scipy_gaussian_kernel_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Preliminaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "from scipy import signal\n",
    "from astropy.convolution import convolve, Gaussian2DKernel\n",
    "from skimage.metrics import structural_similarity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load image with filter centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "fttt2_im_no_center = np.load('images_and_data/fttt2_im_no_center.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 12))\n",
    "plt.imshow(fttt2_im_no_center,  \n",
    "           cmap='gray', interpolation = 'none'), plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Make a `scipy`-only Gaussian 2D kernel similar to `astropy`'s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#print(Gaussian2DKernel.__doc__ )\n",
    "#print(help(Gaussian2DKernel))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inferring from the documentation, the size of `Gaussian2DKernel` is defined by std. It is std*8+1 in both x and y.\n",
    "\n",
    "Test it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(57, 57) 8 8\n"
     ]
    }
   ],
   "source": [
    "kap = Gaussian2DKernel(7)\n",
    "print (np.shape(kap), np.shape(kap)[0]//7, np.shape(kap)[1]//7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scipy_gaussian_2D(std):\n",
    "    '''\n",
    "    2D Gaussian filter kernel similar to astropy\\'s Gaussian2DKernel\n",
    "    (https://docs.astropy.org/en/stable/api/astropy.convolution.Gaussian2DKernel.html#astropy.convolution.Gaussian2DKernel)\n",
    "    using scipy.signal.gaussian \n",
    "    (and inspired by https://gist.github.com/thomasaarholt/267ec4fff40ca9dff1106490ea3b7567)\n",
    "    \n",
    "    Parameters: \n",
    "    std (int) : standard deviation of the Gaussian in pixels\n",
    "    \n",
    "    Returns:\n",
    "    out (2D array): 2D Gaussian filter kernel\n",
    "    '''\n",
    "    ksp1D = signal.gaussian(std*8+1, std)\n",
    "    ksp2D = np.outer(ksp1D, ksp1D)\n",
    "    ksp2D /= (2*np.pi*(std**2))\n",
    "    return ksp2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(57, 57)\n"
     ]
    }
   ],
   "source": [
    "ksp2D = scipy_gaussian_2D(7)\n",
    "print (np.shape(ksp2D))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visual comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2160x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(30, 15))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(kap, cmap='inferno', interpolation = 'none')\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(ksp2D, cmap='inferno', interpolation = 'none');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "apt = (signal.fftconvolve(fttt2_im_no_center, kap, mode='same'))[100:-100,100:-100]\n",
    "spt = (signal.fftconvolve(fttt2_im_no_center, ksp2D, mode='same'))[100:-100,100:-100]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now visual comparison of the the two convolved results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2160x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(30, 15))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(apt, cmap='inferno', interpolation = 'none'), plt.axis('off')\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(spt, cmap='inferno', interpolation = 'none'), plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numerical comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "structural_similarity(apt, spt)"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}