04_Quiz_Conv.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt # for plotting\n",
    "import matplotlib\n",
    "matplotlib.rcParams['figure.dpi']=300 # highres display\n",
    "\n",
    "from scipy import ndimage # for image loading/processing\n",
    "import imageio\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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AgO90dJj6p7XF+uPWw12Oe2hmmn40bwJJXwAAAABAr5imqdx/WX/O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q7NTFZ4GN8LAAAAAAChx+lhNEA8owGA8xAE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\nfE8W0x0AAARjNgsAwuj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WX3BoUDLzTuCLVfNIfVFz//jM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\n1vlMotoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 2400x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convolutions 1D\n",
    "\n",
    "kernel=np.array([1,-2,1])\n",
    "\n",
    "x=np.linspace(-1,1,20)\n",
    "f=np.sin(4*x)+x**2+1.0\n",
    "\n",
    "# inefficient convolution\n",
    "j0=1\n",
    "fnew=0*f\n",
    "for j in range(len(kernel)):\n",
    "    fnew+=np.roll(f,j0-j)*kernel[j]\n",
    "\n",
    "fig,ax=plt.subplots(ncols=1,nrows=2,figsize=(8,4))\n",
    "j=np.array(range(20))\n",
    "ax[0].plot(j,f)\n",
    "ax[0].scatter(j,f)\n",
    "ax[1].plot(j,fnew)\n",
    "ax[1].scatter(j,fnew)\n",
    "ax[1].set_ylim([-0.25,0.25])\n",
    "ax[1].plot(j,0*j,'--',color=\"orange\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3nZ1rc/XsVCu+s17cgdGaaOfqU9buDmd+9LjbQu/x4/fF9w8clbtn14be559/Tuh17ru/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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load the pixel image!\n",
    "face =imageio.imread('Smiley.png')\n",
    "pixel_image=np.transpose(face[:,:,0]) # have to transpose...\n",
    "#pixel_image=pixel_image[:,::-1] # and flip... to get the right view!\n",
    "pixel_image-=pixel_image.min()\n",
    "pixel_image=(pixel_image.astype(dtype='float'))/pixel_image.max() # normalize between 0 and 1!\n",
    "Npixels=np.shape(pixel_image)[0] # assuming a square image!\n",
    "\n",
    "plt.imshow(pixel_image,origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7331P94Sy+cWV7glln1k43T2hbPqxB7snDPK1zy91Tyi7u3vAAB95+5u7J5Rd+3uj86xm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\ntrzSPaFs8eEfdE8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      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convolutions 2D\n",
    "\n",
    "def my_kernel(x,y):\n",
    "    return(np.sin(0.5*(x+y))*np.exp(-0.01*(x**2+y**2)))\n",
    "\n",
    "vals=np.linspace(-10,10,21)\n",
    "x,y=np.meshgrid(vals,vals)\n",
    "kernel=my_kernel(x,y)\n",
    "\n",
    "plt.imshow(kernel,cmap='RdBu',origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()\n",
    "\n",
    "# x=np.linspace(-1,1,20)\n",
    "# f=np.sin(4*x)+x**2+1.0\n",
    "\n",
    "# # inefficient convolution\n",
    "# j0=1\n",
    "# fnew=0*f\n",
    "# for j in range(len(kernel)):\n",
    "#     fnew+=np.roll(f,j0-j)*kernel[j]\n",
    "\n",
    "# fig,ax=plt.subplots(ncols=1,nrows=2,figsize=(8,4))\n",
    "# j=np.array(range(20))\n",
    "# ax[0].plot(j,f)\n",
    "# ax[0].scatter(j,f)\n",
    "# ax[1].plot(j,fnew)\n",
    "# ax[1].scatter(j,fnew)\n",
    "# ax[1].set_ylim([-0.25,0.25])\n",
    "# ax[1].plot(j,0*j,'--',color=\"orange\")\n",
    "# plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z4JdiAAAAAEC2eCkGAAAAAGSLl2IAAAAAQLZ4KQYAAAAAZIugLWBNnWWwFqFaAIALsWz4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\nodT94EK0dhTQd+cGXQjUeyQUmUX1XCyeNZFVi0526PEwQfPMkHOcGKd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2dcaXdb69jTjJ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Li25x9eZZ9/fvrS9dk+9+P8KxOstV77EMSq98u5eVDMG/XWX+yDCThT82AV/Wkpci+L+USGb0U2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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# inefficient convolution\n",
    "jmid=10\n",
    "\n",
    "f=pixel_image\n",
    "fnew=0*f\n",
    "N=21\n",
    "for j0 in range(N):\n",
    "    for j1 in range(N):\n",
    "        fnew+=np.roll(f,[jmid-j0,jmid-j1],axis=[0,1])*kernel[j0,j1]\n",
    "        \n",
    "plt.imshow(fnew,origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8UAAAPGCAYAAADKpjjCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAEAsUQwAAEAsUQwAAECs/wWew5RZFVgOgwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convolutions 2D\n",
    "\n",
    "def my_kernel(x,y):\n",
    "    return(np.sin(0.5*(x-y))*np.exp(-0.01*(x**2+y**2)))\n",
    "\n",
    "vals=np.linspace(-10,10,21)\n",
    "x,y=np.meshgrid(vals,vals)\n",
    "kernel=my_kernel(x,y)\n",
    "\n",
    "plt.imshow(kernel,cmap='RdBu',origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KCBbE20ANFRyTVJv9E4RKRxCpCjY4olmIoC0ZTiXGYDenQm/MVaHCh1yoVko+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\nmWeGOuaq7Y6Py60LPN9TSim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PNre1E1FTrGo2TdN86Tc4n/tpsp3lB2e4EPsijosrcVL7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\nigEAAGhLUQwAAEBbimIAAADa+gc/xDHrPP0pmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# inefficient convolution\n",
    "jmid=10\n",
    "\n",
    "f=pixel_image\n",
    "fnew=0*f\n",
    "N=21\n",
    "for j0 in range(N):\n",
    "    for j1 in range(N):\n",
    "        fnew+=np.roll(f,[jmid-j0,jmid-j1],axis=[0,1])*kernel[j0,j1]\n",
    "        \n",
    "plt.imshow(fnew,origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WbtTB19uok+/3cb6OnrDaTFtPl3m2no/zbF2WZTmf5tl7Pr6PnrDaZaatH/NsPX99HT1h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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convolutions 2D\n",
    "\n",
    "def my_kernel(x,y):\n",
    "    return(np.exp(-0.01*(x**2+y**2)))\n",
    "\n",
    "vals=np.linspace(-10,10,21)\n",
    "x,y=np.meshgrid(vals,vals)\n",
    "kernel=my_kernel(x,y)\n",
    "\n",
    "plt.imshow(kernel,cmap='RdBu',origin='lower',vmin=-1,vmax=1)\n",
    "plt.axis('off')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HoVpzIzCLt11NqRuGXGE4Tw7Mut3n2u92mAUFGXWCtTqBS4ZqfX2dIJxOiBaH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\nwQCDBkO11oHOc247XepUQ22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2EKS5g33I7w8DvUfCyRkb7/T3wlDafD3inAfvAY1t15Cr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\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# inefficient convolution\n",
    "jmid=10\n",
    "\n",
    "f=pixel_image\n",
    "fnew=0*f\n",
    "N=21\n",
    "for j0 in range(N):\n",
    "    for j1 in range(N):\n",
    "        fnew+=np.roll(f,[jmid-j0,jmid-j1],axis=[0,1])*kernel[j0,j1]\n",
    "        \n",
    "plt.imshow(fnew,origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GAAAgligGAAAgligGAAAgligGAAAgligGAAAgligGAAAgligGAAAgligGAAAgligGAAAg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\n1v8C9mmS5SK1/fwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convolutions 2D\n",
    "\n",
    "def my_kernel(x,y):\n",
    "    return(np.cos(0.2*np.sqrt(x**2+y**2))*np.exp(-0.01*(x**2+y**2)))\n",
    "\n",
    "vals=np.linspace(-10,10,21)\n",
    "x,y=np.meshgrid(vals,vals)\n",
    "kernel=my_kernel(x,y)\n",
    "\n",
    "plt.imshow(kernel,cmap='RdBu',origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AWhwvvb9Fy6AawreOSc0v/vvKzi9+nK1VIJ/4qvw16UMzzcwexlVoe78rA7J+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o+6VL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\nAGBZJsUAAAAsy6QYAACAZf03D0JFWuiK2MQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# inefficient convolution\n",
    "jmid=10\n",
    "\n",
    "f=pixel_image\n",
    "fnew=0*f\n",
    "N=21\n",
    "for j0 in range(N):\n",
    "    for j1 in range(N):\n",
    "        fnew+=np.roll(f,[jmid-j0,jmid-j1],axis=[0,1])*kernel[j0,j1]\n",
    "        \n",
    "plt.imshow(fnew,origin='lower')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}