RichieSams/filter.ipynb

## filter.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class ReconstructionFilter:\n",
    "    def __init__(self, filterType):\n",
    "        self.filterType = filterType\n",
    "        self.width = 0.0\n",
    "        self.binSize = 0.0\n",
    "        self.invBinSize = 0.0\n",
    "        self.filterResolution = 32\n",
    "        self.cdf = np.empty(self.filterResolution + 1)\n",
    "        \n",
    "        self.precompute()\n",
    "    \n",
    "    # Public\n",
    "    \n",
    "    def sample(self, x):\n",
    "        negative = x < 0.5;\n",
    "        x = x * 2.0 if negative else (x - 0.5) * 2.0;\n",
    "        \n",
    "        idx = self.filterResolution;\n",
    "        for i in range(1, self.filterResolution + 1):\n",
    "            if (x < self.cdf[i]):\n",
    "                idx = i - 1\n",
    "                break\n",
    "        \n",
    "        pdf = self.cdf[idx + 1] - self.cdf[idx]\n",
    "        u = self.binSize * ((idx) + ((x - self.cdf[idx]) / pdf))\n",
    "\n",
    "        return -u if negative else u\n",
    "    \n",
    "    # Private    \n",
    "    \n",
    "    def precompute(self):\n",
    "        self.width = self.filterWidth()\n",
    "        \n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return\n",
    "        \n",
    "        self.binSize = self.width / (self.filterResolution - 1);\n",
    "        self.invBinSize = (self.filterResolution - 1) / self.width;\n",
    "\n",
    "        normalizationFactor = 0.0\n",
    "        pdf = np.empty(self.filterResolution)\n",
    "        for i in range(self.filterResolution - 1):\n",
    "            temp = self.eval(i * self.binSize)\n",
    "            pdf[i] = temp\n",
    "            normalizationFactor += temp\n",
    "        \n",
    "        pdf[self.filterResolution - 1] = 0.0\n",
    "        \n",
    "        # Normalize. Aka, we want the area under the curve to equal 1.0\n",
    "        for i in range(self.filterResolution - 1):\n",
    "            pdf[i] /= normalizationFactor\n",
    "        \n",
    "        self.cdf[0] = 0.0\n",
    "        for i in range(1, self.filterResolution):\n",
    "            self.cdf[i] = self.cdf[i - 1] + (pdf[i - 1])\n",
    "        self.cdf[self.filterResolution] = 1.0\n",
    "    \n",
    "    def eval(self, x):\n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return 0.0\n",
    "        elif (self.filterType == \"Box\"):\n",
    "            return 1.0 if (x >= -0.5 and x <= 0.5) else 0.0\n",
    "        elif (self.filterType == \"Tent\"):\n",
    "            return 1.0 - abs(x)\n",
    "        elif (self.filterType == \"Gaussian\"):\n",
    "            alpha = 2.0\n",
    "            return max(math.exp(-alpha * x * x) - math.exp(-alpha * 4.0), 0.0)\n",
    "        elif (self.filterType == \"MitchellNetravali\"):\n",
    "            return self.mitchellNetravali(abs(x))\n",
    "        elif (self.filterType == \"CatmullRom\"):\n",
    "            return self.catmullRom(abs(x))\n",
    "        elif (self.filterType == \"Lanczos\"):\n",
    "            return self.lanczos(abs(x))\n",
    "        else:\n",
    "            return 0.0\n",
    "    \n",
    "    def filterWidth(self):\n",
    "        if (self.filterType == \"Dirac\"):\n",
    "            return 0.0\n",
    "        elif (self.filterType == \"Box\"):\n",
    "            return 0.5\n",
    "        elif (self.filterType == \"Tent\"):\n",
    "            return 1.0\n",
    "        elif (self.filterType == \"Gaussian\" or \n",
    "              self.filterType == \"MitchellNetravali\" or\n",
    "              self.filterType == \"CatmullRom\" or \n",
    "              self.filterType == \"Lanczos\"):\n",
    "            return 2.0\n",
    "        else:\n",
    "            return 0.0\n",
    "    \n",
    "    def mitchellNetravali(self, x):\n",
    "        B = 1.0 / 3.0\n",
    "        C = 1.0 / 3.0\n",
    "        if (x < 1.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                ((12.0 - 9.0 * B - 6.0 * C) * x * x * x + \\\n",
    "                 (-18.0 + 12.0 * B + 6.0 * C) * x * x + \\\n",
    "                 (6.0 - 2.0 * B))\n",
    "        elif (x < 2.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                ((-B - 6.0 * C) * x * x * x + \\\n",
    "                 (6.0 * B + 30.0 * C) * x * x + \\\n",
    "                 (-12.0 * B - 48.0 * C) * x + \\\n",
    "                 (8.0 * B + 24.0 * C))\n",
    "        else:\n",
    "            return 0.0\n",
    "\n",
    "    def catmullRom(self, x):\n",
    "        if (x < 1.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                ((12.0 - 3.0) * x * x * x + \\\n",
    "                 (-18.0 + 3.0) * x * x + \\\n",
    "                 6.0)\n",
    "        elif (x < 2.0):\n",
    "            return 1.0 / 6.0 * \\\n",
    "                (-3.0 * x * x * x + \\\n",
    "                 15.0 * x * x - \\\n",
    "                 24.0 * x + \\\n",
    "                 12.0)\n",
    "        else:\n",
    "            return 0.0;\n",
    "\n",
    "    def lanczos(self, x):\n",
    "        if (x == 0.0):\n",
    "            return 1.0;\n",
    "        elif (x < 2.0):\n",
    "            return math.sin(math.pi * x) * \\\n",
    "                   math.sin(math.pi * x * 0.5) / \\\n",
    "                   (math.pi * math.pi * x * x * 0.5);\n",
    "        else:\n",
    "            return 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "randNumbers = np.random.rand(100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x97c7390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diracFilter = ReconstructionFilter(\"Dirac\")\n",
    "\n",
    "diracSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    diracSamples[i] = diracFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(diracSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QSFLjDAJJapxBIEmNMwgkqXEGgSQ1ziCQpMYZBJLUOINAkhpnEEhS4wwCSWqcQSBJjTMI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\ndPfufz+n8wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6203dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxFilter = ReconstructionFilter(\"Box\")\n",
    "\n",
    "boxSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    boxSamples[i] = boxFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(boxSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa73dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tentFilter = ReconstructionFilter(\"Tent\")\n",
    "\n",
    "tentSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    tentSamples[i] = tentFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(tentSamples, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xae5cd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussianFilter = ReconstructionFilter(\"Gaussian\")\n",
    "\n",
    "gaussianSamples = np.empty(100000)\n",
    "for i in range(100000):\n",
    "    gaussianSamples[i] = gaussianFilter.sample(randNumbers[i])\n",
    "\n",
    "plt.hist(gaussianSamples, 50)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}