d8d596",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "src1 = cv2.imread('./data/lena.jpg')\n",
    "src2 = cv2.imread('./data/opencv_logo.png')\n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\")\n",
    "wlmg3 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\")\n",
    "\n",
    "items1 = [wImg1, wImg2, wlmg3]\n",
    "box1 = Box(children=items1)\n",
    "\n",
    "wImg4 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\") \n",
    "wImg5 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\")\n",
    "wImg6 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\")\n",
    "\n",
    "wImg7 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"30%\", height=\"30%\")\n",
    "\n",
    "items2 = [wImg4, wImg5, wImg6]\n",
    "box2 = Box(children=items2)\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", src2)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "#1 Lena jpg에 ROI 설정\n",
    "rows,cols,channels = src2.shape\n",
    "roi = src1[0:rows,0:cols]\n",
    "\n",
    "#2 threshold를 사용하여 원하는 모양과 배경을 나눔\n",
    "gray = cv2.cvtColor(src2,cv2.COLOR_BGR2GRAY)\n",
    "ret,mask = cv2.threshold(gray,160,255,cv2.THRESH_BINARY)\n",
    "mask_inv = cv2.bitwise_not(mask)\n",
    "tmpStream = cv2.imencode(\".jpeg\", mask)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "tmpStream = cv2.imencode(\".jpeg\", mask_inv)[1].tostring()\n",
    "wlmg3.value = tmpStream\n",
    "\n",
    "#3 mask와 lena-ROI and연산 => 흰색 255, 흑 0 이므로 and시 흰색 부분에 lena-roi 입힘\n",
    "src1_bg = cv2.bitwise_and(roi,roi,mask=mask)\n",
    "tmpStream = cv2.imencode(\".jpeg\", src1_bg)[1].tostring()\n",
    "wImg4.value = tmpStream\n",
    "\n",
    "#4 mask-inv와 opencv logo를 and를 활용하여 최종적인 Filter로서 생성\n",
    "src2_fg = cv2.bitwise_and(src2,src2,mask=mask_inv)\n",
    "tmpStream = cv2.imencode(\".jpeg\", src2_fg)[1].tostring()\n",
    "wImg5.value = tmpStream\n",
    "\n",
    "#5 or를 사용하여 최종 filter와 lena-roi에 적용, 흑의 값은 0 이므로 흑의 값에 lena-jpg의 값 그대로 대입\n",
    "dst = cv2.bitwise_or(src1_bg,src2_fg)\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg6.value = tmpStream\n",
    "\n",
    "#6 최종적인 이미지 생성\n",
    "src1[0:rows,0:cols] = dst\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", src1)[1].tostring()\n",
    "wImg7.value = tmpStream\n",
    "\n",
    "display.display(box1)\n",
    "display.display(box2)\n",
    "display.display(wImg7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 반전 영상\n",
    "\n",
    "**비교 범위 연산**  \n",
    "<table class=\"table\">\n",
    "\t<tr>\n",
    "\t\t<td>함수</td>\n",
    "\t\t<td>설명</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.compare()</td>\n",
    "\t\t<td>Performs the per-element comparison of two arrays or an array and scalar value.</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.checkRange()</td>\n",
    "\t\t<td>Checks every element of an input array for invalid values.</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "\t\t<td>cv2.inRange()</td>\n",
    "\t\t<td>Checks if array elements lie between the elements of two other arrays.</td>\n",
    "    </tr>\n",
    "</table>\n",
    "<br>\n",
    "\n",
    "\n",
    "참조:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n= 262144\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a7391a4c1fa04d9e82bee489c222e604",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "src1 = cv2.imread('./data/lena.jpg',cv2.IMREAD_GRAYSCALE)\n",
    "src2 = np.zeros(shape=(512,512))+255\n",
    "\n",
    "src1 = np.int32(src1)\n",
    "src2 = np.int32(src2)\n",
    "\n",
    "dst1 = 255-src1\n",
    "dst2 = cv2.subtract(src2,src1)\n",
    "dst3 = cv2.compare(dst1,dst2,cv2.CMP_EQ)\n",
    "n = cv2.countNonZero(dst3)\n",
    "print('n=',n)\n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\") \n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg3 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst1)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst2)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst3)[1].tostring()\n",
    "wImg3.value = tmpStream\n",
    "\n",
    "items = [wImg1, wImg2,wImg3]\n",
    "box = Box(children=items)\n",
    "\n",
    "display.display(box)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 수학 및 통계 함수\n",
    "<br>\n",
    "\n",
    "#### 영상 정규화\n",
    "**정규화**  \n",
    "<code>cv2.norm(src1,src2[,normType[,mask]])</code>: 정규화<br>\n",
    "**parameter**\n",
    "- src1: input1\n",
    "- src2: input2\n",
    "- normType: 정규화 방법\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.normalize(src,dst[,alpha[,beta[,norm_type[,dtype[,mask]]]]])</code>: 지정한 범위의 정규화<br>\n",
    "**parameter**\n",
    "- src: input\n",
    "- dst: output(None으로 정의한 경우 결과 영상을 새로 생성한다.)\n",
    "- alpha: 정규화 시 최소 값\n",
    "- beta: 정규화 시 최대값\n",
    "- norm_type: Normalization 방법\n",
    "\n",
    "<br>\n",
    "\n",
    "**최대 최소**  \n",
    "<code>cv2.min(src1,src2[,dst])</code>: 두 영상값에서 최소값<br>\n",
    "$$dst = min(src1,src2)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.max(src1,src2[,dst])</code>: 두 영상값에서 최대값<br>\n",
    "$$dst = max(src1,src2)$$\n",
    "<br>\n",
    "\n",
    "<code>cv2.minmaxLoc(src,[, mask])</code>: 영상 내의 최대값, 최소값 및 위치<br>\n",
    "**return**\n",
    "- min: 최소값\n",
    "- max: 최대값\n",
    "- minLoc: 영상 내 최소값 좌표\n",
    "- maxLoc: 영상 내 최대값 좌표\n",
    "\n",
    "<br>\n",
    "참조:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "src:  39.0 245.0 (510, 68) (117, 272)\n",
      "src:  100.0 200.0 (510, 68) (117, 272)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d29a0f7777d34052acffee7ffe2009ad",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "src = cv2.imread('./data/lena.jpg',cv2.IMREAD_GRAYSCALE)\n",
    "\n",
    "minVal, maxVal, minLoc, maxLoc = cv2.minMaxLoc(src)\n",
    "print('src: ',minVal,maxVal,minLoc,maxLoc)\n",
    "\n",
    "dst = cv2.normalize(src,None,100,200,cv2.NORM_MINMAX)\n",
    "minVal,maxVal,minLoc,maxLoc = cv2.minMaxLoc(dst)\n",
    "print('src: ',minVal,maxVal,minLoc,maxLoc)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", src)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "items = [wImg1, wImg2]\n",
    "box = Box(children=items)\n",
    "\n",
    "display.display(box)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 난수  \n",
    "<code>cv2.randu(dst,low,high)</code>: 랜덤한 균일 분포 생성<br>\n",
    "**parameter**\n",
    "- dst: output\n",
    "- low: 최소값\n",
    "- high: 최대값\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.randn(dst,mean,stddev)</code>: 랜덤한 정규 분포 생성<br>\n",
    "**parameter**\n",
    "- dst: output\n",
    "- mean: 평균\n",
    "- stddev: 편차\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.randShuufle(dst[,iterFactor])</code>: 행렬의 원소 랜덤으로 섞음<br>\n",
    "**parameter**\n",
    "- dst: input/output numerical 1D array\n",
    "- iterFactor: 반복해서 섞을 횟수\n",
    "\n",
    "<br>\n",
    "\n",
    "\n",
    "\n",
    "<br>\n",
    "참조:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a><br>\n",
    "\n",
    "#### 2차원 균등분포 난수 좌표"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8c045168d13748e093e6cbde880618d8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dst = np.full((512,512,3),(255,255,255),dtype=np.int32)\n",
    "nPoints=100\n",
    "pts = np.zeros((1,nPoints,2),dtype=np.int32)\n",
    "\n",
    "cv2.setRNGSeed(int(time.time()))\n",
    "cv2.randu(pts,(0,0),(512,512))\n",
    "\n",
    "#draw points\n",
    "for k in range(nPoints):\n",
    "    x,y = pts[0,k][:]\n",
    "    cv2.circle(dst,(x,y),radius=5,color=(0,0,255),thickness=-1)\n",
    "    \n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "display.display(wImg1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2차원 정규분포 난수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ecd00daff5034da99fa5bb554667aecb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dst = np.full((512,512,3),(255,255,255),dtype=np.int32)\n",
    "nPoints=100\n",
    "pts = np.zeros((1,nPoints,2),dtype=np.int32)\n",
    "\n",
    "cv2.setRNGSeed(int(time.time()))\n",
    "cv2.randn(pts,mean=(256,256),stddev=(50,50))\n",
    "\n",
    "#draw points\n",
    "for k in range(nPoints):\n",
    "    x,y = pts[0,k][:]\n",
    "    cv2.circle(dst,(x,y),radius=5,color=(0,0,255),thickness=-1)\n",
    "    \n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "display.display(wImg1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 통계\n",
    "기본적인 통계 기초는 아래 Post참조  \n",
    "<a href=\"https://wjddyd66.github.io/dataanalysis/2019/07/29/Statistics.html\">DataAnalysis-Statistics Post</a><br>\n",
    "<code>cv2.countNonZero(dst,low,high)</code>: 0이 아닌 값 Count<br>\n",
    "<br>\n",
    "\n",
    "<code>cv2.reduce(src, dim, rtype[, dst[, dtype]])</code>: 랜덤한 정규 분포 생성<br>\n",
    "**parameter**\n",
    "- src: input 2D matrix\n",
    "- dim: output Matrix의 차원\n",
    "- rtype: Reduction operation ex)CV_REDUCE_SUM, CV_REDUCE_AVG ...\n",
    "- dtype: output Matrix 원소 자료형태\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.mean(src[, mask])</code>: 행렬의 평균값 계산<br>\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.meanStdDev(src[, mean[, stddev[, mask]]])</code>: 행렬의 평균, 분산 계산<br>\n",
    "**parameter**\n",
    "- src: input\n",
    "- mean: 평균\n",
    "- stddev: 분산\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.calcCovarMatrix(samples, flags[, covar[, mean[, ctype]]])</code>: 행렬의 공분산 계산<br>\n",
    "**parameter**\n",
    "- samples: input\n",
    "- covar: output covariance matrix of the type ctype and square size\n",
    "- ctype: type of the matrixl\n",
    "- mean: input or outpu array의 평균\n",
    "- flags: operation flags\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.Mahalanobis(v1, v2, icovar)</code>: Mahalanobis 거리 계산<br>\n",
    "**parameter**\n",
    "- v1: input1\n",
    "- v2: input2\n",
    "- icovar: inverse covariance matrix\n",
    "\n",
    "$$d(v1,v2) = \\sqrt{\\sum_{ij}{(v1-v2)^T*icovar(i,j)*(v1-v2)}}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "**참고 사항(Mahalanobis 거리)**  \n",
    "Mahalanbis거리의 최종적인 식의 의미는 **거리가 표준편차의 몇배인지를 나타내는 값**이라고 할 수 있다.  \n",
    "이해하기 쉽게 두개의 가정에 대해서 Mahalanbis거리를 생각해보자.  \n",
    "**가정 1**  \n",
    "교통량의 평균이 20대, 1년 내내 교통량이 20대 라고 가정하자.  \n",
    "어느날 갑자기 차량이 21대가 지나가게 되면 Mahalanobis 거리는 매우 큰 값을 가질 것 이다.(icovar의 값이 0에 가까운 매운 작은 값 이기 때문)  \n",
    "**가정 2**  \n",
    "교통량의 평균이 20대, 편차가 3대 라고 가정하자.  \n",
    "어느날 갑자기 차량이 21대가 지나가게 되면 Mahalanobis 거리는 매우 작은 값을 가질 것 이다.(icovar의 값은 <span>$\\sqrt{3}$</span>이므로 1과의 차이가 거의 없다.)  \n",
    "\n",
    "따라서 Mahalanbis distance는 어떤 데이터가 가짜 데이터인지, 아니면 진짜 데이터인지를 구분하는 용도로 주로 사용된다. 즉, 이상치나 극단값을 판별하는데 좋은 계산 수식이 될 수 있다.\n",
    "\n",
    "\n",
    "<br>\n",
    "참조:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a><br>\n",
    "<br>\n",
    "참조:<a href=\"https://darkpgmr.tistory.com/41\">다크 프로그래머 블로그</a><br>\n",
    "\n",
    "#### 통계적 거리 계산"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean= [[12.5   1.25]]\n",
      "cov= [[73750.  34875. ]\n",
      " [34875.  26287.5]]\n",
      "icov= [[ 3.63872307e-05 -4.82740722e-05]\n",
      " [-4.82740722e-05  1.02084955e-04]]\n",
      "(2, 1)\n",
      "(2, 1)\n",
      "(2, 2)\n",
      "<class 'numpy.float64'>\n",
      "<class 'numpy.float64'>\n",
      "<class 'numpy.float64'>\n",
      "dist= 0.5051854992128457\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[0,0,0,100,100,150,-100,-150],[0,50,-50,0,30,100,-20,-100]],dtype=np.float64)\n",
    "X = X.transpose()\n",
    "\n",
    "cov,mean = cv2.calcCovarMatrix(X,mean=None, flags = cv2.COVAR_NORMAL+cv2.COVAR_ROWS)\n",
    "\n",
    "print('mean=',mean)\n",
    "print('cov=',cov)\n",
    "\n",
    "ret,icov = cv2.invert(cov)\n",
    "print('icov=',icov)\n",
    "\n",
    "v1 = np.array([[0],[0]],dtype=np.float64)\n",
    "v2 = np.array([[0],[50]],dtype=np.float64)\n",
    "\n",
    "print(v1.shape)\n",
    "print(v2.shape)\n",
    "print(icov.shape)\n",
    "\n",
    "print(type(v1[0,0]))\n",
    "print(type(v2[0,0]))\n",
    "print(type(icov[0][0]))\n",
    "\n",
    "dist = cv2.Mahalanobis(v1,v2,icov)\n",
    "print('dist=',dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 선형대수\n",
    "선형대수에서 사용하는 Egien Vector, PCA에 대한 내용은 아래 링크 참조  \n",
    "<a href=\"https://wjddyd66.github.io/others/2019/07/24/PCA.html\">PCA Post</a><br>\n",
    "\n",
    "<code>cv2.eigen(src, computeEigenvectors[, eigenvalues[, eigenvectors]])</code>: eigenvalue와 eigenvector 계산<br>\n",
    "**parameter**\n",
    "- src: input matrix(Square & Symmetrical)\n",
    "- eigenvalues: output vector of eigenvalues\n",
    "- eigenvectors: output matrix of eigenvectors\n",
    "- lowindex: optional index of largest eigenvalue/vector\n",
    "- highindex: optional index of samllest eigenvalue/vector\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.PCACompute(data[, mean[, eigenvectors[, maxComponents]]])</code>: 데이터의 분산을 최대한 보존하면서 서로 직교하는 새 축(eigenvector)을 찾아, 고차원 공간의 표본들을 선형 연관성이 없는 저차원 공간으로 변환하는 기법<br>\n",
    "**parameter**\n",
    "- data: input\n",
    "- mean: 평균\n",
    "- flags: operation flags ex)CV_PCA_DATA_AS_ROW, CV_PCA_DATA_AS_COL\n",
    "- maxComponents : maximum number of components that PCA\n",
    "- retainedVariance : Percentage of variance that PCA\n",
    "\n",
    "<br>\n",
    "\n",
    "<code>cv2.PCAProject(data, mean, eigenvectors[, result])</code>: Eigenvector를 활용하여 Data를 Result에 사영<br>\n",
    "**parameter**\n",
    "- data: input\n",
    "- mean: 평균\n",
    "- eigenvectors: Eigenvectors of data\n",
    "- result : output\n",
    "<br>\n",
    "\n",
    "<code>cv2.PCABackProject(data, mean, eigenvectors[, result])</code>: Eigenvector를 활용하여 Data를 Result에 역사영<br>\n",
    "**parameter**\n",
    "- data: input\n",
    "- mean: 평균\n",
    "- eigenvectors: Eigenvectors of data\n",
    "- result : output\n",
    "\n",
    "**참조사항(PCA Projection & PCA backprojection)**  \n",
    "- A: 직교행렬 (eVects)\n",
    "- m: 평균 벡터\n",
    "- x,y,m: 2 x 1 열벡터\n",
    "\n",
    "$$y = A(x-m) \\text{ #PCA projection}$$\n",
    "$$A^{-1}y = A^{-1}A(x-m)$$\n",
    "$$A^{T}y = (x-m) \\text{  }\\because\\text{직교행렬,}A^{-1} = A^T$$\n",
    "$$x = A^Ty+m \\text{ #PCA backprojection}$$\n",
    "\n",
    "참조:<a href=\"https://docs.opencv.org/2.4/modules/core/doc/operations_on_arrays.html\">OpenCV 정식 홈페이지</a><br>\n",
    "\n",
    "#### 거리계산, 공분산 행렬의 고유값과 고유벡터\n",
    "최종적인 목적은 X[0] => x축, X[1]을 Y축으로 으로 값을 나타내는 것 이다.  \n",
    "즉 (2,8)의 X를 공분산(2,2) Eigenvalue, EigenVector를 활용하여 (2,2)로서 표현하는 것이 목적이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eVals= [[92202.13359547]\n",
      " [ 7835.36640453]]\n",
      "eVects= [[ 0.88390424  0.46766793]\n",
      " [-0.46766793  0.88390424]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "83cc664de2a442738dace7ef367e37dc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\x00\\x02\\x01\\x0…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data 선언\n",
    "X = np.array([[0,0,0,100,100,150,-100,-150],[0,50,-50,0,30,100,-20,-100]],dtype=np.float64)\n",
    "# Data Transpose\n",
    "X = X.transpose()\n",
    "# 공분산 평균 구하기\n",
    "cov,mean = cv2.calcCovarMatrix(X,mean=None, flags = cv2.COVAR_NORMAL+cv2.COVAR_ROWS)\n",
    "mean = mean.transpose()\n",
    "\n",
    "# 공분산 Transpose\n",
    "ret,icov = cv2.invert(cov)\n",
    "\n",
    "# 결과 행렬 초기화 및 Parameter 선언\n",
    "dst = np.full((512,512,3),(255,255,255),dtype=np.float64)\n",
    "rows,cols,channel = dst.shape\n",
    "# EigenVector에 대한 대칭으로 그리기 위하여 중앙값 선언\n",
    "centerX = cols//2\n",
    "centerY = rows//2\n",
    "\n",
    "# EigenVecor, EigenVector를 활용하여 대칭인 점을 좌표를 계산하기 위하여 y축 대칭\n",
    "v2 = np.zeros((2,1),dtype=np.float64)\n",
    "FLIP_Y = lambda y:rows-1-y\n",
    "\n",
    "#Mahalanobis distance를 활용하여 거리에 따른 색상 지정\n",
    "for y in range(rows):\n",
    "    for x in range(cols):\n",
    "        v2[0,0] = x-centerX\n",
    "        v2[1,0]=FLIP_Y(y) - centerY #Y축 뒤집기\n",
    "        \n",
    "        icov = np.array(icov,dtype=np.float64)\n",
    "        dist = cv2.Mahalanobis(mean,v2,icov)\n",
    "        \n",
    "        if dist<0.1:\n",
    "            dst[y,x] = [50,50,50]\n",
    "        elif dist<0.3:\n",
    "            dst[y,x] = [100,100,100]\n",
    "        elif dist<0.8:\n",
    "            dst[y,x] = [200,200,200]\n",
    "        else:\n",
    "            dst[y,x] = [250,250,250]\n",
    "\n",
    "# X안의 x, y의 좌표값을 원으로서 표시하는 것\n",
    "for k in range(X.shape[0]):\n",
    "    x,y = X[k,:]\n",
    "    cx = int(x+centerX)\n",
    "    cy = int(y+centerY)\n",
    "    cy = FLIP_Y(cy)\n",
    "    cv2.circle(dst,(cx,cy),radius=5,color=(0,0,255),thickness=-1)\n",
    "    \n",
    "#draw X,Y-axes\n",
    "cv2.line(dst,(0,256),(cols-1,256),(0,0,0))\n",
    "cv2.line(dst,(256,0),(256,rows),(0,0,0))\n",
    "    \n",
    "# calculate eigen vectors\n",
    "ret,eVals,eVects = cv2.eigen(cov)\n",
    "print('eVals=',eVals)\n",
    "print('eVects=',eVects)\n",
    "    \n",
    "def ptsEigenVector(eVal,eVect):\n",
    "    scale = np.sqrt(eVal)\n",
    "    x1 = scale * eVect[0]\n",
    "    y1 = scale * eVect[1]\n",
    "    x2,y2 = -x1,-y1\n",
    "        \n",
    "    x1 +=mean[0,0] + centerX\n",
    "    y1 +=mean[1,0] + centerY\n",
    "    x2 +=mean[0,0] + centerX\n",
    "    y2 +=mean[1,0] + centerY\n",
    "    y1=FLIP_Y(y1)\n",
    "    y2=FLIP_Y(y2)\n",
    "    return x1,y1,x2,y2\n",
    "    \n",
    "    \n",
    "#draw eVects[0]\n",
    "#EigenValue, EigenVector를 활용하여 데이터 X에 대한 분포의의 단축(short axis)그리기\n",
    "x1,y1,x2,y2 = ptsEigenVector(eVals[0],eVects[0])\n",
    "cv2.line(dst,(x1,y1),(x2,y2),(255,0,0),2)\n",
    "    \n",
    "#draw eVects[1]\n",
    "#EigenValue, EigenVector를 활용하여 데이터 Y에 대한 분포의의 단축(short axis)그리기\n",
    "x1,y1,x2,y2 = ptsEigenVector(eVals[1],eVects[1])\n",
    "cv2.line(dst,(x1,y1),(x2,y2),(255,0,0),2)\n",
    "    \n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", dst)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "display.display(wImg1)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### PCA 투영, 역투영"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean= [[12.5   1.25]]\n",
      "eVects= [[ 0.88390424  0.46766793]\n",
      " [-0.46766793  0.88390424]]\n",
      "X= [[   0.    0.]\n",
      " [   0.   50.]\n",
      " [   0.  -50.]\n",
      " [ 100.    0.]\n",
      " [ 100.   30.]\n",
      " [ 150.  100.]\n",
      " [-100.  -20.]\n",
      " [-150. -100.]]\n",
      "Y= [[ -11.63338792    4.74096885]\n",
      " [  11.75000868   48.93618085]\n",
      " [ -35.01678451  -39.45424315]\n",
      " [  76.75703609  -42.02582434]\n",
      " [  90.78707404  -15.50869713]\n",
      " [ 167.71904127   22.98120308]\n",
      " [-109.37717055   33.82967723]\n",
      " [-190.9858171   -13.49926538]]\n",
      "X2= [[ 1.77635684e-15  0.00000000e+00]\n",
      " [ 0.00000000e+00  5.00000000e+01]\n",
      " [ 0.00000000e+00 -5.00000000e+01]\n",
      " [ 1.00000000e+02 -5.32907052e-15]\n",
      " [ 1.00000000e+02  3.00000000e+01]\n",
      " [ 1.50000000e+02  1.00000000e+02]\n",
      " [-1.00000000e+02 -2.00000000e+01]\n",
      " [-1.50000000e+02 -1.00000000e+02]]\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[0,0,0,100,100,150,-100,-150],[0,50,-50,0,30,100,-20,-100]],dtype=np.float64)\n",
    "X = X.transpose()\n",
    "\n",
    "mean,eVects = cv2.PCACompute(X,mean=None)\n",
    "print('mean=',mean)\n",
    "print('eVects=',eVects)\n",
    "\n",
    "print('X=',X)\n",
    "Y=cv2.PCAProject(X,mean,eVects)\n",
    "print('Y=',Y)\n",
    "\n",
    "X2 = cv2.PCABackProject(Y,mean,eVects)\n",
    "print('X2=',X2)\n",
    "print(np.allclose(X,X2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 채널 영상의 PCA 투영"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape= (262144, 3)\n",
      "mean= [[105.41025   99.051216 180.22366 ]]\n",
      "eVects\n",
      "[[ 0.39645132  0.6897987   0.60580885]\n",
      " [-0.6426597  -0.26271227  0.71970195]\n",
      " [ 0.6556028  -0.67465556  0.33915314]]\n",
      "Normalization of eVals\n",
      "[[1.        ]\n",
      " [0.09843972]\n",
      " [0.00989466]]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "de780e88808f456aab42016fe3383320",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
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    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f289e7412fbd482084fa0d4f5d9f329d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0404a2fd358b48cbbed77a6690f99853",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Box(children=(Image(value=b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x01\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xdb\\x00C\\…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "src = cv2.imread('./data/lena.jpg')\n",
    "b,g,r = cv2.split(src)\n",
    "\n",
    "box_layout = Layout(display='flex',\n",
    "                    flex_flow='row',\n",
    "                    border='solid',\n",
    "                   width='100%',)\n",
    "\n",
    "wImg1 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg2 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg3 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg4 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg5 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "wImg6 = widgets.Image(layout = widgets.Layout(border=\"solid\"), width=\"25%\")\n",
    "\n",
    "items1 = [wImg1, wImg2]\n",
    "box1 = Box(children=items1)\n",
    "items2 = [wImg3, wImg4]\n",
    "box2 = Box(children=items2)\n",
    "items3 = [wImg5, wImg6]\n",
    "box3 = Box(children=items3)\n",
    "\n",
    "X=src.reshape(-1,3)\n",
    "print('X.shape=',X.shape)\n",
    "\n",
    "mean,eVects = cv2.PCACompute(X,mean=None)\n",
    "print('mean=',mean)\n",
    "print('eVects')\n",
    "print(eVects)\n",
    "\n",
    "cov2,mean2 = cv2.calcCovarMatrix(X,mean=None, flags = cv2.COVAR_NORMAL+cv2.COVAR_ROWS)\n",
    "ret2,eVals,eVects2 = cv2.eigen(cov)\n",
    "eVals = eVals/eVals.max(axis=0)\n",
    "print('Normalization of eVals')\n",
    "print(eVals)\n",
    "\n",
    "\n",
    "Y=cv2.PCAProject(X,mean,eVects)\n",
    "Y = Y.reshape(src.shape)\n",
    "\n",
    "eImage=cv2.split(Y)\n",
    "\n",
    "for i in range(3):\n",
    "    cv2.normalize(eImage[i],eImage[i],0,255,cv2.NORM_MINMAX)\n",
    "    eImage[i]=eImage[i].astype(np.int32)\n",
    "\n",
    "\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", b)[1].tostring()\n",
    "wImg1.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", eImage[0])[1].tostring()\n",
    "wImg2.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", g)[1].tostring()\n",
    "wImg3.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", eImage[1])[1].tostring()\n",
    "wImg4.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", r)[1].tostring()\n",
    "wImg5.value = tmpStream\n",
    "\n",
    "tmpStream = cv2.imencode(\".jpeg\", eImage[2])[1].tostring()\n",
    "wImg6.value = tmpStream\n",
    "\n",
    "\n",
    "display.display(box1,box2,box3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "위의 결과를 살펴보게 되면 고유값의 크기가 eVals[0] > eVals[1] > eVals[2]순으로 값이 출력된다.  \n",
    "즉, **고유값의 크기가 크다는 것은 투영정보가 많다는 의미**이다.  \n",
    "이로 인하여 각각의 결과를 살펴보게 되면 투영정보에 따라서 이미지의 선명한 정도가 결정되는 것을 알 수 있다.  "
   ]
  }
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