Fourier_apps-Udemy-SA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import timeit\n",
    "import scipy.fftpack\n",
    "import scipy.io as sio\n",
    "from scipy import stats\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from scipy import signal\n",
    "from scipy import interpolate\n",
    "from PIL import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "---\n",
    "# VIDEO: Image smoothing and sharpening\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[226 137 125]\n",
      "  [226 137 125]\n",
      "  [223 137 133]\n",
      "  ...\n",
      "  [230 148 122]\n",
      "  [221 130 110]\n",
      "  [200  99  90]]\n",
      "\n",
      " [[226 137 125]\n",
      "  [226 137 125]\n",
      "  [223 137 133]\n",
      "  ...\n",
      "  [230 148 122]\n",
      "  [221 130 110]\n",
      "  [200  99  90]]\n",
      "\n",
      " [[226 137 125]\n",
      "  [226 137 125]\n",
      "  [223 137 133]\n",
      "  ...\n",
      "  [230 148 122]\n",
      "  [221 130 110]\n",
      "  [200  99  90]]\n",
      "\n",
      " ...\n",
      "\n",
      " [[ 84  18  60]\n",
      "  [ 84  18  60]\n",
      "  [ 92  27  58]\n",
      "  ...\n",
      "  [173  73  84]\n",
      "  [172  68  76]\n",
      "  [177  62  79]]\n",
      "\n",
      " [[ 82  22  57]\n",
      "  [ 82  22  57]\n",
      "  [ 96  32  62]\n",
      "  ...\n",
      "  [179  70  79]\n",
      "  [181  71  81]\n",
      "  [185  74  81]]\n",
      "\n",
      " [[ 82  22  57]\n",
      "  [ 82  22  57]\n",
      "  [ 96  32  62]\n",
      "  ...\n",
      "  [179  70  79]\n",
      "  [181  71  81]\n",
      "  [185  74  81]]]\n",
      "[[162.66666667 162.66666667 164.33333333 ... 166.66666667 153.66666667\n",
      "  129.66666667]\n",
      " [162.66666667 162.66666667 164.33333333 ... 166.66666667 153.66666667\n",
      "  129.66666667]\n",
      " [162.66666667 162.66666667 164.33333333 ... 166.66666667 153.66666667\n",
      "  129.66666667]\n",
      " ...\n",
      " [ 54.          54.          59.         ... 110.         105.33333333\n",
      "  106.        ]\n",
      " [ 53.66666667  53.66666667  63.33333333 ... 109.33333333 111.\n",
      "  113.33333333]\n",
      " [ 53.66666667  53.66666667  63.33333333 ... 109.33333333 111.\n",
      "  113.33333333]]\n"
     ]
    }
   ],
   "source": [
    "# load image and convert to float\n",
    "lenna = np.asarray( Image.open(\"Lenna.png\") )\n",
    "print(lenna)\n",
    "imgL  = np.mean(lenna,axis=2)\n",
    "print(imgL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Original image')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9faf5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot original image\n",
    "plt.subplot2grid((2,2),(0,0))\n",
    "plt.imshow(imgL,cmap=plt.cm.gray)\n",
    "plt.axis('off')\n",
    "plt.title('Original image')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  398.66666667   +0.        j  -287.72647503-1990.99010026j\n",
      "   -192.10176417 +377.61010561j ...   -27.22002507 +808.96468786j\n",
      "   -192.10176417 -377.61010561j  -287.72647503+1990.99010026j]\n",
      " [  228.67096673-1408.76536137j  -986.1658783  +323.93394537j\n",
      "    315.63752333 +492.6229421 j ...  -598.85609847  +71.05764245j\n",
      "    485.98614374 -400.76341859j  -393.02149729 +722.8101574 j]\n",
      " [ -204.97761995 +806.68064526j  -126.86841681 +264.393972  j\n",
      "   -191.44372717 -854.76883622j ... -1309.38572251 +349.84288047j\n",
      "   -871.51069057 -467.74758662j   158.98461284 -161.78960273j]\n",
      " ...\n",
      " [ -250.43947823 -310.13765681j   481.50264079-1358.1122705 j\n",
      "    308.48949566 -363.83094596j ...  -391.01056995+1235.55595586j\n",
      "    -11.6497478  -698.60680369j   -33.55318716  +30.98416251j]\n",
      " [ -204.97761995 -806.68064526j   158.98461284 +161.78960273j\n",
      "   -871.51069057 +467.74758662j ...   724.72017818 +595.13253181j\n",
      "   -191.44372717 +854.76883622j  -126.86841681 -264.393972  j]\n",
      " [  228.67096673+1408.76536137j  -393.02149729 -722.8101574 j\n",
      "    485.98614374 +400.76341859j ... -2183.76032976 -528.53707973j\n",
      "    315.63752333 -492.6229421 j  -986.1658783  -323.93394537j]]\n",
      "----------------------\n",
      "[[5.98812565 7.60672197 6.04894429 ... 6.69632104 6.04894429 7.60672197]\n",
      " [7.26347232 6.94505679 6.37172785 ... 6.40201182 6.44558608 6.7126545 ]\n",
      " [6.72421186 5.68104994 6.77530384 ... 7.21178979 6.89679538 5.42420214]\n",
      " ...\n",
      " [5.98803185 7.27305232 6.16753786 ... 7.16699971 6.54922709 3.82146219]\n",
      " [6.72421186 5.42420214 6.89679538 ... 6.84349874 6.77530384 5.68104994]\n",
      " [7.26347232 6.7126545  6.44558608 ... 7.71726725 6.37172785 6.94505679]]\n"
     ]
    }
   ],
   "source": [
    "# and its power spectrum\n",
    "imgX  = scipy.fftpack.fftshift(scipy.fftpack.fft2(imgL))\n",
    "print(imgX)\n",
    "print(\"----------------------\")\n",
    "powr2 = np.log(np.abs(imgX))\n",
    "print(powr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Amplitude spectrum')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa169668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot2grid((2,3),(1,0))\n",
    "plt.imshow(powr2,cmap=plt.cm.gray)\n",
    "plt.clim([0,15])\n",
    "plt.axis('off')\n",
    "plt.title('Amplitude spectrum')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(512, 512)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(512, 512)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# filter kernel is a Gaussian\n",
    "width = .1 # width of gaussian (normalized Z units)\n",
    "lims  = np.shape(imgL)\n",
    "print(lims)\n",
    "xr    = stats.zscore(np.arange(lims[0]))\n",
    "#print(xr)\n",
    "[x,y] = np.meshgrid(xr,xr)\n",
    "x\n",
    "y\n",
    "# add 1- at beginning of the next line to invert the filter\n",
    "gaus2d = 1-np.exp( -( x**2 + y**2 ) / (2*width**2) )\n",
    "xgaus2d = np.exp( -( x**2 + y**2 ) / (2*width**2) )\n",
    "gaus2d.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.65806744e-130, 5.32788606e-130, 1.70419629e-129, ...,\n",
       "        1.70419629e-129, 5.32788606e-130, 1.65806744e-130],\n",
       "       [5.32788606e-130, 1.71201540e-129, 5.47611240e-129, ...,\n",
       "        5.47611240e-129, 1.71201540e-129, 5.32788606e-130],\n",
       "       [1.70419629e-129, 5.47611240e-129, 1.75160849e-128, ...,\n",
       "        1.75160849e-128, 5.47611240e-129, 1.70419629e-129],\n",
       "       ...,\n",
       "       [1.70419629e-129, 5.47611240e-129, 1.75160849e-128, ...,\n",
       "        1.75160849e-128, 5.47611240e-129, 1.70419629e-129],\n",
       "       [5.32788606e-130, 1.71201540e-129, 5.47611240e-129, ...,\n",
       "        5.47611240e-129, 1.71201540e-129, 5.32788606e-130],\n",
       "       [1.65806744e-130, 5.32788606e-130, 1.70419629e-129, ...,\n",
       "        1.70419629e-129, 5.32788606e-130, 1.65806744e-130]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xgaus2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Gain function')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x87e5080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# show Gaussian\n",
    "plt.subplot2grid((2,3),(1,1))\n",
    "plt.imshow(gaus2d,cmap=plt.cm.gray)\n",
    "plt.axis('off')\n",
    "plt.title('Gain function')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Gain function')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x87e5d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# show Gaussian\n",
    "plt.subplot2grid((2,3),(1,1))\n",
    "plt.imshow(xgaus2d,cmap=plt.cm.gray)\n",
    "plt.axis('off')\n",
    "plt.title('Gain function')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# show modulated spectrum\n",
    "plt.subplot2grid((2,3),(1,2))\n",
    "plt.imshow( np.log(np.abs( np.multiply(imgX,gaus2d)) ) ,cmap=plt.cm.gray)\n",
    "plt.axis('off')\n",
    "plt.clim([0,15])\n",
    "plt.title('Modulated spectrum')\n",
    "\n"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}